add_mesh_extra_objects/__init__.py

@@ -7,7 +7,7 @@
 # dreampainter, cotejrp1, liero, Kayo Phoenix, sugiany, dommetysk, Jambay   #
 # Phymec, Anthony D'Agostino, Pablo Vazquez, Richard Wilks, lijenstina,     #
 # Sjaak-de-Draak, Phil Cote, cotejrp1, xyz presets by elfnor, revolt_randy, #
-# Vladimir Spivak (cwolf3d), #
+# Vladimir Spivak (cwolf3d), Chris Want #
 
 
 bl_info = {

add_mesh_extra_objects/add_mesh_3d_function_surface.py

@@ -4,7 +4,10 @@
 
 # Original by Buerbaum Martin (Pontiac), Elod Csirmaz
 
+import sys
+import os
 import bpy
+import bmesh
 import math
 import numpy
 from mathutils import *
@@ -15,8 +18,29 @@ from bpy.props import (
         IntProperty,
         FloatProperty,
         BoolProperty,
+        EnumProperty
         )
 
+# Default: look in current directory for embedded Tessagon
+TESSAGON_DIRECTORY = os.environ.get('TESSAGON_DIRECTORY',
+                                    os.path.dirname(os.path.abspath(__file__)))
+sys.path.append(TESSAGON_DIRECTORY)
+
+from tessagon.core.tessagon_discovery import TessagonDiscovery
+from tessagon.adaptors.list_adaptor import ListAdaptor
+
+# Create tiling menu with items in nice order
+find_tilings = TessagonDiscovery()
+tilings = find_tilings.with_classification('regular').to_list() + \
+          find_tilings.with_classification('archimedean').to_list() + \
+          find_tilings.with_classification('laves').to_list() + \
+          find_tilings.with_classification('non_edge').to_list() + \
+          find_tilings.with_classification('non_convex').to_list()
+
+tiling_items = [('None', 'No tiling', 'No tiling')]
+for counter, tessagon in enumerate(tilings):
+    name = tessagon.metadata.name
+    tiling_items.append((str(counter), name, name))
 
 # List of safe functions for eval()
 safe_list = ['acos', 'asin', 'atan', 'atan2', 'ceil', 'cos', 'cosh',
@@ -48,7 +72,7 @@ safe_dict['min'] = min
 #                       new mesh (as used in from_pydata)
 # name ... Name of the new mesh (& object)
 
-def create_mesh_object(context, verts, edges, faces, name):
+def create_mesh_object(context, verts, edges, faces, name, recalculate_normals):
 
     # Create new mesh
     mesh = bpy.data.meshes.new(name)
@@ -56,6 +80,12 @@ def create_mesh_object(context, verts, edges, faces, name):
     # Make a mesh from a list of verts/edges/faces
     mesh.from_pydata(verts, edges, faces)
 
+    if recalculate_normals:
+        bm = bmesh.new()
+        bm.from_mesh(mesh)
+        bmesh.ops.recalc_face_normals(bm, faces = bm.faces)
+        bm.to_mesh(mesh)
+
     # Update mesh geometry after adding stuff
     mesh.update()
 
@@ -228,7 +258,7 @@ class AddZFunctionSurface(Operator):
 
                 edgeloop_prev = edgeloop_cur
 
-            base = create_mesh_object(context, verts, [], faces, "Z Function")
+            base = create_mesh_object(context, verts, [], faces, "Z Function", false)
         else:
             self.report({'WARNING'}, "Z Equation - No expression is given")
 
@@ -240,7 +270,8 @@ class AddZFunctionSurface(Operator):
 def xyz_function_surface_faces(self, x_eq, y_eq, z_eq,
             range_u_min, range_u_max, range_u_step, wrap_u,
             range_v_min, range_v_max, range_v_step, wrap_v,
-            a_eq, b_eq, c_eq, f_eq, g_eq, h_eq, n, close_v):
+            a_eq, b_eq, c_eq, f_eq, g_eq, h_eq, n, close_v,
+            tiling_type):
 
     verts = []
     faces = []
@@ -305,17 +336,11 @@ def xyz_function_surface_faces(self, x_eq, y_eq, z_eq,
         print("\n[Add X, Y, Z Function Surface]:\n\n", traceback.format_exc(limit=1))
         return [], []
 
-    for vN in range(vRange):
-        v = range_v_min + (vN * vStep)
-
-        for uN in range(uRange):
-            u = range_u_min + (uN * uStep)
 
+    def eval_f(u, v):
         safe_dict['u'] = u
         safe_dict['v'] = v
 
-            safe_dict['n'] = n
-
         # Try to evaluate the equations.
         try:
             safe_dict['a'] = float(eval(*expr_args_a))
@@ -325,16 +350,42 @@ def xyz_function_surface_faces(self, x_eq, y_eq, z_eq,
             safe_dict['g'] = float(eval(*expr_args_g))
             safe_dict['h'] = float(eval(*expr_args_h))
 
-                verts.append((
-                    float(eval(*expr_args_x)),
+            return (float(eval(*expr_args_x)),
                     float(eval(*expr_args_y)),
-                    float(eval(*expr_args_z))))
+                    float(eval(*expr_args_z)))
+
         except:
             import traceback
             self.report({'WARNING'}, "Error evaluating expression(s) - "
                         "Check the console for more info")
             print("\n[Add X, Y, Z Function Surface]:\n\n", traceback.format_exc(limit=1))
+            return None
+
+    if tiling_type != 'None':
+        tessagon_class = tilings[int(tiling_type)]
+        options = {
+            'function': eval_f,
+            'u_range': [range_u_min, range_u_max],
+            'v_range': [range_v_min, range_v_max],
+            'u_num': range_u_step,
+            'v_num': range_v_step,
+            'u_cyclic': wrap_u,
+            'v_cyclic': wrap_v,
+            'adaptor_class' : ListAdaptor
+        }
+        tessagon = tessagon_class(**options)
+        hash = tessagon.create_mesh()
+        return hash['vert_list'], hash['face_list']
+
+    for vN in range(vRange):
+        v = range_v_min + (vN * vStep)
+
+        for uN in range(uRange):
+            u = range_u_min + (uN * uStep)
+            xyz = eval_f(u, v)
+            if xyz is None:
                 return [], []
+            verts.append(xyz)
 
     for vN in range(range_v_step):
         vNext = vN + 1
@@ -366,7 +417,6 @@ def xyz_function_surface_faces(self, x_eq, y_eq, z_eq,
 
     return verts, faces
 
-
 # Original Script "Parametric.py" by Ed Mackey.
 # -> http://www.blinken.com/blender-plugins.php
 # Partly converted for Blender 2.5 by tuga3d.
@@ -470,6 +520,12 @@ class AddXYZFunctionSurface(Operator):
                             "V values (only if U is wrapped)",
                 default=False
                 )
+    tiling_type : EnumProperty(
+                name='Tiling',
+                description='Tiling type',
+                items=tiling_items,
+                default='None'
+                )
     n_eq: IntProperty(
                 name="Number of objects (n=0..N-1)",
                 description="The parameter n will be the index "
@@ -511,7 +567,7 @@ class AddXYZFunctionSurface(Operator):
     show_wire : BoolProperty(
             name="Show wireframe",
             default=True,
-            description="Add the object’s wireframe over solid drawing"
+            description="Add the object's wireframe over solid drawing"
             )
     edit_mode : BoolProperty(
             name="Show in edit mode",
@@ -520,6 +576,9 @@ class AddXYZFunctionSurface(Operator):
             )
 
     def execute(self, context):
+        tiling_type = self.tiling_type
+        recalculate_normals = (tiling_type != 'None')
+
         for n in range(0, self.n_eq):
             verts, faces = xyz_function_surface_faces(
                                 self,
@@ -541,12 +600,14 @@ class AddXYZFunctionSurface(Operator):
                                 self.g_eq,
                                 self.h_eq,
                                 n,
-                                self.close_v
+                                self.close_v,
+                                self.tiling_type
                                 )
             if not verts:
                 return {'CANCELLED'}
 
-            obj = create_mesh_object(context, verts, [], faces, "XYZ Function")
+            obj = create_mesh_object(context, verts, [], faces, "XYZ Function",
+                                     recalculate_normals)
 
         if self.show_wire:
             context.active_object.show_wire = True

add_mesh_extra_objects/tessagon/__init__.py

@@ -0,0 +1,2 @@
+from .version import __version__
+from .core.tessagon_discovery import TessagonDiscovery  # noqa: F401

add_mesh_extra_objects/tessagon/adaptors/blender_adaptor.py

@@ -0,0 +1,27 @@
+import bmesh
+
+
+class BlenderAdaptor:
+    def __init__(self, **kwargs):
+        self.bm = None
+
+    def create_empty_mesh(self):
+        self.bm = bmesh.new()
+
+    def initialize_colors(self):
+        pass
+
+    def create_vert(self, coords):
+        return self.bm.verts.new(coords)
+
+    def create_face(self, verts):
+        return self.bm.faces.new(verts)
+
+    def color_face(self, face, color_index):
+        face.material_index = color_index
+
+    def finish_mesh(self):
+        bmesh.ops.recalc_face_normals(self.bm, faces=self.bm.faces)
+
+    def get_mesh(self):
+        return self.bm

add_mesh_extra_objects/tessagon/adaptors/list_adaptor.py

@@ -0,0 +1,33 @@
+class ListAdaptor:
+
+    def __init__(self, **kwargs):
+        self.vert_list = None
+        self.face_list = None
+        self.color_list = None
+
+    def create_empty_mesh(self):
+        self.vert_list = []
+        self.face_list = []
+        self.color_list = []
+
+    def initialize_colors(self):
+        self.color_list = [0]*len(self.face_list)
+
+    def create_vert(self, coords):
+        self.vert_list.append(coords)
+        return (len(self.vert_list) - 1)
+
+    def create_face(self, verts):
+        self.face_list.append(verts)
+        return (len(self.face_list) - 1)
+
+    def color_face(self, face, color_index):
+        self.color_list[face] = color_index
+
+    def finish_mesh(self):
+        pass
+
+    def get_mesh(self):
+        return {'vert_list': self.vert_list,
+                'face_list': self.face_list,
+                'color_list': self.color_list}

add_mesh_extra_objects/tessagon/adaptors/vtk_adaptor.py

@@ -0,0 +1,48 @@
+import vtk
+
+
+class VtkAdaptor:
+    def __init__(self, **kwargs):
+        self.point_count = 0
+        self.face_count = 0
+        self.points = None
+        self.polys = None
+        self.poly_data = None
+        self.scalars = None
+
+    def create_empty_mesh(self):
+        self.pcoords = vtk.vtkFloatArray()
+        self.pcoords.SetNumberOfComponents(3)
+        self.points = vtk.vtkPoints()
+        self.polys = vtk.vtkCellArray()
+        self.poly_data = vtk.vtkPolyData()
+
+    def initialize_colors(self):
+        self.scalars = vtk.vtkFloatArray()
+        self.scalars.SetNumberOfComponents(1)
+        self.scalars.SetNumberOfTuples(self.face_count)
+
+    def create_vert(self, coords):
+        self.pcoords.InsertNextTuple3(*coords)
+        index = self.point_count
+        self.point_count += 1
+        return index
+
+    def create_face(self, verts):
+        self.polys.InsertNextCell(len(verts), verts)
+        index = self.face_count
+        self.face_count += 1
+        return index
+
+    def color_face(self, face, color_index):
+        self.scalars.SetTuple1(face, color_index)
+
+    def finish_mesh(self):
+        self.points.SetData(self.pcoords)
+        self.poly_data.SetPoints(self.points)
+        self.poly_data.SetPolys(self.polys)
+        if self.scalars:
+            self.poly_data.GetCellData().SetScalars(self.scalars)
+
+    def get_mesh(self):
+        return self.poly_data

add_mesh_extra_objects/tessagon/core/__init__.py

@@ -0,0 +1,22 @@
+import re
+
+# A couple of general purpose functions for manipulating
+# camel case class names and snake case function/method names.
+# (Mostly used for some questionable dynamic method creation ...).
+# TODO: setup demos to use this
+
+
+def class_name_to_method_name(class_name, prefix=''):
+    method_name = prefix
+    method_name += re.sub(r'(?<!^)(?=[A-Z])', '_', class_name).lower()
+    return method_name
+
+
+def class_to_method_name(cls, prefix=''):
+    # E.g., if cls is HexTessagon and prefix is 'whatever_',
+    # this function returns 'whatever_hex_tessagon'
+    return class_name_to_method_name(cls.__name__, prefix)
+
+
+def method_name_to_class_name(method_name):
+    return ''.join(word.title() for word in method_name.split('_'))

add_mesh_extra_objects/tessagon/core/abstract_tile.py

@@ -0,0 +1,236 @@
+from tessagon.core.value_blend import ValueBlend
+
+
+class AbstractTile(ValueBlend):
+    def __init__(self, tessagon, **kwargs):
+        self.tessagon = tessagon
+        self.f = tessagon.f
+
+        # Verts/faces indexed with 'left', 'right', 'center'
+        self.u_symmetric = kwargs.get('u_symmetric', False)
+        # Verts/faces indexed with 'bottom', 'middle', 'top'
+        self.v_symmetric = kwargs.get('v_symmetric', False)
+
+        # Verts/faces with 'rotate' and a number.
+        # Only rot_symmetric = 180 supported
+        # TODO: implement rot_symmetric = 90 as needed
+        self.rot_symmetric = kwargs.get('rot_symmetry', None)
+
+        self.id = None
+        # This is not necessary to any of the calculations, just
+        # makes debugging easier
+        if 'id' in kwargs:
+            self.id = kwargs['id']
+
+        # This is an identifier that is set by the generator (a tuple)
+        # Really this should be merged with the id thingy above
+        self.fingerprint = kwargs.get('fingerprint') or None
+
+        # Corners is list of tuples:
+        #   [bottomleft, bottomright, topleft, topright]
+        self.corners = None
+        self._init_corners(**kwargs)
+
+        self.neighbors = {
+            'top': None,
+            'bottom': None,
+            'left': None,
+            'right': None
+        }
+
+        # Are the neighbors ordered backwards?
+        # e.g., a tile with twist['right'] set to True:
+        #  self tile: right edge has v=0 at the bottom and v=1 at the top
+        #  right neighbor: left edge has v=1 at the bottom and v=0 at the top
+        #  (the right tile has twist['left'] true
+        self.twist = {
+            'top': False,
+            'bottom': False,
+            'left': False,
+            'right': False
+        }
+
+    def set_neighbors(self, **kwargs):
+        if 'top' in kwargs:
+            self.neighbors['top'] = kwargs['top']
+        if 'bottom' in kwargs:
+            self.neighbors['bottom'] = kwargs['bottom']
+        if 'left' in kwargs:
+            self.neighbors['left'] = kwargs['left']
+        if 'right' in kwargs:
+            self.neighbors['right'] = kwargs['right']
+
+    def get_neighbor_tile(self, neighbor_keys):
+        tile = self
+        for key in self._neighbor_path(neighbor_keys):
+            if not tile.neighbors[key]:
+                return None
+            tile = tile.neighbors[key]
+        return tile
+
+    @property
+    def left(self):
+        return self.get_neighbor_tile(["left"])
+
+    @property
+    def right(self):
+        return self.get_neighbor_tile(["right"])
+
+    @property
+    def top(self):
+        return self.get_neighbor_tile(["top"])
+
+    @property
+    def bottom(self):
+        return self.get_neighbor_tile(["bottom"])
+
+    def inspect(self, **kwargs):
+        # For debugging topology
+        if not self.id:
+            return
+        prefix = 'Tile'
+        if 'tile_number' in kwargs:
+            prefix += " #%s" % (kwargs['tile_number'])
+        print("%s (%s):" % (prefix, self.__class__.__name__))
+        print("  - self:      %s" % (self.id))
+        print('  - neighbors:')
+        for key in ['top', 'left', 'right', 'bottom']:
+            if self.neighbors[key]:
+                tile = self.neighbors[key]
+                if tile.id:
+                    print("    - %s" % (self._neighbor_str(key)))
+        print("  - corners: (%2.4f, %2.4f)  (%2.4f, %2.4f)" %
+              tuple(self.corners[2] + self.corners[3]))
+        print("             (%2.4f, %2.4f)  (%2.4f, %2.4f)" %
+              tuple(self.corners[0] + self.corners[1]))
+        print("  - twist:", self.twist)
+        if self.fingerprint:
+            print("  - fingerprint:", self.fingerprint)
+        print('')
+
+    # Below are protected
+
+    # A couple of abstract methods that will be useful for finding
+    # and setting the vertices and faces on a tile
+    def _get_nested_list_value(self, nested_list, index_keys):
+        if not isinstance(index_keys, list):
+            return nested_list[index_keys]
+        value = nested_list
+        for index in index_keys:
+            value = value[index]
+
+        return value
+
+    def _set_nested_list_value(self, nested_list, index_keys, value):
+        if not isinstance(index_keys, list):
+            nested_list[index_keys] = value
+            return
+        reference = nested_list
+        for index in index_keys[0:-1]:
+            reference = reference[index]
+        reference[index_keys[-1]] = value
+
+    def _neighbor_path(self, neighbor_keys):
+        # Note: it is assumed that len(neighbor_keys) in [1, 2]
+        # if len(neighbor_keys) == 1, the neighbor meets on an edge
+        # if len(neighbor_keys) == 2, the neighbor meets at a corner,
+        #     and are diagonal for each other, e.g., ['left', 'top']
+        # If the boundary is twisted, need to be careful because
+        # left and become right, or top can become bottom on the
+        # other side of the twisted boundary: try to traverse the
+        # non-twisted boundary first to make the math easier
+        if len(neighbor_keys) < 2:
+            return neighbor_keys
+        if self._should_twist_u(neighbor_keys):
+            if (neighbor_keys[0] in ['top', 'bottom']):
+                return [neighbor_keys[1], neighbor_keys[0]]
+        elif self._should_twist_v(neighbor_keys):
+            if (neighbor_keys[0] in ['left', 'right']):
+                return [neighbor_keys[1], neighbor_keys[0]]
+        return neighbor_keys
+
+    def _index_path(self, index_keys, neighbor_keys):
+        path = index_keys
+        if self._should_twist_u(neighbor_keys):
+            path = self._u_flip(path)
+        if self._should_twist_v(neighbor_keys):
+            path = self._v_flip(path)
+        return path
+
+    def _permute_value(self, index_keys, vals):
+        # abstract function to permute values in a list
+        # e.g., 'left' and 'right' in u_flip below
+        if isinstance(index_keys, list):
+            return [self._permute_value(u, vals) for u in index_keys]
+        for i in range(len(vals)):
+            if index_keys == vals[i]:
+                return vals[(i+1) % len(vals)]
+
+        return index_keys
+
+    def _swap_value(self, index_keys, val1, val2):
+        # abstract function to swap two values in a list
+        # e.g., 'left' and 'right' in u_flip below
+        return self._permute_value(index_keys, [val1, val2])
+
+    def _u_flip(self, index_keys):
+        # swap each left with right (and vice versa) in list
+        if not self.u_symmetric:
+            return index_keys
+        return self._swap_value(index_keys, 'left', 'right')
+
+    def _v_flip(self, index_keys):
+        # swap each top with bottom (and vice versa) in list
+        if not self.v_symmetric:
+            return index_keys
+        return self._swap_value(index_keys, 'bottom', 'top')
+
+    def _rotate_index(self, index_keys):
+        # rotate
+        if not self.rot_symmetric:
+            return index_keys
+        elif self.rot_symmetric == 180:
+            keys = self._permute_value(index_keys, ['rotate0', 'rotate180'])
+            keys = self._permute_value(keys, ['left', 'right'])
+            keys = self._permute_value(keys, ['top', 'bottom'])
+            return keys
+        elif self.rot_symmetric == 90:
+            return self._permute_value(index_keys,
+                                       ['rotate0', 'rotate90'
+                                        'rotate180', 'rotate270'])
+
+    def _v_index(self, index_keys):
+        # find either 'top' or 'bottom' in the list
+        if ('bottom' in index_keys):
+            return 'bottom'
+        if ('top' in index_keys):
+            return 'top'
+        raise ValueError("no v_index found in %s" % (index_keys))
+
+    def _u_index(self, index_keys):
+        # find either 'right' or 'left' in the list
+        if ('left' in index_keys):
+            return 'left'
+        if ('right' in index_keys):
+            return 'right'
+        raise ValueError("no u_index found in %s" % (index_keys))
+
+    def _should_twist_u(self, neighbor_keys):
+        # e.g., twist['bottom'] is True, and neigbor_keys has 'bottom' in it
+        for twist in ['top', 'bottom']:
+            if self.twist[twist] and twist in neighbor_keys:
+                return True
+        return False
+
+    def _should_twist_v(self, neighbor_keys):
+        # e.g., twist['left'] is True, and neigbor_keys has 'left' in it
+        for twist in ['left', 'right']:
+            if self.twist[twist] and twist in neighbor_keys:
+                return True
+        return False
+
+    def _neighbor_str(self, key):
+        tile = self.neighbors[key]
+        if tile:
+            return "%-9s%s" % ("%s:" % (key), tile.id)
+        return "%s: None" % (key)

add_mesh_extra_objects/tessagon/core/alternating_tile.py

@@ -0,0 +1,15 @@
+from tessagon.core.tile import Tile
+
+
+class AlternatingTile(Tile):
+    def validate(self):
+        this_tile_type = self.tile_type
+        for name in self.neighbors:
+            neighbor = self.neighbors[name]
+            if neighbor and (neighbor.tile_type + this_tile_type != 1):
+                raise ValueError("Tiles have bad parity "
+                                 "(hint: maybe use an even number of tiles)")
+
+    @property
+    def tile_type(self):
+        return sum(self.fingerprint) % 2

add_mesh_extra_objects/tessagon/core/grid_tile_generator.py

@@ -0,0 +1,83 @@
+from tessagon.core.tile_generator import TileGenerator
+
+
+class GridTileGenerator(TileGenerator):
+    def __init__(self, tessagon, **kwargs):
+        super().__init__(tessagon, **kwargs)
+
+        self.tiles = None
+
+    def initialize_tiles(self, **kwargs):
+        tiles = [[None for i in range(self.v_num)] for j in range(self.u_num)]
+
+        for u in range(self.u_num):
+            u_ratio0 = float(u) / self.u_num
+            u_ratio1 = float(u + 1) / self.u_num
+            v_shear0 = u * self.v_shear
+            v_shear1 = (u + 1) * self.v_shear
+            for v in range(self.v_num):
+                v_ratio0 = float(v) / self.v_num
+                v_ratio1 = float(v + 1) / self.v_num
+                u_shear0 = v * self.u_shear
+                u_shear1 = (v + 1) * self.u_shear
+                corners = [self.blend(u_ratio0 + u_shear0 + self.u_phase,
+                                      v_ratio0 + v_shear0 + self.v_phase),
+                           self.blend(u_ratio1 + u_shear0 + self.u_phase,
+                                      v_ratio0 + v_shear1 + self.v_phase),
+                           self.blend(u_ratio0 + u_shear1 + self.u_phase,
+                                      v_ratio1 + v_shear0 + self.v_phase),
+                           self.blend(u_ratio1 + u_shear1 + self.u_phase,
+                                      v_ratio1 + v_shear1 + self.v_phase)]
+
+                tiles[u][v] = self.create_tile(u, v, corners, **kwargs)
+
+        self.tiles = tiles
+        return tiles
+
+    def initialize_neighbors(self, **kwargs):
+        tiles = self.tiles
+        for u in range(self.u_num):
+            u_prev = (u - 1) % self.u_num
+            u_next = (u + 1) % self.u_num
+            for v in range(self.v_num):
+                v_prev = (v - 1) % self.v_num
+                v_next = (v + 1) % self.v_num
+                tile = tiles[u][v]
+
+                if not self.u_cyclic and u == 0:
+                    left = None
+                elif self.v_twist and u == 0:
+                    left = tiles[u_prev][self.v_num - v - 1]
+                    tile.twist['left'] = True
+                else:
+                    left = tiles[u_prev][v]
+
+                if not self.v_cyclic and v == self.v_num - 1:
+                    top = None
+                elif self.u_twist and v == self.v_num - 1:
+                    top = tiles[self.u_num - u - 1][v_next]
+                    tile.twist['top'] = True
+                else:
+                    top = tiles[u][v_next]
+
+                if not self.u_cyclic and u == self.u_num - 1:
+                    right = None
+                elif self.v_twist and u == self.u_num - 1:
+                    right = tiles[u_next][self.v_num - v - 1]
+                    tile.twist['right'] = True
+                else:
+                    right = tiles[u_next][v]
+
+                if not self.v_cyclic and v == 0:
+                    bottom = None
+                elif self.u_twist and v == 0:
+                    bottom = tiles[self.u_num - u - 1][v_prev]
+                    tile.twist['bottom'] = True
+                else:
+                    bottom = tiles[u][v_prev]
+
+                tile.set_neighbors(left=left, right=right, top=top,
+                                   bottom=bottom)
+
+    def get_tiles(self):
+        return [j for i in self.tiles for j in i]

add_mesh_extra_objects/tessagon/core/parallelogram_tile_generator.py

@@ -0,0 +1,198 @@
+from tessagon.core.tile_generator import TileGenerator
+
+
+class ParallelogramTileGenerator(TileGenerator):
+    # This generates tiles that are rotated and combined
+    # with a sheer transformation
+    # (Turning a collection of tiles into a parallelogram.)
+    # This is done so that the tile patterns can still be cyclic.
+
+    def __init__(self, tessagon, **kwargs):
+        super().__init__(tessagon, **kwargs)
+
+        # parallelogram_vectors is a pair of pairs, e.g, [[9,1], [-1, 3]]
+        # This means:
+        #  * For one side of the paralellogram go 9 tiles across, 1 tile up
+        #  * From there, the next side you get by going -1 tiles across,
+        #    3 tiles up
+        # (Other sides are obvious. It's a parallelogram.)
+        self.p = kwargs['parallelogram_vectors']
+        self.determinant = \
+            self.p[0][0] * self.p[1][1] - self.p[1][0] * self.p[0][1]
+        self.validate_parallelogram()
+
+        # Rows
+        self.inverse = [[self.p[1][1] / (self.determinant * self.u_num),
+                         -self.p[1][0] / (self.determinant * self.u_num)],
+                        [-self.p[0][1] / (self.determinant * self.v_num),
+                         self.p[0][0] / (self.determinant * self.v_num)]]
+
+        self.color_pattern = kwargs.get('color_pattern') or None
+
+        self.id_prefix = 'parallelogram_tiles'
+
+        # Mapped via a fingerprint
+        self.tiles = {}
+
+    def validate_parallelogram(self):
+        error = None
+        if self.p[0][0] <= 0:
+            error = "First parallelogram vector can't have negative u"
+        elif self.p[1][1] <= 0:
+            error = "Second parallelogram vector can't have negative v"
+        if self.determinant == 0:
+            error = "Parallelogram vector are colinear"
+        elif self.determinant < 0:
+            error = "First parallelogram vector is to the left of second"
+        if error:
+            raise ValueError(error)
+
+    def initialize_tiles(self):
+        tiles = {}
+        fingerprint_range = self.fingerprint_range()
+        for u in fingerprint_range[0]:
+            for v in fingerprint_range[1]:
+                fingerprint = self.normalize_fingerprint(u, v)
+                fingerprint_str = str(fingerprint)
+                if fingerprint_str not in tiles:
+                    if self.valid_fingerprint(*fingerprint):
+                        tiles[fingerprint_str] = self.make_tile(*fingerprint)
+        self.tiles = tiles
+        return tiles
+
+    def initialize_neighbors(self):
+        for tile in self.get_tiles():
+            u = tile.fingerprint[0]
+            v = tile.fingerprint[1]
+
+            fingerprint = self.normalize_fingerprint(u - 1, v)
+            fingerprint_str = str(fingerprint)
+            left = self.tiles.get(fingerprint_str)
+
+            fingerprint = self.normalize_fingerprint(u + 1, v)
+            fingerprint_str = str(fingerprint)
+            right = self.tiles.get(fingerprint_str)
+
+            fingerprint = self.normalize_fingerprint(u, v - 1)
+            fingerprint_str = str(fingerprint)
+            bottom = self.tiles.get(fingerprint_str)
+
+            fingerprint = self.normalize_fingerprint(u, v + 1)
+            fingerprint_str = str(fingerprint)
+            top = self.tiles.get(fingerprint_str)
+
+            tile.set_neighbors(left=left, right=right, top=top,
+                               bottom=bottom)
+
+    def get_tiles(self):
+        return self.tiles.values()
+
+    def make_tile(self, *fingerprint):
+        corners = self.make_corners(*fingerprint)
+        return self.create_tile(fingerprint[0],
+                                fingerprint[1],
+                                corners)
+
+    def make_corners(self, *fingerprint):
+        u = fingerprint[0]
+        v = fingerprint[1]
+
+        return [
+            self.make_corner(u, v),
+            self.make_corner(u + 1, v),
+            self.make_corner(u, v + 1),
+            self.make_corner(u + 1, v + 1),
+        ]
+
+    def make_corner(self, u, v):
+        c0 = self.inverse[0][0] * u + self.inverse[0][1] * v
+        c1 = self.inverse[1][0] * u + self.inverse[1][1] * v
+        return self.blend(c0, c1)
+
+    def valid_fingerprint(self, u, v):
+        # Valid = all corners of tile with this fingerprint
+        #         are in the parallelogram (may be wrapped if cyclic)
+
+        # Assume u, v have been normalized already
+        if not self.point_in_parallelogram(u, v):
+            return False
+
+        fingerprint = self.normalize_fingerprint(u + 1, v)
+        if not self.point_in_parallelogram(*fingerprint):
+            return False
+
+        fingerprint = self.normalize_fingerprint(u, v + 1)
+        if not self.point_in_parallelogram(*fingerprint):
+            return False
+
+        fingerprint = self.normalize_fingerprint(u + 1, v + 1)
+        if not self.point_in_parallelogram(*fingerprint):
+            return False
+
+        return True
+
+    def parallelogram_coord(self, u, v):
+        # Convert to be in [0, self.u_num] x [0, self.v_num]
+        # (ideally if in the parallelogram)
+
+        u_coord = (u * self.p[1][1] - v * self.p[1][0]) / self.determinant
+        v_coord = (v * self.p[0][0] - u * self.p[0][1]) / self.determinant
+
+        return (u_coord, v_coord)
+
+    def point_in_parallelogram(self, u, v):
+        parallelogram_uv = self.parallelogram_coord(u, v)
+
+        if 0.0 <= parallelogram_uv[0] <= self.u_num:
+            if 0.0 <= parallelogram_uv[1] <= self.v_num:
+                return True
+        return False
+
+    def normalize_fingerprint(self, u, v):
+        # Return a canonical fingerprint for tile with this fingerprint
+        # Tiles that are essentually the same (due to cyclic/wrapping)
+        # will have the same fingerprint.
+        # The goal is to not create such tiles more than once
+        while (True):
+            u_old = u
+            v_old = v
+            parallelogram_uv = self.parallelogram_coord(u, v)
+            if (self.u_cyclic):
+                if parallelogram_uv[0] >= self.u_num:
+                    u -= (self.u_num * self.p[0][0])
+                    v -= (self.u_num * self.p[0][1])
+                elif parallelogram_uv[0] < 0.0:
+                    u += (self.u_num * self.p[0][0])
+                    v += (self.u_num * self.p[0][1])
+
+            if (self.v_cyclic):
+                if parallelogram_uv[1] >= self.v_num:
+                    u -= (self.v_num * self.p[1][0])
+                    v -= (self.v_num * self.p[1][1])
+                elif parallelogram_uv[1] < 0.0:
+                    u += (self.v_num * self.p[1][0])
+                    v += (self.v_num * self.p[1][1])
+            if u == u_old and v == v_old:
+                return (u, v)
+
+    def fingerprint_range(self):
+        # Maximum extents of what the ranges can be ...
+        # (Then we can loop over these ranges and see if tiles
+        #  with these fingerprints are valid.)
+        u_min = min(0,
+                    self.u_num * self.p[0][0],
+                    self.v_num * self.p[1][0],
+                    self.u_num * self.p[0][0] + self.v_num * self.p[1][0])
+        u_max = max(0,
+                    self.u_num * self.p[0][0],
+                    self.v_num * self.p[1][0],
+                    self.u_num * self.p[0][0] + self.v_num * self.p[1][0])
+        v_min = min(0,
+                    self.u_num * self.p[0][1],
+                    self.v_num * self.p[1][1],
+                    self.u_num * self.p[0][1] + self.v_num * self.p[1][1])
+        v_max = max(0,
+                    self.u_num * self.p[0][1],
+                    self.v_num * self.p[1][1],
+                    self.u_num * self.p[0][1] + self.v_num * self.p[1][1])
+        return (range(u_min, u_max), range(v_min, v_max))

add_mesh_extra_objects/tessagon/core/tessagon.py

@@ -0,0 +1,161 @@
+from tessagon.core.grid_tile_generator import GridTileGenerator
+from tessagon.core.parallelogram_tile_generator \
+    import ParallelogramTileGenerator
+
+
+class Tessagon:
+    tile_class = None
+    metadata = None
+
+    def __init__(self, **kwargs):
+        if 'tile_generator' in kwargs:
+            self.tile_generator = kwargs['tile_generator'](self, **kwargs)
+        elif 'rot_factor' in kwargs:
+            # Deprecated?
+            rot_factor = kwargs['rot_factor']
+            extra_args = {'parallelogram_vectors':
+                          [[rot_factor, -1], [1, rot_factor]]}
+
+            self.tile_generator = \
+                ParallelogramTileGenerator(self,
+                                           **{**kwargs, **extra_args})
+        elif 'parallelogram_vectors' in kwargs:
+            self.tile_generator = ParallelogramTileGenerator(self, **kwargs)
+        else:
+            self.tile_generator = GridTileGenerator(self, **kwargs)
+
+        self._initialize_function(**kwargs)
+
+        # Optional post processing function
+        self.post_process = None
+        if 'post_process' in kwargs:
+            self.post_process = kwargs['post_process']
+
+        if 'adaptor_class' in kwargs:
+            adaptor_class = kwargs['adaptor_class']
+            self.mesh_adaptor = adaptor_class(**kwargs)
+        else:
+            raise ValueError('Must provide a mesh adaptor class')
+
+        self.color_pattern = kwargs.get('color_pattern') or None
+
+        self.tiles = None
+        self.face_types = {}
+        self.vert_types = {}
+
+        self._process_extra_parameters(**kwargs)
+
+    def create_mesh(self):
+        self._initialize_tiles()
+
+        self.mesh_adaptor.create_empty_mesh()
+
+        self._calculate_verts()
+        self._calculate_faces()
+
+        if self.color_pattern:
+            self._calculate_colors()
+
+        self.mesh_adaptor.finish_mesh()
+
+        if self.post_process:
+            # Run user defined post-processing code
+            # Need to pass self here (this could be designed better)
+            self.post_process(self)
+
+        return self.mesh_adaptor.get_mesh()
+
+    def inspect(self):
+        print("\n=== %s ===\n" % (self.__class__.__name__))
+        for i in range(len(self.tiles)):
+            self.tiles[i].inspect(tile_number=i)
+
+    # Note, would like these to be a class properties,
+    # but the designers of Python flip-flop about
+    # how to implement it.
+    @classmethod
+    def num_color_patterns(cls):
+        if cls.metadata is None:
+            return 0
+        return cls.metadata.num_color_patterns
+
+    @classmethod
+    def num_extra_parameters(cls):
+        if cls.metadata is None:
+            return 0
+        return len(cls.metadata.extra_parameters)
+
+    # Below are protected
+
+    def _initialize_function(self, **kwargs):
+        self.f = None
+
+        if 'simple_2d' in kwargs:
+            u_multiplier_2d = 1.0
+            if self.metadata and self.metadata.uv_ratio:
+                v_multiplier_2d = 1.0 / self.metadata.uv_ratio
+            else:
+                v_multiplier_2d = 1.0
+
+            tile_aspect = self.tile_generator.v_num / self.tile_generator.u_num
+            multiplier_2d = kwargs.get('multiplier_2d', 1.0)
+            u_multiplier_2d *= multiplier_2d
+            v_multiplier_2d *= multiplier_2d * tile_aspect
+
+            translate_2d = kwargs.get('translate_2d', (0, 0))
+            # Simple xy-plane
+            self.f = lambda u, v: (translate_2d[0] + u_multiplier_2d * u,
+                                   translate_2d[1] + v_multiplier_2d * v,
+                                   0.0)
+
+            # Just to test how the corners are going to map ...
+            # top_left = self.tile_generator.corners[0]
+            # bottom_right = self.tile_generator.corners[3]
+            # print(self.f(*top_left), self.f(*bottom_right))
+        elif 'function' in kwargs:
+            self.f = kwargs['function']
+        else:
+            raise ValueError('Must specify a function')
+
+    def _initialize_tiles(self):
+        self.tiles = self.tile_generator.create_tiles()
+
+    def _calculate_verts(self):
+        for tile in self.tiles:
+            tile.calculate_verts()
+
+    def _calculate_faces(self):
+        for tile in self.tiles:
+            tile.calculate_faces()
+
+    def _calculate_colors(self):
+        self.mesh_adaptor.initialize_colors()
+        for tile in self.tiles:
+            tile.calculate_colors()
+
+    def _process_extra_parameters(self, **kwargs):
+        self.extra_parameters = {}
+        parameters_info = self.metadata.extra_parameters
+        if not parameters_info:
+            return
+
+        for parameter in parameters_info:
+            parameter_info = parameters_info[parameter]
+            if parameter not in kwargs:
+                continue
+            value = kwargs.get(parameter)
+            if parameter_info['type'] == 'float':
+                self._process_float_extra_parameter(parameter,
+                                                    value,
+                                                    parameter_info)
+
+    def _process_float_extra_parameter(self, parameter, value, parameter_info):
+        max_value = parameter_info.get('max')
+        min_value = parameter_info.get('min')
+        if max_value is not None and value > max_value:
+            raise ValueError('Parameter {} ({}) exceeds maximum ({})'
+                             .format(parameter, value, max_value))
+        if min_value is not None and value < min_value:
+            raise ValueError('Parameter {} ({}) below minimum ({})'
+                             .format(parameter, value, min_value))
+        self.extra_parameters[parameter] = value

add_mesh_extra_objects/tessagon/core/tessagon_discovery.py

@@ -0,0 +1,116 @@
+from tessagon.types.hex_tessagon import HexTessagon
+from tessagon.types.tri_tessagon import TriTessagon
+from tessagon.types.octo_tessagon import OctoTessagon
+from tessagon.types.rhombus_tessagon import RhombusTessagon
+from tessagon.types.hex_tri_tessagon import HexTriTessagon
+from tessagon.types.hex_square_tri_tessagon import HexSquareTriTessagon
+from tessagon.types.square_tessagon import SquareTessagon
+from tessagon.types.pythagorean_tessagon import PythagoreanTessagon
+from tessagon.types.brick_tessagon import BrickTessagon
+from tessagon.types.dodeca_tessagon import DodecaTessagon
+from tessagon.types.square_tri_tessagon import SquareTriTessagon
+from tessagon.types.weave_tessagon import WeaveTessagon
+from tessagon.types.floret_tessagon import FloretTessagon
+from tessagon.types.hex_big_tri_tessagon import HexBigTriTessagon
+from tessagon.types.zig_zag_tessagon import ZigZagTessagon
+from tessagon.types.dissected_square_tessagon import DissectedSquareTessagon
+from tessagon.types.square_tri2_tessagon import SquareTri2Tessagon
+from tessagon.types.dodeca_tri_tessagon import DodecaTriTessagon
+from tessagon.types.dissected_triangle_tessagon \
+    import DissectedTriangleTessagon
+from tessagon.types.dissected_hex_quad_tessagon \
+    import DissectedHexQuadTessagon
+from tessagon.types.dissected_hex_tri_tessagon \
+    import DissectedHexTriTessagon
+from tessagon.types.penta_tessagon import PentaTessagon
+from tessagon.types.penta2_tessagon import Penta2Tessagon
+from tessagon.types.big_hex_tri_tessagon import BigHexTriTessagon
+from tessagon.types.stanley_park_tessagon import StanleyParkTessagon
+from tessagon.types.valemount_tessagon import ValemountTessagon
+from tessagon.types.cloverdale_tessagon import CloverdaleTessagon
+from tessagon.types.islamic_hex_stars_tessagon import IslamicHexStarsTessagon
+from tessagon.types.islamic_stars_crosses_tessagon \
+    import IslamicStarsCrossesTessagon
+
+ALL = [SquareTessagon,
+       HexTessagon,
+       TriTessagon,
+
+       OctoTessagon,
+       HexTriTessagon,
+       HexSquareTriTessagon,
+       DodecaTessagon,
+       SquareTriTessagon,
+       SquareTri2Tessagon,
+       DodecaTriTessagon,
+       BigHexTriTessagon,
+
+       RhombusTessagon,
+       FloretTessagon,
+       DissectedSquareTessagon,
+       DissectedTriangleTessagon,
+       DissectedHexQuadTessagon,
+       DissectedHexTriTessagon,
+       PentaTessagon,
+       Penta2Tessagon,
+
+       PythagoreanTessagon,
+       BrickTessagon,
+       WeaveTessagon,
+       HexBigTriTessagon,
+       ZigZagTessagon,
+       ValemountTessagon,
+       CloverdaleTessagon,
+
+       StanleyParkTessagon,
+       IslamicHexStarsTessagon,
+       IslamicStarsCrossesTessagon]
+
+
+class TessagonDiscovery:
+    def __init__(self, **kwargs):
+        self.classes = kwargs.get('classes', ALL)
+
+    def count(self):
+        return len(self.classes)
+
+    def to_list(self):
+        return self.classes
+
+    def inverse(self):
+        other_classes = list(set(ALL) - set(self.classes))
+        return TessagonDiscovery(classes=other_classes)
+
+    def __add__(self, other):
+        new_classes = list(set(self.classes) | set(other.classes))
+        return TessagonDiscovery(classes=new_classes)
+
+    def __sub__(self, other):
+        new_classes = list(set(self.classes) - set(other.classes))
+        return TessagonDiscovery(classes=new_classes)
+
+    def with_color_patterns(self):
+        results = []
+        for klass in self.classes:
+            if klass.metadata is None:
+                continue
+            if klass.metadata.has_color_patterns:
+                results.append(klass)
+        return TessagonDiscovery(classes=results)
+
+    def with_classification(self, classification):
+        results = []
+        for klass in self.classes:
+            if klass.metadata is None:
+                continue
+            if klass.metadata.has_classification(classification):
+                results.append(klass)
+        return TessagonDiscovery(classes=results)
+
+    @classmethod
+    def get_class(cls, class_name):
+        if class_name in globals():
+            klass = globals()[class_name]
+            if klass in ALL:
+                return klass
+        raise ValueError(class_name + ' is not recognized by Tessagon')

add_mesh_extra_objects/tessagon/core/tessagon_metadata.py

@@ -0,0 +1,61 @@
+class TessagonMetadata:
+    CLASSIFICATION_MAP = {
+        'regular': 'Regular tiling',
+        'archimedean': 'Archimedean tiling',
+        'laves': 'Laves tiling',
+        'non_edge': 'Non-edge-to-edge tiling',
+        'non_convex': 'Non-convex tiling'
+    }
+
+    def __init__(self, **kwargs):
+        self._name = kwargs.get('name')
+        if not self._name:
+            raise ValueError('No name set')
+        self._num_color_patterns = kwargs.get('num_color_patterns', 0)
+        self._classification = kwargs.get('classification', 'misc')
+        self._shapes = kwargs.get('shapes', [])
+        self._sides = kwargs.get('sides', [])
+        self._uv_ratio = kwargs.get('uv_ratio', None)
+        self._extra_parameters = kwargs.get('extra_parameters', {})
+
+    @property
+    def name(self):
+        return self._name
+
+    @property
+    def num_color_patterns(self):
+        return self._num_color_patterns
+
+    @property
+    def has_color_patterns(self):
+        return self._num_color_patterns > 0
+
+    def has_shape(self, shape):
+        if shape in self._shapes:
+            return True
+        return False
+
+    @property
+    def classification(self):
+        return self._classification
+
+    def has_classification(self, classification):
+        return self._classification == classification
+
+    @property
+    def human_readable_classification(self):
+        return self.__class__.CLASSIFICATION_MAP[self._classification]
+
+    @property
+    def uv_ratio(self):
+        # Aspect ratio U/V for best looking proportions
+        # Roughly, assuming a uniform input function,
+        # we would want to select the u, v inputs so that:
+        #   (u_range[1] - u_range[0]) / u_num
+        #          = uv_ratio * (v_range[1] - v_range[0]) / v_num
+        # Or scale the input function so get similar proportions.
+        return self._uv_ratio
+
+    @property
+    def extra_parameters(self):
+        return self._extra_parameters

add_mesh_extra_objects/tessagon/core/tile.py

@@ -0,0 +1,338 @@
+from tessagon.core.abstract_tile import AbstractTile
+
+
+class Tile(AbstractTile):
+
+    def __init__(self, tessagon, **kwargs):
+        super().__init__(tessagon, **kwargs)
+
+        self.mesh_adaptor = tessagon.mesh_adaptor
+
+        self.verts = self.init_verts()
+        self.faces = self.init_faces()
+        self.color_pattern = kwargs.get('color_pattern') or None
+        if self.faces and self.color_pattern:
+            self.face_paths = self.all_face_paths()
+
+    def validate(self):
+        # Subclass decides if this should be done
+        pass
+
+    def add_vert(self, index_keys, ratio_u, ratio_v, **kwargs):
+        # Use the mesh adaptor to create a vertex.
+        # In reality, multiple vertices may get defined if symmetry is declared
+        vert = self._get_vert(index_keys)
+        if vert is None:
+            coords = self.f(*self.blend(ratio_u, ratio_v))
+            vert = self.mesh_adaptor.create_vert(coords)
+
+            self._set_vert(index_keys, vert)
+            if 'vert_type' in kwargs:
+                if not kwargs['vert_type'] in self.tessagon.vert_types:
+                    self.tessagon.vert_types[kwargs['vert_type']] = []
+                self.tessagon.vert_types[kwargs['vert_type']].append(vert)
+
+        if vert is not None:
+            equivalent_verts = kwargs.get('equivalent', [])
+            for equivalent_vert in equivalent_verts:
+                self.set_equivalent_vert(*equivalent_vert, vert)
+
+        # We add additional vertices by flipping 'left', 'right' etc
+        # if the tile has some kind of symmetry defined
+        self._create_symmetric_verts(index_keys, ratio_u, ratio_v, **kwargs)
+
+        # On the boundary, make sure equivalent vertices are set on
+        # neighbor tiles
+        self._set_equivalent_neighbor_verts(index_keys, vert, **kwargs)
+
+        return vert
+
+    def set_equivalent_vert(self, neighbor_keys, index_keys, vert, **kwargs):
+        # On boundary, the vert on a neighbor is equivalent to this vert
+        # This is usually only called indirectly via add_vert, but check out
+        # PythagoreanTile for an example of direct usage
+        if vert is None:
+            return None
+
+        tile = self.get_neighbor_tile(neighbor_keys)
+        if tile is None:
+            return None
+
+        tile._set_vert(self._index_path(index_keys, neighbor_keys), vert)
+
+    def add_face(self, index_keys, vert_index_keys_list, **kwargs):
+        # Use the mesh adaptor to create a face.
+        # In reality, multiple faces may get defined if symmetry is declared
+        face = self._get_face(index_keys)
+
+        if face is None:
+            verts = self._get_verts_from_list(vert_index_keys_list)
+            if verts is not None:
+                face = \
+                    self._make_face(index_keys, verts, **kwargs)
+
+        if face is not None:
+            equivalent_faces = kwargs.get('equivalent', [])
+            for equivalent_face in equivalent_faces:
+                self.set_equivalent_face(*equivalent_face, face)
+
+        # We add additional faces by flipping 'left', 'right' etc
+        # if the tile has some kind of symmetry defined
+        self._create_symmetric_faces(index_keys, vert_index_keys_list,
+                                     **kwargs)
+
+        return face
+
+    def _make_face(self, index_keys, verts, **kwargs):
+        face = self.mesh_adaptor.create_face(verts)
+        self._set_face(index_keys, face)
+
+        # The tessagon might keep a list of specific face types
+        if 'face_type' in kwargs:
+            if not kwargs['face_type'] in self.tessagon.face_types:
+                self.tessagon.face_types[kwargs['face_type']] = []
+            self.tessagon.face_types[kwargs['face_type']].append(face)
+
+        # On the boundary, make sure equivalent faces are set on neighbor tiles
+        self._set_equivalent_neighbor_faces(index_keys, face, **kwargs)
+
+        return face
+
+    def num_color_patterns(self):
+        return self.tessagon.num_color_patterns()
+
+    def calculate_colors(self):
+        if self.color_pattern > self.num_color_patterns():
+            raise ValueError("color_pattern must be below %d" %
+                             (self.num_color_patterns()))
+        method_name = "color_pattern%d" % (self.color_pattern)
+        method = getattr(self, method_name)
+        if not callable(method):
+            raise ValueError("%s is not a callable color pattern" %
+                             (method_name))
+        method()
+
+    def color_face(self, index_keys, color_index):
+        face = self._get_face(index_keys)
+        if face is None:
+            return
+        self.mesh_adaptor.color_face(face, color_index)
+
+    def set_equivalent_face(self, neighbor_keys, index_keys, face, **kwargs):
+        # On boundary, the face on a neighbor is equivalent to this face
+        # This is usually only called indirectly via add_face, but check out
+        # PythagoreanTile for an example of direct usage
+        tile = self.get_neighbor_tile(neighbor_keys)
+        if tile is None:
+            return None
+        tile._set_face(self._index_path(index_keys, neighbor_keys), face)
+
+    def all_face_paths(self, faces=None, base_path=None):
+        if faces is None:
+            faces = self.faces
+        if base_path is None:
+            base_path = []
+
+        paths = []
+        for index in faces:
+            new_base_path = base_path + [index]
+            if type(faces[index]) is dict:
+                paths += self.all_face_paths(faces[index], new_base_path)
+            else:
+                paths.append(new_base_path)
+        return paths
+
+    def color_paths(self, paths, color, color_other=None):
+        for path in self.face_paths:
+            if path in paths:
+                self.color_face(path, color)
+            elif color_other:
+                self.color_face(path, color_other)
+
+    def color_paths_hash(self, hash, color_other=None):
+        for path in self.face_paths:
+            for color in hash:
+                done = False
+                if path in hash[color]:
+                    self.color_face(path, color)
+                    done = True
+                    break
+            if color_other and not done:
+                self.color_face(path, color_other)
+
+    # Below are protected
+
+    def _get_vert(self, index_keys):
+        return self._get_nested_list_value(self.verts, index_keys)
+
+    def _set_vert(self, index_keys, value):
+        self._set_nested_list_value(self.verts, index_keys, value)
+
+    def _get_face(self, index_keys):
+        return self._get_nested_list_value(self.faces, index_keys)
+
+    def _set_face(self, index_keys, value):
+        self._set_nested_list_value(self.faces, index_keys, value)
+
+    def _get_neighbor_vert(self, neighbor_keys, index_keys):
+        # See comment about neighbors in AbstractTile
+        tile = self.get_neighbor_tile(neighbor_keys)
+        if tile is None:
+            return None
+        return tile._get_vert(self._index_path(index_keys, neighbor_keys))
+
+    def _create_symmetric_verts(self, index_keys, ratio_u, ratio_v, **kwargs):
+        # The 'symmetry' keyword is just to ensure we don't recurse forever
+        if 'symmetry' not in kwargs:
+            extra_args = {'symmetry': True}
+            if self.rot_symmetric == 180:
+                rot_keys = self._rotate_index(index_keys)
+                self.add_vert(rot_keys, 1.0 - ratio_u, 1 - ratio_v,
+                              **{**kwargs, **extra_args})
+
+            elif self.rot_symmetric == 90:
+                rot_keys = self._rotate_index(index_keys)
+                self.add_vert(rot_keys, 1.0 - ratio_v, ratio_u,
+                              **{**kwargs, **extra_args})
+
+                rot_keys = self._rotate_index(rot_keys)
+                self.add_vert(rot_keys, 1.0 - ratio_u, 1 - ratio_v,
+                              **{**kwargs, **extra_args})
+
+                rot_keys = self._rotate_index(rot_keys)
+                self.add_vert(rot_keys, ratio_v, 1 - ratio_u,
+                              **{**kwargs, **extra_args})
+
+            if self.u_symmetric:
+                # Add reflection about u
+                u_flip_keys = self._u_flip(index_keys)
+                self.add_vert(u_flip_keys, 1.0 - ratio_u, ratio_v,
+                              **{**kwargs, **extra_args})
+                if self.v_symmetric:
+                    # Add diagonally across
+                    uv_flip_keys = self._v_flip(u_flip_keys)
+                    self.add_vert(uv_flip_keys, 1.0 - ratio_u, 1.0 - ratio_v,
+                                  **{**kwargs, **extra_args})
+            if self.v_symmetric:
+                # Add reflection about v
+                v_flip_keys = self._v_flip(index_keys)
+                self.add_vert(v_flip_keys, ratio_u, 1.0 - ratio_v,
+                              **{**kwargs, **extra_args})
+
+    def _set_equivalent_neighbor_verts(self, index_keys, vert, **kwargs):
+        if 'u_boundary' in kwargs:
+            self._set_u_equivalent_vert(index_keys, vert, **kwargs)
+        if 'v_boundary' in kwargs:
+            self._set_v_equivalent_vert(index_keys, vert, **kwargs)
+        if 'corner' in kwargs:
+            self._set_u_equivalent_vert(index_keys, vert, **kwargs)
+            self._set_v_equivalent_vert(index_keys, vert, **kwargs)
+            self._set_uv_equivalent_vert(index_keys, vert, **kwargs)
+
+    # Handle vert on left/right boundary
+    def _set_u_equivalent_vert(self, index_keys, vert, **kwargs):
+        u_index = self._u_index(index_keys)
+        u_flip_keys = self._u_flip(index_keys)
+        self.set_equivalent_vert([u_index], u_flip_keys, vert, **kwargs)
+
+    # Handle vert on top/bottom boundary
+    def _set_v_equivalent_vert(self, index_keys, vert, **kwargs):
+        v_index = self._v_index(index_keys)
+        v_flip_keys = self._v_flip(index_keys)
+        self.set_equivalent_vert([v_index], v_flip_keys, vert, **kwargs)
+
+    # Handle vert on corner, equivalent to vert on diagonal tile
+    def _set_uv_equivalent_vert(self, index_keys, vert, **kwargs):
+        u_index = self._u_index(index_keys)
+        v_index = self._v_index(index_keys)
+        u_flip_keys = self._u_flip(index_keys)
+        uv_flip_keys = self._v_flip(u_flip_keys)
+        self.set_equivalent_vert([u_index, v_index], uv_flip_keys, vert,
+                                 **kwargs)
+
+    def _get_verts_from_list(self, vert_index_keys_list):
+        verts = []
+        for vert_index_keys in vert_index_keys_list:
+            if isinstance(vert_index_keys, list) \
+               and isinstance(vert_index_keys[0], list):
+                vert = self._get_neighbor_vert(vert_index_keys[0],
+                                               vert_index_keys[1])
+            else:
+                vert = self._get_vert(vert_index_keys)
+
+            if vert is None:
+                return None
+            verts.append(vert)
+
+        return verts
+
+    def _create_symmetric_faces(self, index_keys, vert_index_keys_list,
+                                **kwargs):
+        # The 'symmetry' keyword is just to ensure we don't recurse forever
+        if 'symmetry' not in kwargs:
+            extra_args = {'symmetry': True}
+            if self.rot_symmetric == 180:
+                rot_keys = self._rotate_index(index_keys)
+                rot_vert_index_keys_list \
+                    = self._rotate_index(vert_index_keys_list)
+                if 'equivalent' in kwargs:
+                    equivalent_faces = kwargs['equivalent']
+                    kwargs = kwargs.copy()
+                    kwargs['equivalent'] = \
+                        [self._rotate_index(equivalent_face)
+                         for equivalent_face in equivalent_faces]
+
+                self.add_face(rot_keys, rot_vert_index_keys_list,
+                              **{**kwargs, **extra_args})
+            if self.u_symmetric:
+                # Add reflection about u
+                u_flip_keys = self._u_flip(index_keys)
+                u_flip_vert_index_keys_list \
+                    = self._u_flip(vert_index_keys_list)
+                self.add_face(u_flip_keys, u_flip_vert_index_keys_list,
+                              **{**kwargs, **extra_args})
+                if self.v_symmetric:
+                    # Add diagonally across
+                    uv_flip_keys = self._v_flip(u_flip_keys)
+                    uv_flip_vert_index_keys_list \
+                        = self._v_flip(u_flip_vert_index_keys_list)
+                    self.add_face(uv_flip_keys, uv_flip_vert_index_keys_list,
+                                  **{**kwargs, **extra_args})
+            if self.v_symmetric:
+                # Add reflection about v
+                v_flip_keys = self._v_flip(index_keys)
+                v_flip_vert_index_keys_list \
+                    = self._v_flip(vert_index_keys_list)
+                self.add_face(v_flip_keys, v_flip_vert_index_keys_list,
+                              **{**kwargs, **extra_args})
+
+    def _set_equivalent_neighbor_faces(self, index_keys, face, **kwargs):
+        if 'u_boundary' in kwargs:
+            self._set_u_equivalent_face(index_keys, face, **kwargs)
+        if 'v_boundary' in kwargs:
+            self._set_v_equivalent_face(index_keys, face, **kwargs)
+        if 'corner' in kwargs:
+            self._set_u_equivalent_face(index_keys, face, **kwargs)
+            self._set_v_equivalent_face(index_keys, face, **kwargs)
+            self._set_uv_equivalent_face(index_keys, face, **kwargs)
+
+    # Handle face on left/right boundary
+    def _set_u_equivalent_face(self, index_keys, face, **kwargs):
+        u_index = self._u_index(index_keys)
+        u_flip_keys = self._u_flip(index_keys)
+        self.set_equivalent_face([u_index], u_flip_keys, face, **kwargs)
+
+    # Handle face on top/bottom boundary
+    def _set_v_equivalent_face(self, index_keys, face, **kwargs):
+        v_index = self._v_index(index_keys)
+        v_flip_keys = self._v_flip(index_keys)
+        self.set_equivalent_face([v_index], v_flip_keys, face, **kwargs)
+
+    # Handle face on corner, equivalent to face on diagonal tile
+    def _set_uv_equivalent_face(self, index_keys, face, **kwargs):
+        u_index = self._u_index(index_keys)
+        v_index = self._v_index(index_keys)
+        u_flip_keys = self._u_flip(index_keys)
+        uv_flip_keys = self._v_flip(u_flip_keys)
+        self.set_equivalent_face([u_index, v_index], uv_flip_keys, face,
+                                 **kwargs)

add_mesh_extra_objects/tessagon/core/tile_generator.py

@@ -0,0 +1,69 @@
+from tessagon.core.value_blend import ValueBlend
+
+
+class TileGenerator(ValueBlend):
+    # This is intended to be an abstract class to generate tiles,
+    # but it's quite tied to a grid structure, so it might make
+    # sense to merge with GridTileGenerator
+    def __init__(self, tessagon, **kwargs):
+        self.tessagon = tessagon
+
+        # Corners is list of tuples:
+        #   [topleft, topright, bottomleft, bottomright]
+        self.corners = None
+        self._init_corners(**kwargs)
+
+        self.u_num = kwargs.get('u_num')
+        self.v_num = kwargs.get('v_num')
+        if not self.u_num or not self.v_num:
+            raise ValueError("Make sure u_num and v_num intervals are set")
+
+        self.u_cyclic = kwargs.get('u_cyclic', True)
+        self.v_cyclic = kwargs.get('v_cyclic', True)
+        self.v_twist = kwargs.get('v_twist', False)
+        self.u_twist = kwargs.get('u_twist', False)
+
+        # TODO: delete these?
+        self.u_phase = kwargs.get('u_phase', 0.0)
+        self.v_phase = kwargs.get('v_phase', 0.0)
+        self.u_shear = kwargs.get('u_shear', 0.0)
+        self.v_shear = kwargs.get('v_shear', 0.0)
+
+        # Note: id_prefix is not used for calculation, just debugging
+        self.id_prefix = self.tessagon.__class__.__name__
+        if 'id_prefix' in kwargs:
+            self.id_prefix = kwargs['id_prefix']
+        self.fingerprint_offset = kwargs.get('fingerprint_offset') or None
+
+        self.color_pattern = kwargs.get('color_pattern') or None
+
+    def create_tile(self, u, v, corners, **kwargs):
+        extra_args = {'corners': corners,
+                      'fingerprint': [u, v]}
+        if self.fingerprint_offset:
+            extra_args['fingerprint'][0] += self.fingerprint_offset[0]
+            extra_args['fingerprint'][1] += self.fingerprint_offset[1]
+
+        if self.id_prefix:
+            extra_args['id'] = "%s[%d][%d]" % (self.id_prefix, u, v)
+
+        if self.color_pattern:
+            extra_args['color_pattern'] = self.color_pattern
+
+        extra_parameters = self.tessagon.extra_parameters
+        if extra_parameters:
+            for parameter in extra_parameters:
+                extra_args[parameter] = extra_parameters[parameter]
+
+        tile_class = self.tessagon.__class__.tile_class
+        return tile_class(self.tessagon,
+                          **{**kwargs, **extra_args})
+
+    def create_tiles(self):
+        self.initialize_tiles()
+        self.initialize_neighbors()
+        tiles = self.get_tiles()
+        for tile in tiles:
+            tile.validate()
+
+        return tiles

add_mesh_extra_objects/tessagon/core/tile_utils.py

@@ -0,0 +1,46 @@
+def right_tile(index_keys):
+    return [['right'], index_keys]
+
+
+def left_tile(index_keys):
+    return [['left'], index_keys]
+
+
+def top_tile(index_keys):
+    return [['top'], index_keys]
+
+
+def bottom_tile(index_keys):
+    return [['bottom'], index_keys]
+
+
+def left_top_tile(index_keys):
+    return [['left', 'top'], index_keys]
+
+
+def left_bottom_tile(index_keys):
+    return [['left', 'bottom'], index_keys]
+
+
+def right_top_tile(index_keys):
+    return [['right', 'top'], index_keys]
+
+
+def right_bottom_tile(index_keys):
+    return [['right', 'bottom'], index_keys]
+
+
+def bottom_left_tile(index_keys):
+    return [['bottom', 'left'], index_keys]
+
+
+def bottom_right_tile(index_keys):
+    return [['bottom', 'right'], index_keys]
+
+
+def top_left_tile(index_keys):
+    return [['top', 'left'], index_keys]
+
+
+def top_right_tile(index_keys):
+    return [['top', 'right'], index_keys]

add_mesh_extra_objects/tessagon/core/value_blend.py

@@ -0,0 +1,35 @@
+class ValueBlend:
+
+    def _init_corners(self, **kwargs):
+        # Corners is list of tuples:
+        #   [bottomleft, bottomright, topleft, topright]
+        if 'corners' in kwargs:
+            self.corners = kwargs['corners']
+            if len(self.corners) != 4 or \
+               any(len(v) != 2 for v in self.corners):
+                raise ValueError("corner should be a list of four tuples, "
+                                 "set either option 'corners' "
+                                 "or options 'u_range' and 'v_range'")
+        elif 'u_range' in kwargs and 'v_range' in kwargs:
+            self.corners = [[kwargs['u_range'][0], kwargs['v_range'][0]],
+                            [kwargs['u_range'][1], kwargs['v_range'][0]],
+                            [kwargs['u_range'][0], kwargs['v_range'][1]],
+                            [kwargs['u_range'][1], kwargs['v_range'][1]]]
+        else:
+            raise ValueError("Must set either option "
+                             "'corners' or options 'u_range' and 'v_range'")
+
+    def _blend_tuples(self, tuple1, tuple2, ratio):
+        out = [None, None]
+        for i in range(2):
+            out[i] = (1 - ratio) * tuple1[i] + ratio * tuple2[i]
+        return out
+
+    def blend(self, ratio_u, ratio_v):
+        uv0 = self._blend_tuples(self.corners[0],
+                                 self.corners[1],
+                                 ratio_u)
+        uv1 = self._blend_tuples(self.corners[2],
+                                 self.corners[3],
+                                 ratio_u)
+        return self._blend_tuples(uv0, uv1, ratio_v)

add_mesh_extra_objects/tessagon/misc/shapes.py

@@ -0,0 +1,157 @@
+from math import sin, cos, sqrt, pi
+
+
+def plane(u, v):
+    # u_cyclic = False, v_cyclic = False
+    return [u, v, 0]
+
+
+def other_plane(u, v):
+    # u_cyclic = False, v_cyclic = False
+    return [v, u, 0]
+
+
+def general_torus(r1, r2, u, v):
+    x = (r1 + r2*cos(v*2*pi))*cos(u*2*pi)
+    y = (r1 + r2*cos(v*2*pi))*sin(u*2*pi)
+    z = r2*sin(v*2*pi)
+    return [x, y, z]
+
+
+def normalize_value(v):
+    if (v < 0.0):
+        while (v < 0.0):
+            v += 1.0
+    else:
+        while (v > 1.0):
+            v -= 1.0
+    return v
+
+
+def warp_var(v, factor):
+    # For any factor, maps 0-->0, 1-->1
+    # factor = 0 is identity
+    # factor > 0 for a wee pinch at v = 1/2
+    v = normalize_value(v)
+    h = 2 * (v - 0.5)
+    i = h + factor*h**3
+    return 0.5*(1.0 + i / (1.0 + factor))
+
+
+def torus(u, v):
+    # u_cyclic = True, v_cyclic = True
+    r1 = 5.0
+    r2 = 1.0
+    return general_torus(r1, r2, u, warp_var(v, 0.2))
+
+
+def other_torus(u, v):
+    # u_cyclic = True, v_cyclic = True
+    return torus(v, u)
+
+
+def general_cylinder(r, h, u, v):
+    x = r*cos(u*2*pi)
+    y = r*sin(u*2*pi)
+    z = h*(v - 0.5)
+    return [x, y, z]
+
+
+def cylinder(u, v):
+    # u_cyclic = True, v_cyclic = False
+    r = 5.0
+    h = 3.5
+    return general_cylinder(r, h, u, v)
+
+
+def other_cylinder(u, v):
+    # u_cyclic = False, v_cyclic = True
+    return cylinder(v, u)
+
+
+def general_paraboloid(scale1, scale2, displace, u, v):
+    return [scale1*u, scale1*v, displace + scale2 * (u**2 + v**2)]
+
+
+def paraboloid(u, v):
+    # u_cyclic = False, v_cyclic = False
+    return general_paraboloid(4, 3, -3, u, v)
+
+
+def general_one_sheet_hyperboloid(scale1, scale2, u, v):
+    c = scale1 * sqrt(1 + u**2)
+    v1 = 2*pi*v
+    x = c * cos(v1)
+    y = c * sin(v1)
+    z = scale2 * u
+    return [x, y, z]
+
+
+def one_sheet_hyperboloid(u, v):
+    # u_cyclic = False, v_cyclic = True
+    return general_one_sheet_hyperboloid(3, 2, u, v)
+
+
+def general_ellipsoid(r1, r2, r3, u, v):
+    # u_cyclic = True, v_cyclic = False
+    u1 = 2*pi*u
+    v1 = pi*normalize_value(warp_var(v + 0.5, 0.8)-0.5)
+    sinv1 = sin(v1)
+    return [r1 * cos(u1) * sinv1, r2 * sin(u1) * sinv1, r3 * cos(v1)]
+
+
+def sphere(u, v):
+    return general_ellipsoid(4, 4, 4, u, v)
+
+
+def general_mobius(r, h, u, v):
+    offset = h*(v-0.5)*sin(u*pi)
+    x = (r + offset)*cos(u*2*pi)
+    y = (r + offset)*sin(u*2*pi)
+    z = h*(v-0.5)*cos(u*pi)
+    return [x, y, z]
+
+
+def mobius(u, v):
+    # u_cyclic = False, v_cyclic = True
+    # u_twist = True, v_twist = False
+    r = 5.0
+    h = 2.0
+    return general_mobius(r, h, v, u)
+
+
+def other_mobius(u, v):
+    # u_cyclic = True, v_cyclic = False
+    # u_twist = False, v_twist = True
+    return mobius(v, u)
+
+
+def general_klein(scale, u, v):
+    # Adapted from http://paulbourke.net/geometry/klein/
+    u1 = 2*pi*normalize_value(warp_var(u + 0.5, 0.6)-0.5)
+    v1 = 2*pi*normalize_value(v+0.25)
+
+    c1 = cos(u1)
+    c2 = sin(u1)
+    r = 4.0 - 2.0*c1
+
+    if u1 <= pi:
+        x = 6*c1*(1.0 + c2) + r*c1*cos(v1)
+        y = 16*c2 + r*c2*cos(v1)
+    else:
+        x = 6*c1*(1.0 + c2) + r*cos(v1+pi)
+        y = 16*c2
+    z = r * sin(v1)
+    return [scale*x, scale*y, scale*z]
+
+
+def klein(u, v):
+    # u_cyclic = True, v_cyclic = True
+    # u_twist = False, v_twist = True
+    return general_klein(0.25, u, v)
+
+
+def other_klein(u, v):
+    # u_cyclic = True, v_cyclic = True
+    # u_twist = True, v_twist = False
+    return general_klein(0.25, v, u)

add_mesh_extra_objects/tessagon/types/big_hex_tri_tessagon.py

@@ -0,0 +1,175 @@
+from math import atan2, sqrt, sin, cos, pi
+from tessagon.core.tessagon import Tessagon
+from tessagon.core.alternating_tile import AlternatingTile
+from tessagon.core.tessagon_metadata import TessagonMetadata
+from tessagon.core.tile_utils import right_tile, left_tile, \
+    top_tile, top_left_tile, bottom_tile
+
+metadata = TessagonMetadata(name='Big Hexagons and Triangles',
+                            num_color_patterns=1,
+                            classification='archimedean',
+                            shapes=['hexagons', 'triangles'],
+                            sides=[6, 3],
+                            uv_ratio=1.0/sqrt(3),
+                            extra_parameters={
+                                'hexagon_ratio': {
+                                    'type': 'float',
+                                    'min': 0.0,
+                                    # Any higher than 0.70, and verts are
+                                    # pushed to neighboring tiles
+                                    'max': 0.70,
+                                    'default': 0.5,
+                                    'description':
+                                    'Control the size of the Hexagons'
+                                }
+                            })
+
+
+class BigHexTriTile(AlternatingTile):
+    #  See the SVG for decomposition:
+    # https://raw.githubusercontent.com/cwant/tessagon/master/documentation/code/big_hex_tri.svg
+
+    def __init__(self, tessagon, **kwargs):
+        super().__init__(tessagon, **kwargs)
+        self.u_symmetric = False
+        self.v_symmetric = False
+
+        self.hexagon_ratio = kwargs.get('hexagon_ratio', 0.5)
+
+        # in u units
+        self.hex_radius = 4 * self.hexagon_ratio / sqrt(7)
+        # multiplier to get v units ...
+        self.uv_ratio = self.tessagon.metadata.uv_ratio
+
+        # Tilt
+        self.theta_offset = -atan2(1, 3 * sqrt(3)) + pi/6
+        self.hex_theta = [(self.theta_offset + number * pi / 3.0)
+                          for number in range(6)]
+
+    def hex_vert_coord(self, center, number):
+        # number in range(6)
+        return [center[0] +
+                self.hex_radius * cos(self.hex_theta[number]),
+                center[1] +
+                self.hex_radius * sin(self.hex_theta[number]) * self.uv_ratio]
+
+    def init_verts(self):
+        if self.tile_type == 0:
+            verts = {0: None,
+                     1: None}
+        else:
+            verts = {2: None,
+                     3: None,
+                     4: None,
+                     5: None}
+
+        return verts
+
+    def init_faces(self):
+        if self.tile_type == 0:
+            faces = {'A': None,
+                     'B': None,
+                     'C': None,
+                     'D': None,
+                     'E': None,
+                     'F': None,
+                     'G': None,
+                     'H': None}
+        else:
+            faces = {'I': None,
+                     'J': None,
+                     'K': None,
+                     'L': None,
+                     'M': None,
+                     'N': None,
+                     'O': None,
+                     'P': None,
+                     'Q': None,
+                     'R': None}
+
+        return faces
+
+    def calculate_verts(self):
+        if self.tile_type == 0:
+            self.add_vert([0], *self.hex_vert_coord([0, 1], 5))
+            self.add_vert([1], *self.hex_vert_coord([1, 0], 2))
+        else:
+            self.add_vert([2], *self.hex_vert_coord([1, 1], 3))
+            self.add_vert([3], *self.hex_vert_coord([1, 1], 4))
+            self.add_vert([4], *self.hex_vert_coord([0, 0], 1))
+            self.add_vert([5], *self.hex_vert_coord([0, 0], 0))
+
+    def calculate_faces(self):
+        if self.tile_type == 0:
+            self.add_face('A',
+                          [0,
+                           top_tile(5),
+                           top_tile(4),
+                           top_left_tile(1),
+                           left_tile(2),
+                           left_tile(3)],
+                          equivalent=[top_tile('T'),
+                                      top_left_tile('H'),
+                                      left_tile('I')])
+
+            self.add_face('B',
+                          [0,
+                           right_tile(2),
+                           top_tile(5)],
+                          equivalent=[top_tile('S'),
+                                      right_tile('K')])
+
+            self.add_face('C',
+                          [0,
+                           right_tile(4),
+                           right_tile(2)],
+                          equivalent=[right_tile('L')])
+
+            self.add_face('D',
+                          [0,
+                           1,
+                           right_tile(4)],
+                          equivalent=[right_tile('M')])
+
+            self.add_face('E',
+                          [1,
+                           0,
+                           left_tile(3)],
+                          equivalent=[left_tile('P')])
+
+            self.add_face('F',
+                          [1,
+                           left_tile(3),
+                           left_tile(5)],
+                          equivalent=[left_tile('Q')])
+
+            self.add_face('G',
+                          [1,
+                           left_tile(5),
+                           bottom_tile(2)],
+                          equivalent=[left_tile('R')])
+
+        else:
+            self.add_face('N',
+                          [2,
+                           4,
+                           3])
+
+            self.add_face('O',
+                          [3,
+                           4,
+                           5])
+
+    def color_pattern1(self):
+        if self.tile_type == 0:
+            self.color_face('A', 2)
+            self.color_face('B', 1)
+            self.color_face('D', 1)
+            self.color_face('F', 1)
+        else:
+            self.color_face('N', 1)
+
+
+class BigHexTriTessagon(Tessagon):
+    tile_class = BigHexTriTile
+    metadata = metadata

add_mesh_extra_objects/tessagon/types/brick_tessagon.py

@@ -0,0 +1,76 @@
+from tessagon.core.tile import Tile
+from tessagon.core.tessagon import Tessagon
+from tessagon.core.tessagon_metadata import TessagonMetadata
+from tessagon.core.tile_utils import left_tile, bottom_tile
+
+metadata = TessagonMetadata(name='Bricks',
+                            num_color_patterns=1,
+                            classification='non_edge',
+                            shapes=['rectangles'],
+                            sides=[4],
+                            uv_ratio=1.0)
+
+
+class BrickTile(Tile):
+    #                 top
+    #
+    #    -o..o-      -o..o- r
+    # ^  .|..|.    l .|..|. i
+    # |  .o--o.    e .o--o. g
+    # |  .|..|.    f .|..|. h
+    # |  -o..o-    t -o..o- t
+    # V
+    #   U --->       bottom
+
+    def __init__(self, tessagon, **kwargs):
+        super().__init__(tessagon, **kwargs)
+        self.u_symmetric = True
+        self.v_symmetric = True
+
+    def init_verts(self):
+        return {'left': {'top': None, 'middle': None, 'bottom': None},
+                'right': {'top': None, 'middle': None, 'bottom': None}}
+
+    def init_faces(self):
+        return {'left': None, 'right': None, 'top': None, 'bottom': None}
+
+    def calculate_verts(self):
+        # corners: set bottom-left ... symmetry takes care of other 3 corners
+        self.add_vert(['left', 'bottom'], 0.25, 0.0, v_boundary=True)
+
+        # left middle, symmetry also creates right middle
+        self.add_vert(['left', 'middle'], 0.25, 0.5)
+
+    def calculate_faces(self):
+        # Add left, symmetry gives the right side face
+        self.add_face('left',
+                      [['left', 'top'],
+                       ['left', 'middle'],
+                       ['left', 'bottom'],
+                       # Verts on neighbor tiles:
+                       left_tile(['right', 'bottom']),
+                       left_tile(['right', 'middle']),
+                       left_tile(['right', 'top'])],
+                      u_boundary=True)
+
+        # Add bottom, symmetry gives the top face
+        self.add_face('bottom',
+                      [['right', 'bottom'],
+                       ['right', 'middle'],
+                       ['left', 'middle'],
+                       ['left', 'bottom'],
+                       # Verts on neighbor tiles:
+                       bottom_tile(['left', 'middle']),
+                       bottom_tile(['right', 'middle'])],
+                      v_boundary=True)
+
+    def color_pattern1(self):
+        self.color_paths([
+            ['left'],
+            ['right']
+        ], 1, 0)
+
+
+class BrickTessagon(Tessagon):
+    tile_class = BrickTile
+    metadata = metadata

add_mesh_extra_objects/tessagon/types/cloverdale_tessagon.py

@@ -0,0 +1,143 @@
+from math import sqrt
+from tessagon.core.tile import Tile
+from tessagon.core.tessagon import Tessagon
+from tessagon.core.tessagon_metadata import TessagonMetadata
+from tessagon.core.tile_utils import left_tile, top_left_tile, top_tile
+
+metadata = TessagonMetadata(name='Cloverdale',
+                            num_color_patterns=1,
+                            classification='non_edge',
+                            shapes=['squares', 'pentagons'],
+                            sides=[4, 5],
+                            uv_ratio=1.0)
+
+
+class CloverdaleTile(Tile):
+    # See the SVG for decomposition:
+    # https://raw.githubusercontent.com/cwant/tessagon/master/documentation/code/cloverdale.svg
+
+    def __init__(self, tessagon, **kwargs):
+        super().__init__(tessagon, **kwargs)
+        self.u_symmetric = True
+        self.v_symmetric = True
+
+    def init_verts(self):
+        return {'left': {'top': {'inner': None,
+                                 'outer': None,
+                                 'u_border': None,
+                                 'v_border': None},
+                         'middle': {'inner': None,
+                                    'outer': None},
+                         'bottom': {'inner': None,
+                                    'outer': None,
+                                    'u_border': None,
+                                    'v_border': None}},
+                'center': {'top': {'inner': None,
+                                   'outer': None},
+                           'middle': None,
+                           'bottom': {'inner': None,
+                                      'outer': None}},
+                'right': {'top': {'inner': None,
+                                  'outer': None,
+                                  'u_border': None,
+                                  'v_border': None},
+                          'middle': {'inner': None,
+                                     'outer': None},
+                          'bottom': {'inner': None,
+                                     'outer': None,
+                                     'u_border': None,
+                                     'v_border': None}}}
+
+    def init_faces(self):
+        return {'left': {'top': {'square': None,
+                                 'u_pentagon': None,
+                                 'v_pentagon': None},
+                         'bottom': {'square': None,
+                                    'u_pentagon': None,
+                                    'v_pentagon': None},
+                         'middle': {'square': None}},
+                'center': {'top': {'square': None},
+                           'bottom': {'square': None}},
+                'right': {'top': {'square': None,
+                                  'u_pentagon': None,
+                                  'v_pentagon': None},
+                          'bottom': {'square': None,
+                                     'u_pentagon': None,
+                                     'v_pentagon': None},
+                          'middle': {'square': None}}}
+
+    def calculate_verts(self):
+        # a is the side length of square
+        # c is half diagonal of square
+        c = 1.0 / (sqrt(2.0) + 4.0)
+        a = sqrt(2.0) * c
+
+        # left top corner
+        self.add_vert(['left', 'top', 'inner'],
+                      a / 2.0 + c, 1.0 - (a / 2.0 + c))
+        self.add_vert(['left', 'top', 'outer'], a / 2.0, 1.0 - a / 2.0)
+        self.add_vert(['left', 'top', 'u_border'],
+                      0.0, 1.0 - a / 2.0, u_boundary=True)
+        self.add_vert(['left', 'top', 'v_border'],
+                      a / 2.0, 1.0, v_boundary=True)
+
+        self.add_vert(['left', 'middle', 'inner'], a / 2.0, 0.5)
+        self.add_vert(['left', 'middle', 'outer'], 0.0, 0.5, u_boundary=True)
+
+        self.add_vert(['center', 'top', 'inner'], 0.5, 1.0 - a / 2.0)
+        self.add_vert(['center', 'top', 'outer'], 0.5, 1.0, v_boundary=True)
+        self.add_vert(['center', 'middle'], 0.5, 0.5)
+
+    def calculate_faces(self):
+        # Middle star
+        self.add_face(['left', 'top', 'square'],
+                      [['left', 'top', 'v_border'],
+                       ['left', 'top', 'outer'],
+                       ['left', 'top', 'u_border'],
+                       left_tile(['right', 'top', 'outer']),
+                       left_tile(['right', 'top', 'v_border']),
+                       top_left_tile(['right', 'bottom', 'outer']),
+                       top_tile(['left', 'bottom', 'u_border']),
+                       top_tile(['left', 'bottom', 'outer'])],
+                      face_type='star',
+                      corner=True)
+
+        self.add_face(['left', 'top', 'u_pentagon'],
+                      [['left', 'top', 'u_border'],
+                       ['left', 'top', 'outer'],
+                       ['left', 'top', 'inner'],
+                       ['left', 'middle', 'inner'],
+                       ['left', 'middle', 'outer']])
+
+        self.add_face(['left', 'top', 'v_pentagon'],
+                      [['left', 'top', 'v_border'],
+                       ['center', 'top', 'outer'],
+                       ['center', 'top', 'inner'],
+                       ['left', 'top', 'inner'],
+                       ['left', 'top', 'outer']])
+
+        self.add_face(['center', 'top', 'square'],
+                      [['center', 'middle'],
+                       ['left', 'top', 'inner'],
+                       ['center', 'top', 'inner'],
+                       ['right', 'top', 'inner']])
+
+        self.add_face(['left', 'middle', 'square'],
+                      [['center', 'middle'],
+                       ['left', 'bottom', 'inner'],
+                       ['left', 'middle', 'inner'],
+                       ['left', 'top', 'inner']])
+
+    def color_pattern1(self):
+        self.color_face(['left', 'top', 'square'], 1)
+        self.color_face(['left', 'middle', 'square'], 1)
+        self.color_face(['center', 'top', 'square'], 1)
+        self.color_face(['right', 'middle', 'square'], 1)
+        self.color_face(['center', 'bottom', 'square'], 1)
+        self.color_face(['left', 'top', 'u_pentagon'], 0)
+        self.color_face(['left', 'top', 'v_pentagon'], 0)
+
+
+class CloverdaleTessagon(Tessagon):
+    tile_class = CloverdaleTile
+    metadata = metadata

add_mesh_extra_objects/tessagon/types/dissected_hex_quad_tessagon.py

@@ -0,0 +1,167 @@
+from math import sqrt
+from tessagon.core.tile import Tile
+from tessagon.core.tessagon import Tessagon
+from tessagon.core.tessagon_metadata import TessagonMetadata
+from tessagon.core.tile_utils import left_tile
+
+metadata = TessagonMetadata(name='Hexagons Dissected with Quads',
+                            num_color_patterns=2,
+                            classification='laves',
+                            shapes=['quads'],
+                            sides=[4],
+                            uv_ratio=1.0/sqrt(3.0))
+
+
+class DissectedHexQuadTile(Tile):
+    # 19 verts, 14 quad faces (10 internal, 4 on boundary)
+    #
+    #  O+++++++++++++++++++O+++++++++++++++++++O
+    #   +                  +                  +
+    #    +                 +                 +
+    #     +                +                +
+    #      +               +               +
+    #        +             +             +
+    #         +           +O+           +
+    #          +      ++       ++      +
+    #           +  ++             ++  +
+    #          ++O                   O++
+    #       ++    +                 +    ++
+    #   ++         ++             ++         ++
+    #  O             +           +             O
+    #  +              +         +              +
+    #  +               +       +               +
+    #  +                +     +                +
+    #  +                 +   +                 +
+    #  O+++++++++++++++++++O+++++++++++++++++++O
+    #  +                  + +                  +
+    #  +                 +   +                 +
+    #  +                +     +                +
+    #  +               +       +               +
+    #  +              +         +              +
+    #  O             +           +             O
+    #   ++         ++             ++         ++
+    #       ++    +                 +    ++
+    #          ++O                   O++
+    #           +  ++             ++  +
+    #          +      ++       ++      +
+    #         +           + +           +
+    #        +             O             +
+    #      +               +               +
+    #     +                +                +
+    #    +                 +                 +
+    #   +                  +                  +
+    #  O+++++++++++++++++++O+++++++++++++++++++O
+
+    def __init__(self, tessagon, **kwargs):
+        super().__init__(tessagon, **kwargs)
+        self.u_symmetric = True
+        self.v_symmetric = True
+
+    def init_verts(self):
+        return {'left': {'top': {'corner': None,
+                                 'interior': None,
+                                 'u_boundary': None},
+                         'middle': None,
+                         'bottom': {'corner': None,
+                                    'interior': None,
+                                    'u_boundary': None}},
+                'right': {'top': {'corner': None,
+                                  'interior': None,
+                                  'u_boundary': None},
+                          'middle': None,
+                          'bottom': {'corner': None,
+                                     'interior': None,
+                                     'u_boundary': None}},
+                'center': {'middle': None,
+                           'top': {'v_boundary': None,
+                                   'interior': None},
+                           'bottom': {'v_boundary': None,
+                                      'interior': None}}}
+
+    def init_faces(self):
+        return {'left': {'top': {'v_boundary': None,
+                                 'u_boundary': None,
+                                 'middle': None},
+                         'bottom': {'v_boundary': None,
+                                    'u_boundary': None,
+                                    'middle': None}},
+                'right': {'top': {'v_boundary': None,
+                                  'u_boundary': None,
+                                  'middle': None},
+                          'bottom': {'v_boundary': None,
+                                     'u_boundary': None,
+                                     'middle': None}},
+                'center': {'top': None,
+                           'bottom': None}}
+
+    def calculate_verts(self):
+        self.add_vert(['left', 'top', 'corner'], 0, 1, corner=True)
+        self.add_vert(['left', 'top', 'interior'], 0.25, 0.75)
+        self.add_vert(['left', 'top', 'u_boundary'], 0, 2.0/3.0,
+                      u_boundary=True)
+
+        self.add_vert(['left', 'middle'], 0, 0.5, u_boundary=True)
+
+        self.add_vert(['center', 'middle'], 0.5, 0.5)
+
+        self.add_vert(['center', 'top', 'v_boundary'], 0.5, 1.0,
+                      v_boundary=True)
+        self.add_vert(['center', 'top', 'interior'], 0.5, 5.0/6.0)
+
+    def calculate_faces(self):
+        self.add_face(['left', 'top', 'v_boundary'],
+                      [['left', 'top', 'corner'],
+                       ['center', 'top', 'v_boundary'],
+                       ['center', 'top', 'interior'],
+                       ['left', 'top', 'interior']])
+
+        self.add_face(['left', 'top', 'u_boundary'],
+                      [['left', 'top', 'corner'],
+                       ['left', 'top', 'interior'],
+                       ['left', 'top', 'u_boundary'],
+                       left_tile(['right', 'top', 'interior'])],
+                      u_boundary=True)
+
+        self.add_face(['left', 'top', 'middle'],
+                      [['left', 'top', 'interior'],
+                       ['center', 'middle'],
+                       ['left', 'middle'],
+                       ['left', 'top', 'u_boundary']])
+
+        self.add_face(['center', 'top'],
+                      [['center', 'middle'],
+                       ['left', 'top', 'interior'],
+                       ['center', 'top', 'interior'],
+                       ['right', 'top', 'interior']])
+
+    def color_pattern1(self):
+        self.color_paths([['left', 'top', 'middle'],
+                          ['center', 'top'],
+                          ['right', 'top', 'middle'],
+                          ['left', 'bottom', 'middle'],
+                          ['center', 'bottom'],
+                          ['right', 'bottom', 'middle']], 1, 0)
+
+    def color_pattern2(self):
+        if self.fingerprint[0] % 3 == 0:
+            self.color_paths([['left', 'top', 'middle'],
+                              ['center', 'top'],
+                              ['right', 'top', 'middle'],
+                              ['left', 'bottom', 'middle'],
+                              ['center', 'bottom'],
+                              ['right', 'bottom', 'middle']], 1, 0)
+        elif self.fingerprint[0] % 3 == 1:
+            self.color_paths([
+                ['right', 'top', 'v_boundary'],
+                ['right', 'bottom', 'v_boundary']], 1, 0)
+        elif self.fingerprint[0] % 3 == 2:
+            self.color_paths([
+                ['left', 'top', 'v_boundary'],
+                ['left', 'top', 'u_boundary'],
+                ['left', 'bottom', 'v_boundary'],
+                ['left', 'bottom', 'u_boundary']], 1, 0)
+
+
+class DissectedHexQuadTessagon(Tessagon):
+    tile_class = DissectedHexQuadTile
+    metadata = metadata

add_mesh_extra_objects/tessagon/types/dissected_hex_tri_tessagon.py

@@ -0,0 +1,135 @@
+from math import sqrt
+from tessagon.types.dissected_hex_quad_tessagon import DissectedHexQuadTile
+from tessagon.core.tessagon import Tessagon
+from tessagon.core.tessagon_metadata import TessagonMetadata
+
+metadata = TessagonMetadata(name='Hexagons Dissected with Triangles',
+                            num_color_patterns=1,
+                            classification='laves',
+                            shapes=['triangles'],
+                            sides=[3],
+                            uv_ratio=1.0/sqrt(3.0))
+
+
+# Uses the same configuration of vertices as DissectedHexQuadTile
+class DissectedHexTriTile(DissectedHexQuadTile):
+
+    # 19 verts, 24 internal triangle faces
+    #
+    #  O+++++++++++++++++++O+++++++++++++++++++O
+    #  ++ ++               +               ++ ++
+    #  + +    ++           +           ++    + +
+    #  +  +      ++        +        ++      +  +
+    #  +   +         +     +     +         +   +
+    #  +     +          ++ + ++          +     +
+    #  +      +           +O+           +      +
+    #  +       +      ++   +   ++      +       +
+    #  +        +  ++      +      ++  +        +
+    #  +       ++O         +         O++       +
+    #  +    ++    +        +        +    ++    +
+    #  +++         ++      +      ++         +++
+    #  O+            +     +     +            +O
+    #  +   ++         +    +    +         ++   +
+    #  +      ++       +   +   +       ++      +
+    #  +          ++    +  +  +    ++          +
+    #  +             ++  + + +  ++             +
+    #  +                 +++++                 +
+    #  O+++++++++++++++++++O+++++++++++++++++++O
+    #  +             ++  + + +  ++             +
+    #  +          ++    +  +  +    ++          +
+    #  +      ++       +   +   +       ++      +
+    #  +   ++         +    +    +         ++   +
+    #  ++            +     +     +            ++
+    #  O++         ++      +      ++         ++O
+    #  +    ++    +        +        +    ++    +
+    #  +       ++O         +         O++       +
+    #  +        +  +       +      ++  +        +
+    #  +       +      ++   +   ++      +       +
+    #  +      +           +O+           +      +
+    #  +     +          ++ + ++          +     +
+    #  +   +         +     +     +         +   +
+    #  +  +      ++        +        ++      +  +
+    #  + +    ++           +           ++    + +
+    #  ++ ++               +               ++ ++
+    #  O+++++++++++++++++++++++++++++++++++++++O
+
+    def init_faces(self):
+        return {'left': {'top': {'v_boundary': None,
+                                 'u_boundary': None,
+                                 'middle': None,
+                                 'center': None,
+                                 'interior1': None,  # Touches corner
+                                 'interior2': None},
+                         'bottom': {'v_boundary': None,
+                                    'u_boundary': None,
+                                    'middle': None,
+                                    'center': None,
+                                    'interior1': None,
+                                    'interior2': None}},
+                'right': {'top': {'v_boundary': None,
+                                  'u_boundary': None,
+                                  'middle': None,
+                                  'center': None,
+                                  'interior1': None,
+                                  'interior2': None},
+                          'bottom': {'v_boundary': None,
+                                     'u_boundary': None,
+                                     'middle': None,
+                                     'center': None,
+                                     'interior1': None,
+                                     'interior2': None}}}
+
+    def calculate_faces(self):
+        self.add_face(['left', 'top', 'v_boundary'],
+                      [['left', 'top', 'corner'],
+                       ['center', 'top', 'v_boundary'],
+                       ['center', 'top', 'interior']])
+
+        self.add_face(['left', 'top', 'interior1'],
+                      [['left', 'top', 'corner'],
+                       ['center', 'top', 'interior'],
+                       ['left', 'top', 'interior']])
+
+        self.add_face(['left', 'top', 'u_boundary'],
+                      [['left', 'top', 'corner'],
+                       ['left', 'top', 'interior'],
+                       ['left', 'top', 'u_boundary']])
+
+        self.add_face(['left', 'top', 'middle'],
+                      [['center', 'middle'],
+                       ['left', 'middle'],
+                       ['left', 'top', 'u_boundary']])
+
+        self.add_face(['left', 'top', 'interior2'],
+                      [['left', 'top', 'interior'],
+                       ['center', 'middle'],
+                       ['left', 'top', 'u_boundary']])
+
+        self.add_face(['left', 'top', 'center'],
+                      [['center', 'middle'],
+                       ['left', 'top', 'interior'],
+                       ['center', 'top', 'interior']])
+
+    def color_pattern1(self):
+        self.color_paths([
+            ['left', 'top', 'v_boundary'],
+            ['left', 'top', 'u_boundary'],
+            ['left', 'top', 'middle'],
+            ['left', 'top', 'center'],
+
+            ['right', 'top', 'interior1'],
+            ['right', 'top', 'interior2'],
+
+            ['right', 'bottom', 'v_boundary'],
+            ['right', 'bottom', 'u_boundary'],
+            ['right', 'bottom', 'middle'],
+            ['right', 'bottom', 'center'],
+
+            ['left', 'bottom', 'interior1'],
+            ['left', 'bottom', 'interior2'],
+        ], 1, 0)
+
+
+class DissectedHexTriTessagon(Tessagon):
+    tile_class = DissectedHexTriTile
+    metadata = metadata

add_mesh_extra_objects/tessagon/types/dissected_square_tessagon.py

@@ -0,0 +1,112 @@
+from tessagon.core.tessagon import Tessagon
+from tessagon.core.tile import Tile
+from tessagon.core.tessagon_metadata import TessagonMetadata
+
+metadata = TessagonMetadata(name='Dissected Square',
+                            num_color_patterns=2,
+                            classification='laves',
+                            shapes=['triangles'],
+                            sides=[3],
+                            uv_ratio=1.0)
+
+
+class DissectedSquareTile(Tile):
+
+    #    VERTS:     a = ['top', 'left']
+    #    a---b---c  b = ['top', 'center']
+    # ^  |\..|../|  c = ['top', 'right']
+    # |  |.\.|./.|  d = ['middle', 'left']
+    # |  d---e---f  e = ['middle', 'center']
+    # |  |../|\..|  f = ['middle', 'right']
+    #    |./.|.\.|  g = ['bottom', 'left']
+    # V  g---h---i  h = ['bottom', 'center']
+    #               i = ['bottom', 'right']
+    #     U --->
+
+    #    FACES:
+    #    o---o---o  A = ['top', 'left', 'middle']
+    # ^  |\.B|C./|  B = ['top', 'left', 'center']
+    # |  |A\.|./D|  C = ['top', 'right', 'center']
+    # |  o---o---o  D = ['top', 'right', 'middle']
+    # |  |E./|\.H|  E = ['bottom', 'left', 'middle']
+    #    |./F|G\.|  F = ['bottom', 'left', 'center']
+    # V  o-------o  G = ['bottom', 'right', 'center']
+    #               H = ['bottom', 'right', 'middle']
+    #     U --->
+
+    def __init__(self, tessagon, **kwargs):
+        super().__init__(tessagon, **kwargs)
+        self.u_symmetric = True
+        self.v_symmetric = True
+
+    def init_verts(self):
+        return {'top': {'left': None,
+                        'center': None,
+                        'right': None},
+                'middle': {'left': None,
+                           'center': None,
+                           'right': None},
+                'bottom': {'left': None,
+                           'center': None,
+                           'right': None}}
+
+    def init_faces(self):
+        return {'top': {'left': {'middle': None, 'center': None},
+                        'right': {'middle': None, 'center': None}},
+                'bottom': {'left': {'middle': None, 'center': None},
+                           'right': {'middle': None, 'center': None}}}
+
+    def calculate_verts(self):
+        # Symmetry allow you to get nine verts for the price of four.
+        self.add_vert(['top', 'left'], 0, 1.0, corner=True)
+        self.add_vert(['middle', 'left'], 0, 0.5, u_boundary=True)
+        self.add_vert(['top', 'center'], 0.5, 1.0, v_boundary=True)
+        self.add_vert(['middle', 'center'], 0.5, 0.5)
+
+    def calculate_faces(self):
+        # Symmetry allows you to create eight faces for the price of two
+        self.add_face(['top', 'left', 'middle'],
+                      [['top', 'left'],
+                       ['middle', 'left'],
+                       ['middle', 'center']])
+        self.add_face(['top', 'left', 'center'],
+                      [['top', 'left'],
+                       ['middle', 'center'],
+                       ['top', 'center']])
+
+    def color_pattern1(self):
+        self.color_paths([['top', 'left', 'center'],
+                          ['top', 'right', 'middle'],
+                          ['bottom', 'right', 'center'],
+                          ['bottom', 'left', 'middle']], 1, 0)
+
+    def color_pattern2(self):
+        if (self.fingerprint[0] // 2 + self.fingerprint[1] // 2) % 2 == 0:
+            self.color_tiles(1, 0)
+        else:
+            self.color_tiles(0, 1)
+
+    def color_tiles(self, color1, color2):
+        if self.fingerprint[0] % 2 == 0:
+            if self.fingerprint[1] % 2 == 0:
+                self.color_paths([['top', 'left', 'center'],
+                                  ['bottom', 'right', 'middle']],
+                                 color2, color1)
+            else:
+                self.color_paths([['bottom', 'left', 'center'],
+                                  ['top', 'right', 'middle']],
+                                 color2, color1)
+        else:
+            if self.fingerprint[1] % 2 == 0:
+                self.color_paths([['top', 'right', 'center'],
+                                  ['bottom', 'left', 'middle']],
+                                 color2, color1)
+            else:
+                self.color_paths([['bottom', 'right', 'center'],
+                                  ['top', 'left', 'middle']],
+                                 color2, color1)
+
+
+class DissectedSquareTessagon(Tessagon):
+    tile_class = DissectedSquareTile
+    metadata = metadata

add_mesh_extra_objects/tessagon/types/dissected_triangle_tessagon.py

@@ -0,0 +1,130 @@
+from math import sqrt
+from tessagon.core.tile import Tile
+from tessagon.core.tessagon import Tessagon
+from tessagon.core.tessagon_metadata import TessagonMetadata
+from tessagon.core.tile_utils import top_tile
+
+metadata = TessagonMetadata(name='Dissected Triangle',
+                            num_color_patterns=1,
+                            classification='laves',
+                            shapes=['triangles'],
+                            sides=[3],
+                            uv_ratio=sqrt(3.0))
+
+
+class DissectedTriangleTile(Tile):
+    #     11 verts:
+    #
+    #     O++++++++++++O      +      O++++++++++++O
+    #     ++ ++         ++    +    ++         ++ ++
+    #     + +   +++       +   +   +       +++   + +
+    #     +  +      ++     +  +  +     ++      +  +
+    #     +   +        ++   + + +   ++        +   +
+    #     +    O++++++++++++++O++++++++++++++O    +
+    #     +   +        ++   + + +   ++        +   +
+    #     +  +      ++     +  +  +     ++      +  +
+    #     + +   +++       +   +   +       +++   + +
+    #     ++ ++         ++    +    ++         ++ ++
+    #     O++++++++++++O      +      O++++++++++++O
+    #
+    #     14 faces (10 internal, 4 on boundary)
+    #
+    #     O++++++++++++O      +      O++++++++++++O
+    #     ++ ++         ++    +    ++         ++ ++
+    #     + +   +++  3    + 4 + 5 +  6    +++   + +
+    #     +  +  2   ++     +  +  +     ++   7  +  +
+    #     +   +        ++   + + +   ++        +   +
+    #     + 1  O++++++++++++++O++++++++++++++O  8 +
+    #     +   +        ++   + + +   ++        +   +
+    #     +  +   9  ++     +  +  +     ++  14  +  +
+    #     + +   +++  10   +   +   +  13   +++   + +
+    #     ++ ++         ++    +    ++         ++ ++
+    #     O++++++++++++O   11 + 12   O++++++++++++O
+
+    def __init__(self, tessagon, **kwargs):
+        super().__init__(tessagon, **kwargs)
+        self.u_symmetric = True
+        self.v_symmetric = True
+
+    def init_verts(self):
+        return {'left': {'top': {'corner': None,
+                                 'v_boundary': None},
+                         'middle': None,
+                         'bottom': {'corner': None,
+                                    'v_boundary': None}},
+                'right': {'top': {'corner': None,
+                                  'v_boundary': None},
+                          'middle': None,
+                          'bottom': {'corner': None,
+                                     'v_boundary': None}},
+                'center': None}
+
+    def init_faces(self):
+        return {'left': {'top': {'center': None,
+                                 'interior1': None,  # closest to center
+                                 'interior2': None},
+                         'middle': None,
+                         'bottom': {'center': None,
+                                    'interior1': None,  # closest to center
+                                    'interior2': None}},
+                'right': {'top': {'center': None,
+                                  'interior1': None,  # closest to center
+                                  'interior2': None},
+                          'middle': None,
+                          'bottom': {'center': None,
+                                     'interior1': None,  # closest to center
+                                     'interior2': None}}}
+
+    def calculate_verts(self):
+        # Four corners, via symmetry
+        self.add_vert(['left', 'top', 'corner'], 0, 1, corner=True)
+        # The center vert
+        self.add_vert('center', 0.5, 0.5)
+        # Vert on boundary
+        self.add_vert(['left', 'top', 'v_boundary'], 1.0/3.0, 1,
+                      v_boundary=True)
+        # Interior vert
+        self.add_vert(['left', 'middle'], 1.0/6.0, 0.5)
+
+    def calculate_faces(self):
+        self.add_face(['left', 'middle'],
+                      [['left', 'middle'],
+                       ['left', 'top', 'corner'],
+                       ['left', 'bottom', 'corner']])
+
+        self.add_face(['left', 'top', 'center'],
+                      [['center'],
+                       ['left', 'top', 'v_boundary'],
+                       top_tile(['center'])], v_boundary=True)
+
+        self.add_face(['left', 'top', 'interior1'],
+                      [['center'],
+                       ['left', 'top', 'v_boundary'],
+                       ['left', 'top', 'corner']])
+
+        self.add_face(['left', 'top', 'interior2'],
+                      [['center'],
+                       ['left', 'middle'],
+                       ['left', 'top', 'corner']])
+
+    def color_pattern1(self):
+        if self.fingerprint[1] % 3 == 0:
+            self.color_paths([['left', 'middle'],
+                              ['right', 'middle']], 1, 0)
+        elif self.fingerprint[1] % 3 == 2:
+            self.color_paths([['left', 'top', 'interior2'],
+                              ['right', 'top', 'interior2'],
+                              ['left', 'top', 'interior1'],
+                              ['right', 'top', 'interior1']], 1, 0)
+            self.color_paths([['left', 'bottom', 'center'],
+                              ['right', 'bottom', 'center']], 1, 0)
+        else:
+            self.color_paths([['left', 'bottom', 'interior2'],
+                              ['right', 'bottom', 'interior2'],
+                              ['left', 'bottom', 'interior1'],
+                              ['right', 'bottom', 'interior1']], 1, 0)
+
+
+class DissectedTriangleTessagon(Tessagon):
+    tile_class = DissectedTriangleTile
+    metadata = metadata

add_mesh_extra_objects/tessagon/types/dodeca_tessagon.py

@@ -0,0 +1,208 @@
+from math import sqrt
+from tessagon.core.tile import Tile
+from tessagon.core.tessagon import Tessagon
+from tessagon.core.tessagon_metadata import TessagonMetadata
+from tessagon.core.tile_utils import top_tile, left_tile, left_top_tile
+
+# Will my brain survive this one?
+
+metadata = TessagonMetadata(name='Dodecagons, Hexagons, and Squares',
+                            num_color_patterns=1,
+                            classification='archimedean',
+                            shapes=['dodecagons', 'hexagons', 'squares'],
+                            sides=[12, 6, 4],
+                            uv_ratio=1.0/sqrt(3.0))
+
+
+class DodecaTile(Tile):
+    # 24 verts, 19 faces (7 internal, 12 on boundary)
+    # The angles make it hard to draw all edges, some excluded
+
+    #     .......|.4.|.......
+    #     .      o---o      .
+    #     .  12 /     \  12 .
+    #     .    o   6   o    .
+    #     --o ..\     /.. o--
+    #     .  \.4.o---o.4./  .
+    #  ^  . 6 o         o 6 .
+    #  |  .  /           \  .
+    #  |  --o             o--
+    #  |  .4|      12     |4. Number is verts in face
+    #  |  --o             o--
+    #     .  \           /  .
+    #  V  . 6 o         o 6 .
+    #     .  /...o---o...\  .
+    #     --o.4./     \.4.o--
+    #     .    o   6   o    .
+    #     .     \     /     .
+    #     .  12  o---o  12  .
+    #     .......|.4.|.......
+    #
+    #            U ---->
+
+    def __init__(self, tessagon, **kwargs):
+        super().__init__(tessagon, **kwargs)
+        self.u_symmetric = True
+        self.v_symmetric = True
+
+    def init_verts(self):
+        # u_square means on the square that is on the U-boundary
+        return {'top': {'left': {'u_square': None,
+                                 'v_square': None,
+                                 # Inner square, sort v-distance from middle
+                                 'sq1': None,
+                                 'sq2': None,
+                                 'sq3': None,
+                                 'sq4': None},
+                        'right': {'u_square': None,
+                                  'v_square': None,
+                                  'sq1': None,
+                                  'sq2': None,
+                                  'sq3': None,
+                                  'sq4': None}},
+                'bottom': {'left': {'u_square': None,
+                                    'v_square': None,
+                                    'sq1': None,
+                                    'sq2': None,
+                                    'sq3': None,
+                                    'sq4': None},
+                           'right': {'u_square': None,
+                                     'v_square': None,
+                                     'sq1': None,
+                                     'sq2': None,
+                                     'sq3': None,
+                                     'sq4': None}}}
+
+    def init_faces(self):
+        return {'dodec': {'top': {'left': None,
+                                  'right': None},
+                          'bottom': {'left': None,
+                                     'right': None},
+                          'middle': None},
+                'hex': {'top': {'left': None,
+                                'center': None,
+                                'right': None},
+                        'bottom': {'left': None,
+                                   'center': None,
+                                   'right': None}},
+                'square': {'top': {'left': None,
+                                   'center': None,
+                                   'right': None},
+                           'bottom': {'left': None,
+                                      'center': None,
+                                      'right': None},
+                           'middle': {'left': None,
+                                      'right': None}}}
+
+    def calculate_verts(self):
+        # u_unit is the length of the edges expressed as a
+        # proportion of the tile
+        u_unit = 1.0 / (3.0 + sqrt(3))
+        u_h = 0.5*sqrt(3)*u_unit  # height of triangle of side u_unit
+
+        u1 = 0.5*u_unit
+        u2 = 0.5 - u1 - u_h
+        u3 = 0.5 - u_unit
+        u4 = 0.5 - u1
+
+        v_unit = 1.0 / (3.0*(1.0 + sqrt(3)))
+        v_h = 0.5*sqrt(3)*v_unit  # height of triangle of side v_unit
+        v1 = 1.0 - 0.5*v_unit
+        v2 = v1 - v_h
+        v3 = 0.5 + 2*v_h + 0.5*v_unit
+        v4 = 0.5 + v_h + v_unit
+        v5 = 0.5 + v_h + 0.5*v_unit
+        v6 = 0.5 + 0.5*v_unit
+
+        # Define top left region, other verts defined through symmetry
+        self.add_vert(['top', 'left', 'v_square'], u4, v1)
+        self.add_vert(['top', 'left', 'u_square'], u1, v6)
+        self.add_vert(['top', 'left', 'sq1'], u2, v5)
+        self.add_vert(['top', 'left', 'sq2'], u4, v4)
+        self.add_vert(['top', 'left', 'sq3'], u1, v3)
+        self.add_vert(['top', 'left', 'sq4'], u3, v2)
+
+    def calculate_faces(self):
+        # Top left Dodecagon
+        self.add_face(['dodec', 'top', 'left'],
+                      [['top', 'left', 'v_square'],
+                       ['top', 'left', 'sq4'],
+                       ['top', 'left', 'sq3'],
+                       left_tile(['top', 'right', 'sq3']),
+                       left_tile(['top', 'right', 'sq4']),
+                       left_tile(['top', 'right', 'v_square']),
+                       left_top_tile(['bottom', 'right', 'v_square']),
+                       left_top_tile(['bottom', 'right', 'sq4']),
+                       left_top_tile(['bottom', 'right', 'sq3']),
+                       top_tile(['bottom', 'left', 'sq3']),
+                       top_tile(['bottom', 'left', 'sq4']),
+                       top_tile(['bottom', 'left', 'v_square'])],
+                      face_type='dodecagon', corner=True)
+        # Middle Dodecagon
+        self.add_face(['dodec', 'middle'],
+                      [['top', 'left', 'u_square'],
+                       ['top', 'left', 'sq1'],
+                       ['top', 'left', 'sq2'],
+                       ['top', 'right', 'sq2'],
+                       ['top', 'right', 'sq1'],
+                       ['top', 'right', 'u_square'],
+                       ['bottom', 'right', 'u_square'],
+                       ['bottom', 'right', 'sq1'],
+                       ['bottom', 'right', 'sq2'],
+                       ['bottom', 'left', 'sq2'],
+                       ['bottom', 'left', 'sq1'],
+                       ['bottom', 'left', 'u_square']],
+                      face_type='dodecagon')
+        # Upper square
+        self.add_face(['square', 'top', 'center'],
+                      [['top', 'left', 'v_square'],
+                       ['top', 'right', 'v_square'],
+                       top_tile(['bottom', 'right', 'v_square']),
+                       top_tile(['bottom', 'left', 'v_square'])],
+                      face_type='square', v_boundary=True)
+        # Left square
+        self.add_face(['square', 'middle', 'left'],
+                      [['top', 'left', 'u_square'],
+                       ['bottom', 'left', 'u_square'],
+                       left_tile(['bottom', 'right', 'u_square']),
+                       left_tile(['top', 'right', 'u_square'])],
+                      face_type='square', u_boundary=True)
+        # Interior square
+        self.add_face(['square', 'top', 'left'],
+                      [['top', 'left', 'sq1'],
+                       ['top', 'left', 'sq2'],
+                       ['top', 'left', 'sq4'],
+                       ['top', 'left', 'sq3']],
+                      face_type='square')
+        # Top Hex
+        self.add_face(['hex', 'top', 'center'],
+                      [['top', 'left', 'sq2'],
+                       ['top', 'left', 'sq4'],
+                       ['top', 'left', 'v_square'],
+                       ['top', 'right', 'v_square'],
+                       ['top', 'right', 'sq4'],
+                       ['top', 'right', 'sq2']],
+                      face_type='hexagon')
+        # Left Hex
+        self.add_face(['hex', 'top', 'left'],
+                      [['top', 'left', 'sq3'],
+                       ['top', 'left', 'sq1'],
+                       ['top', 'left', 'u_square'],
+                       left_tile(['top', 'right', 'u_square']),
+                       left_tile(['top', 'right', 'sq1']),
+                       left_tile(['top', 'right', 'sq3'])],
+                      face_type='hexagon', u_boundary=True)
+
+    def color_pattern1(self):
+        self.color_face(['dodec', 'middle'], 1)
+        self.color_face(['dodec', 'top', 'left'], 1)
+
+        self.color_face(['hex', 'top', 'left'], 2)
+        self.color_face(['hex', 'top', 'center'], 2)
+        self.color_face(['hex', 'bottom', 'left'], 2)
+        self.color_face(['hex', 'bottom', 'center'], 2)
+
+
+class DodecaTessagon(Tessagon):
+    tile_class = DodecaTile
+    metadata = metadata

add_mesh_extra_objects/tessagon/types/dodeca_tri_tessagon.py

@@ -0,0 +1,145 @@
+from math import sqrt
+from tessagon.core.tile import Tile
+from tessagon.core.tessagon import Tessagon
+from tessagon.core.tessagon_metadata import TessagonMetadata
+from tessagon.core.tile_utils import bottom_tile, left_tile, bottom_left_tile
+
+metadata = TessagonMetadata(name='Dodecagons and Triangles',
+                            num_color_patterns=1,
+                            classification='archimedean',
+                            shapes=['dodecagons', 'triangles'],
+                            sides=[12, 3],
+                            uv_ratio=sqrt(3.0))
+
+
+class DodecaTriTile(Tile):
+    # 14 verts, 11 faces (3 internal, 8 on boundary)
+    # The angles make it hard to draw all edges, some excluded
+
+    #     . ....|3.o---o.3|......
+    #  ^  .     o         o     .
+    #  |  . 12 /           \ 12 .
+    #  |  .   o             o   .
+    #  |  .-o3|      12     |3o-. Number is verts in face
+    #  |  .   o             o   .
+    #     .    \           /    .
+    #  V  . 12  o         o 12  .
+    #     . ....|3.o---o.3|......
+    #
+    #            U ---->
+
+    def __init__(self, tessagon, **kwargs):
+        super().__init__(tessagon, **kwargs)
+        self.u_symmetric = True
+        self.v_symmetric = True
+
+    def init_verts(self):
+        # u_square means on the square that is on the U-boundary
+        return {'left': {'top': {'v_boundary': None,
+                                 'diag': None,
+                                 'tri': None},  # on the triangle
+                         'middle': None,
+                         'bottom': {'v_boundary': None,
+                                    'diag': None,
+                                    'tri': None}},
+                'right': {'top': {'v_boundary': None,
+                                  'diag': None,
+                                  'tri': None},  # on the triangle
+                          'middle': None,
+                          'bottom': {'v_boundary': None,
+                                     'diag': None,
+                                     'tri': None}}}
+
+    def init_faces(self):
+        return {'dodec': {'left': {'top': None,
+                                   'bottom': None},
+                          'right': {'top': None,
+                                    'bottom': None},
+                          'center': None},
+                'tri': {'left': {'top': None,
+                                 'middle': None,
+                                 'bottom': None},
+                        'right': {'top': None,
+                                  'middle': None,
+                                  'bottom': None}}}
+
+    def calculate_verts(self):
+        # u_unit is the length of the edges expressed as a
+        # proportion of the tile
+        u_unit = 1.0 / (3.0 + 2.0 * sqrt(3))
+        u_h = 0.5*sqrt(3)*u_unit  # height of triangle of side u_unit
+
+        u1 = 0.5*u_unit
+        u2 = u1 + u_h
+        u3 = u2 + u1
+        u4 = u3 + u_h
+
+        v_unit = 1.0 / (2.0 + sqrt(3))
+        v_h = 0.5*sqrt(3)*v_unit  # height of triangle of side v_unit
+        v1 = 0
+        v2 = 0.5 * v_unit
+        v3 = v2 + v_h
+        v4 = 0.5
+
+        # Sweet symmetry makes this easy work
+        self.add_vert(['left', 'middle'], u1, v4)  # 2 verts added
+        self.add_vert(['left', 'bottom', 'v_boundary'], u4, v1,
+                      v_boundary=True)  # 4 verts
+        self.add_vert(['left', 'bottom', 'diag'], u3, v2)  # 4 verts
+        self.add_vert(['left', 'bottom', 'tri'], u2, v3)  # 4 verts
+
+    def calculate_faces(self):
+        # Top left Dodecagon
+        self.add_face(['dodec', 'left', 'bottom'],
+                      [['left', 'middle'],
+                       ['left', 'bottom', 'tri'],
+                       ['left', 'bottom', 'diag'],
+                       bottom_tile(['left', 'top', 'diag']),
+                       bottom_tile(['left', 'top', 'tri']),
+                       bottom_tile(['left', 'middle']),
+                       bottom_left_tile(['right', 'middle']),
+                       bottom_left_tile(['right', 'top', 'tri']),
+                       bottom_left_tile(['right', 'top', 'diag']),
+                       left_tile(['right', 'bottom', 'diag']),
+                       left_tile(['right', 'bottom', 'tri']),
+                       left_tile(['right', 'middle'])],
+                      face_type='dodecagon', corner=True)
+
+        # Middle Dodecagon
+        self.add_face(['dodec', 'center'],
+                      [['left', 'bottom', 'tri'],
+                       ['left', 'bottom', 'diag'],
+                       ['left', 'bottom', 'v_boundary'],
+                       ['right', 'bottom', 'v_boundary'],
+                       ['right', 'bottom', 'diag'],
+                       ['right', 'bottom', 'tri'],
+                       ['right', 'top', 'tri'],
+                       ['right', 'top', 'diag'],
+                       ['right', 'top', 'v_boundary'],
+                       ['left', 'top', 'v_boundary'],
+                       ['left', 'top', 'diag'],
+                       ['left', 'top', 'tri']],
+                      face_type='dodecagon')
+
+        # Left triangle
+        self.add_face(['tri', 'left', 'middle'],
+                      [['left', 'top', 'tri'],
+                       ['left', 'bottom', 'tri'],
+                       ['left', 'middle']],
+                      face_type='triangle')
+
+        # bottom-left triangle
+        self.add_face(['tri', 'left', 'bottom'],
+                      [['left', 'bottom', 'diag'],
+                       ['left', 'bottom', 'v_boundary'],
+                       bottom_tile(['left', 'top', 'diag'])],
+                      face_type='triangle', v_boundary=True)
+
+    def color_pattern1(self):
+        self.color_paths([['dodec', 'left', 'bottom'],
+                          ['dodec', 'center']], 1, 0)
+
+
+class DodecaTriTessagon(Tessagon):
+    tile_class = DodecaTriTile
+    metadata = metadata

add_mesh_extra_objects/tessagon/types/floret_tessagon.py

@@ -0,0 +1,192 @@
+from math import atan2, sqrt, sin, cos, pi
+from tessagon.core.tessagon import Tessagon
+from tessagon.core.alternating_tile import AlternatingTile
+from tessagon.core.tessagon_metadata import TessagonMetadata
+from tessagon.core.tile_utils import right_tile, left_tile, \
+    top_tile, top_left_tile, top_right_tile, \
+    bottom_tile, bottom_right_tile
+
+metadata = TessagonMetadata(name='Florets',
+                            num_color_patterns=3,
+                            classification='laves',
+                            shapes=['pentagons'],
+                            sides=[5],
+                            uv_ratio=1.0/sqrt(3))
+
+
+class FloretTile(AlternatingTile):
+    #  See the SVG for decomposition:
+    # https://raw.githubusercontent.com/cwant/tessagon/master/documentation/code/floret.svg
+
+    def __init__(self, tessagon, **kwargs):
+        super().__init__(tessagon, **kwargs)
+        self.u_symmetric = False
+        self.v_symmetric = False
+
+        # multiplier to get v units ...
+        self.uv_ratio = self.tessagon.metadata.uv_ratio
+
+        # Tilt
+        theta_offset1 = pi/3 - atan2(sqrt(3), 9)
+        theta_offset2 = pi/6
+
+        # No hexagons in this pattern, but verts lie of hexagons
+        # radius is in u inits
+        self.hexagons = [
+            {'radius': 4 / sqrt(21),
+             'hex_theta': [(theta_offset1 + number * pi / 3.0)
+                           for number in range(6)]},
+            # Just guessing ...
+            {'radius': 2 / (3 * self.uv_ratio),
+             'hex_theta': [(theta_offset2 + number * pi / 3.0)
+                           for number in range(6)]},
+        ]
+
+    def hex_vert_coord(self, hexagon_num, center, number):
+        # hexagon_num in range(2)
+        # number in range(6)
+        hexagon = self.hexagons[hexagon_num]
+        return [center[0] +
+                hexagon['radius'] * cos(hexagon['hex_theta'][number]),
+                center[1] +
+                hexagon['radius'] * sin(hexagon['hex_theta'][number]) *
+                self.uv_ratio]
+
+    def init_verts(self):
+        if self.tile_type == 0:
+            verts = {i: None for i in range(6)}
+        else:
+            verts = {i: None for i in range(6, 14)}
+
+        return verts
+
+    def init_faces(self):
+        if self.tile_type == 0:
+            faces = {c: None for c in ['A', 'B', 'C', 'D']}
+        else:
+            faces = {c: None for c in ['E', 'F', 'G', 'H', 'I', 'J', 'K', 'L']}
+
+        return faces
+
+    def calculate_verts(self):
+        if self.tile_type == 0:
+            self.add_vert([2], *self.hex_vert_coord(0, [0, 0], 0))
+            self.add_vert([3], *self.hex_vert_coord(0, [1, 1], 3))
+        else:
+            self.add_vert([6], 1, 0,
+                          equivalent=[right_tile(0),
+                                      bottom_right_tile(13),
+                                      bottom_tile(5)])
+            self.add_vert([7], *self.hex_vert_coord(0, [1, 0], 2))
+            self.add_vert([8], *self.hex_vert_coord(1, [0, 1], 4),
+                          equivalent=[left_tile(1)])
+            self.add_vert([9], *self.hex_vert_coord(0, [0, 1], 4))
+            self.add_vert([10], *self.hex_vert_coord(0, [1, 0], 1))
+            self.add_vert([11], *self.hex_vert_coord(1, [0, 1], 5),
+                          equivalent=[right_tile(4)])
+            self.add_vert([12], *self.hex_vert_coord(0, [0, 1], 5))
+            self.add_vert([13], 0, 1,
+                          equivalent=[left_tile(5),
+                                      top_left_tile(6),
+                                      top_tile(0)])
+
+    def calculate_faces(self):
+        # All of tile type 0 faces overlap tiles of type 1
+        if self.tile_type == 0:
+            return
+
+        # Tile 'E' is handled as Tile 'K' on another tile
+        # Tile 'F' is handled as Tile 'L' on another tile
+        self.add_face('G', [6,
+                            10,
+                            9,
+                            8,
+                            7])
+
+        self.add_face('H', [11,
+                            10,
+                            6,
+                            right_tile(2),
+                            right_tile(3)],
+                      equivalent=[right_tile('B')])
+
+        self.add_face('I', [8,
+                            9,
+                            13,
+                            left_tile(3),
+                            left_tile(2)],
+                      equivalent=[left_tile('C')])
+
+        self.add_face('J', [13,
+                            9,
+                            10,
+                            11,
+                            12])
+
+        self.add_face('K', [12,
+                            11,
+                            right_tile(3),
+                            right_tile(5),
+                            top_right_tile(7)],
+                      equivalent=[right_tile('D'),
+                                  top_right_tile('E')])
+
+        self.add_face('L', [13,
+                            12,
+                            top_right_tile(7),
+                            top_tile(1),
+                            top_tile(2)],
+                      equivalent=[top_right_tile('F'),
+                                  top_tile('A')])
+
+    def floret_fingerprint(self, face):
+        fingerprint = list(self.fingerprint.copy())
+
+        fingerprint[0] = fingerprint[0] // 2 + fingerprint[1] // 2
+
+        if face in ['F']:
+            fingerprint[0] -= 1
+        elif face in ['K']:
+            fingerprint[0] += 1
+
+        if self.fingerprint[0] % 2 == 0:
+            if face in ['A', 'B']:
+                fingerprint[0] -= 1
+        else:
+            if face in ['C', 'D']:
+                fingerprint[0] += 1
+
+        if face in ['A', 'B', 'E', 'F', 'G', 'H']:
+            fingerprint[1] -= 1
+
+        return fingerprint
+
+    def color_pattern1(self):
+        pattern = [0, 0, 1]
+
+        for face in self.faces:
+            fingerprint = self.floret_fingerprint(face)
+            offset = (fingerprint[0] + fingerprint[1]) % 3
+            self.color_face(face, pattern[offset])
+
+    def color_pattern2(self):
+        for face in self.faces:
+            fingerprint = self.floret_fingerprint(face)
+            color = (fingerprint[0] + fingerprint[1]) % 3
+            self.color_face(face, color)
+
+    def color_pattern3(self):
+        # Follow a straight line in the pattern to see this ...
+        pattern = [[2, 0, 2, 2, 0, 2],
+                   [2, 1, 2, 0, 0, 0]]
+
+        for face in self.faces:
+            fingerprint = self.floret_fingerprint(face)
+            row = fingerprint[1] % 2
+            column = (fingerprint[0] - 2 * fingerprint[1]) % 6
+            self.color_face(face, pattern[row][column])
+
+
+class FloretTessagon(Tessagon):
+    tile_class = FloretTile
+    metadata = metadata

add_mesh_extra_objects/tessagon/types/hex_big_tri_tessagon.py

@@ -0,0 +1,132 @@
+from math import sqrt, atan2, sin, cos, pi
+from tessagon.core.tessagon import Tessagon
+from tessagon.core.alternating_tile import AlternatingTile
+from tessagon.core.tessagon_metadata import TessagonMetadata
+from tessagon.core.tile_utils import \
+    left_tile, top_tile, top_left_tile, \
+    right_tile, bottom_tile
+
+metadata = TessagonMetadata(name='Hexagons and Big Triangles',
+                            num_color_patterns=2,
+                            classification='non_edge',
+                            shapes=['hexagons', 'triangles'],
+                            sides=[6, 3],
+                            uv_ratio=1.0/sqrt(3.0))
+
+
+class HexBigTriTile(AlternatingTile):
+    def __init__(self, tessagon, **kwargs):
+        super().__init__(tessagon, **kwargs)
+
+        self.u_symmetric = False
+        self.v_symmetric = False
+
+        # Future use to control hexagon size?
+        self.hexagon_ratio = 0.5
+
+        # in u units
+        self.hex_radius = 4 * self.hexagon_ratio / sqrt(7)
+        # multiplier to get v units ...
+        self.uv_ratio = self.tessagon.metadata.uv_ratio
+
+        # Tilt
+        self.theta_offset = -atan2(1, 3 * sqrt(3)) + pi/6
+        self.hex_theta = [(self.theta_offset + number * pi / 3.0)
+                          for number in range(6)]
+
+    def hex_vert_coord(self, center, number):
+        # number in range(6)
+        return [center[0] +
+                self.hex_radius * cos(self.hex_theta[number]),
+                center[1] +
+                self.hex_radius * sin(self.hex_theta[number]) * self.uv_ratio]
+
+    def init_verts(self):
+        if self.tile_type == 0:
+            verts = {0: None,
+                     1: None}
+        else:
+            verts = {2: None,
+                     3: None,
+                     4: None,
+                     5: None}
+
+        return verts
+
+    def init_faces(self):
+        if self.tile_type == 0:
+            faces = {'A': None,
+                     'B': None,
+                     'C': None,
+                     'D': None}
+        else:
+            faces = {'E': None,
+                     'F': None,
+                     'G': None,
+                     'H': None,
+                     'I': None,
+                     'J': None}
+
+        return faces
+
+    def calculate_verts(self):
+        if self.tile_type == 0:
+            self.add_vert([0], *self.hex_vert_coord([0, 1], 5))
+            self.add_vert([1], *self.hex_vert_coord([1, 0], 2))
+        else:
+            self.add_vert([2], *self.hex_vert_coord([1, 1], 3))
+            self.add_vert([3], *self.hex_vert_coord([1, 1], 4))
+            self.add_vert([4], *self.hex_vert_coord([0, 0], 1))
+            self.add_vert([5], *self.hex_vert_coord([0, 0], 0))
+
+    def calculate_faces(self):
+        if self.tile_type != 0:
+            return
+
+        # Top Hexagon
+        self.add_face('A',
+                      [0,
+                       left_tile(3),
+                       left_tile(2),
+                       top_left_tile(1),
+                       top_tile(4),
+                       top_tile(5)],
+                      equivalent=[left_tile('F'),
+                                  top_left_tile('D'),
+                                  top_tile('I')])
+
+        # Left Triangle
+        self.add_face('B',
+                      [1,
+                       0,
+                       left_tile(3),
+                       left_tile(4),
+                       left_tile(5),
+                       bottom_tile(2)],
+                      equivalent=[bottom_tile('E'),
+                                  left_tile('H')])
+
+        # Right Triangle
+        self.add_face('C',
+                      [0,
+                       1,
+                       right_tile(4),
+                       right_tile(3),
+                       right_tile(2),
+                       top_tile(5)],
+                      equivalent=[right_tile('G'),
+                                  top_tile('J')])
+
+    def color_pattern1(self):
+        if self.tile_type == 0:
+            self.color_face('A', 1)
+
+    def color_pattern2(self):
+        if self.tile_type == 0:
+            self.color_face('A', 1)
+            self.color_face('B', 2)
+
+
+class HexBigTriTessagon(Tessagon):
+    tile_class = HexBigTriTile
+    metadata = metadata

add_mesh_extra_objects/tessagon/types/hex_square_tri_tessagon.py

@@ -0,0 +1,169 @@
+from math import sqrt
+from tessagon.core.tile import Tile
+from tessagon.core.tessagon import Tessagon
+from tessagon.core.tessagon_metadata import TessagonMetadata
+from tessagon.core.tile_utils import left_tile, top_tile, left_top_tile
+
+metadata = TessagonMetadata(name='Hexagons, Squares, and Triangles',
+                            num_color_patterns=1,
+                            classification='archimedean',
+                            shapes=['hexagons', 'squares', 'triangles'],
+                            sides=[6, 4, 3],
+                            uv_ratio=1.0/sqrt(3.0))
+
+
+class HexSquareTriTile(Tile):
+    # 14 verts, 19 faces (7 internal, 12 on boundary)
+    # The angles make it hard to draw all edges, some excluded
+    #
+    #     ...|...|...  6..|.4.|..6
+    #     ...o---o...  ...o---o...
+    #  ^  o ..\./...o  o.4.\3/.4.o
+    #  |  .\...o.../.  3\...o.../3 Numbers are faces with # sides
+    #  |  --o.....o--  --o.....o--
+    #  |  ..|.....|..  4.|..6..|.4
+    #  |  --o.... o--  --o.... o--
+    #     ./.. o...\.  3/.. o...\3
+    #  V  o.../.\...o  o.4./3\.4.o
+    #     ...o---o...  ...o---o...
+    #     ...|...|...  6..|.4.|..6
+    #
+    #       U ---->
+
+    def __init__(self, tessagon, **kwargs):
+        super().__init__(tessagon, **kwargs)
+        self.u_symmetric = True
+        self.v_symmetric = True
+
+    def init_verts(self):
+        # u_square means on the square that is on the U-boundary
+        return {'top': {'left': {'u_boundary': None,
+                                 'u_square': None,
+                                 'v_square': None},
+                        'right': {'u_boundary': None,
+                                  'u_square': None,
+                                  'v_square': None},
+                        'center': None},
+                'bottom': {'left': {'u_boundary': None,
+                                    'u_square': None,
+                                    'v_square': None},
+                           'right': {'u_boundary': None,
+                                     'u_square': None,
+                                     'v_square': None},
+                           'center': None}}
+
+    def init_faces(self):
+        # Whelp!
+        return {'hex': {'top': {'left': None,
+                                'right': None},
+                        'bottom': {'left': None,
+                                   'right': None},
+                        'middle': None},
+                'tri': {'top': {'left': None,
+                                'center': None,
+                                'right': None},
+                        'bottom': {'left': None,
+                                   'center': None,
+                                   'right': None}},
+                'square': {'top': {'left': None,
+                                   'center': None,
+                                   'right': None},
+                           'bottom': {'left': None,
+                                      'center': None,
+                                      'right': None},
+                           'middle': {'left': None,
+                                      'right': None}}}
+
+    def calculate_verts(self):
+        # u_unit is the length of the edges expressed as a
+        # proportion of the tile
+        u_unit = 1.0 / (1.0 + sqrt(3))
+        u0 = 0
+        u1 = 0.5*u_unit
+        u2 = 0.5*(1.0-u_unit)
+        u3 = 0.5
+
+        v_unit = 1.0 / (3.0 + sqrt(3))
+        v0 = 1.0 - 0.5*v_unit
+        v1 = 1.0 - v_unit
+        v2 = 0.5 + v_unit
+        v3 = 0.5 + 0.5*v_unit
+
+        # Define top left square, other verts defined through symmetry
+        self.add_vert(['top', 'left', 'v_square'], u2, v0)
+        self.add_vert(['top', 'center'], u3, v2)
+        self.add_vert(['top', 'left', 'u_square'], u1, v3)
+        self.add_vert(['top', 'left', 'u_boundary'], u0, v1, u_boundary=True)
+
+    def calculate_faces(self):
+        # Middle hexagon
+        self.add_face(['hex', 'middle'],
+                      [['top', 'center'],
+                       ['top', 'left', 'u_square'],
+                       ['bottom', 'left', 'u_square'],
+                       ['bottom', 'center'],
+                       ['bottom', 'right', 'u_square'],
+                       ['top', 'right', 'u_square']],
+                      face_type='hexagon')
+
+        # Six top-left faces, rest defined via symmetry
+        # Top square
+        self.add_face(['square', 'top', 'center'],
+                      [['top', 'left', 'v_square'],
+                       ['top', 'right', 'v_square'],
+                       top_tile(['bottom', 'right', 'v_square']),
+                       top_tile(['bottom', 'left', 'v_square'])],
+                      face_type='square', v_boundary=True)
+        # Left square
+        self.add_face(['square', 'middle', 'left'],
+                      [['top', 'left', 'u_square'],
+                       ['bottom', 'left', 'u_square'],
+                       left_tile(['bottom', 'right', 'u_square']),
+                       left_tile(['top', 'right', 'u_square'])],
+                      face_type='square', u_boundary=True)
+        # Interior square
+        self.add_face(['square', 'top', 'left'],
+                      [['top', 'left', 'v_square'],
+                       ['top', 'center'],
+                       ['top', 'left', 'u_square'],
+                       ['top', 'left', 'u_boundary']],
+                      face_type='square')
+        # Upper triangle
+        self.add_face(['tri', 'top', 'center'],
+                      [['top', 'center'],
+                       ['top', 'left', 'v_square'],
+                       ['top', 'right', 'v_square']],
+                      face_type='triangle')
+        # Left triangle
+        self.add_face(['tri', 'top', 'left'],
+                      [['top', 'left', 'u_square'],
+                       ['top', 'left', 'u_boundary'],
+                       left_tile(['top', 'right', 'u_square'])],
+                      face_type='triangle', u_boundary=True)
+        # Corner hexagon
+        self.add_face(['hex', 'top', 'left'],
+                      [['top', 'left', 'v_square'],
+                       ['top', 'left', 'u_boundary'],
+                       left_tile(['top', 'right', 'v_square']),
+                       left_top_tile(['bottom', 'right', 'v_square']),
+                       top_tile(['bottom', 'left', 'u_boundary']),
+                       top_tile(['bottom', 'left', 'v_square'])],
+                      face_type='hexagon', corner=True)
+
+    def color_pattern1(self):
+        self.color_face(['hex', 'middle'], 1)
+        self.color_face(['hex', 'top', 'left'], 1)
+
+        # TODO: I'm not sure why I have to explicitely color
+        # 'right' and 'bottom' faces (I thought symmetry would do this?)
+        self.color_face(['square', 'top', 'center'], 2)
+        self.color_face(['square', 'top', 'left'], 2)
+        self.color_face(['square', 'top', 'right'], 2)
+        self.color_face(['square', 'middle', 'left'], 2)
+        self.color_face(['square', 'bottom', 'left'], 2)
+        self.color_face(['square', 'bottom', 'right'], 2)
+
+
+class HexSquareTriTessagon(Tessagon):
+    tile_class = HexSquareTriTile
+    metadata = metadata

add_mesh_extra_objects/tessagon/types/hex_tessagon.py

@@ -0,0 +1,129 @@
+from math import sqrt
+from tessagon.core.tessagon import Tessagon
+from tessagon.core.tile import Tile
+from tessagon.core.tessagon_metadata import TessagonMetadata
+from tessagon.core.tile_utils import top_tile, top_left_tile, left_tile
+
+metadata = TessagonMetadata(name='Regular Hexagons',
+                            num_color_patterns=2,
+                            classification='regular',
+                            shapes=['hexagons'],
+                            sides=[6],
+                            uv_ratio=1.0/sqrt(3.0))
+
+
+class HexTile(Tile):
+    #    VERTS:
+    #    ..|..
+    #    ..a..  a = ['top', 'center']
+    # ^  ./.\.  b = ['top', 'left']
+    # |  b...c  c = ['top', 'right']
+    # |  |...|  d = ['bottom', 'left']
+    # |  d...e  e = ['bottom', 'right']
+    # |  .\./.  f = ['bottom', 'center']
+    #    ..f..
+    # V  ..|..
+    #
+    #     U --->
+
+    #    FACES:
+    #    A.|.B
+    #    ..o..  A = ['top', 'left']
+    # ^  ./.\.  B = ['top', 'right']
+    # |  o...o  C = ['middle']
+    # |  |.C.|  D = ['bottom', 'left']
+    # |  o...o  E = ['bottom', 'right']
+    # |  .\./.
+    #    ..o..
+    # V  D.|.E
+    #
+    #     U --->
+
+    def __init__(self, tessagon, **kwargs):
+        super().__init__(tessagon, **kwargs)
+        self.u_symmetric = True
+        self.v_symmetric = True
+
+    def init_verts(self):
+        return {'top': {'left': None,
+                        'center': None,
+                        'right': None},
+                'bottom': {'left': None,
+                           'center': None,
+                           'right': None}}
+
+    def init_faces(self):
+        return {'top': {'left': None,
+                        'right': None},
+                'middle': None,
+                'bottom': {'left': None,
+                           'right': None}}
+
+    def calculate_verts(self):
+        # Symmetry allow you to get six verts for the price of two.
+
+        # Next line also defines the vert at ['bottom', 'center']
+        self.add_vert(['top', 'center'], 0.5, 5.0/6.0)
+
+        # Next line also defines the verts at: ['bottom', 'left']
+        #                                      ['bottom', 'right']
+        #                                      ['top', 'right']
+        self.add_vert(['top', 'left'], 0, 2.0/3.0, u_boundary=True)
+
+    def calculate_faces(self):
+        # Symmetry allows you to create five faces for the price of two
+        self.add_face('middle', [['top', 'center'],
+                                 ['top', 'left'],
+                                 ['bottom', 'left'],
+                                 ['bottom', 'center'],
+                                 ['bottom', 'right'],
+                                 ['top', 'right']])
+
+        # The next line also defines the faces at: ['top', 'right']
+        #                                          ['bottom', 'right']
+        #                                          ['bottom', 'left']
+        self.add_face(['top', 'left'],
+                      # The first two verts of the face are on this tile
+                      [['top', 'left'],
+                       ['top', 'center'],
+                       # The other four verts are on neighboring tiles.
+                       # E.g., the next one is the ['bottom', 'center']
+                       # vert on the top neighbor tile.
+                       top_tile(['bottom', 'center']),
+                       top_tile(['bottom', 'left']),
+                       top_left_tile(['bottom', 'center']),
+                       left_tile(['top', 'center'])],
+                      # Defining the face as a 'corner' also associates the
+                      # created face as one that is shared with
+                      # neighboring tiles.
+                      corner=True)
+
+    def color_pattern1(self):
+        if self.fingerprint[0] % 3 == 0:
+            self.color_paths([['top', 'left'],
+                              ['bottom', 'left']], 1, 0)
+        elif self.fingerprint[0] % 3 == 1:
+            self.color_paths([['middle']], 1, 0)
+        else:
+            self.color_paths([['top', 'right'],
+                              ['bottom', 'right']], 1, 0)
+
+    def color_pattern2(self):
+        if self.fingerprint[0] % 3 == 0:
+            self.color_paths_hash({1: [['top', 'left'],
+                                       ['bottom', 'left']],
+                                   2: [['top', 'right'],
+                                       ['bottom', 'right']]}, 0)
+        elif self.fingerprint[0] % 3 == 1:
+            self.color_paths_hash({1: [['middle']],
+                                   2: [['top', 'left'],
+                                       ['bottom', 'left']]}, 0)
+        else:
+            self.color_paths_hash({2: [['middle']],
+                                   1: [['top', 'right'],
+                                       ['bottom', 'right']]}, 0)
+
+
+class HexTessagon(Tessagon):
+    tile_class = HexTile
+    metadata = metadata

add_mesh_extra_objects/tessagon/types/hex_tri_tessagon.py

@@ -0,0 +1,101 @@
+from math import sqrt
+from tessagon.core.tile import Tile
+from tessagon.core.tessagon import Tessagon
+from tessagon.core.tessagon_metadata import TessagonMetadata
+from tessagon.core.tile_utils import left_tile, left_top_tile, top_tile
+metadata = TessagonMetadata(name='Hexagons and Triangles',
+                            num_color_patterns=1,
+                            classification='archimedean',
+                            shapes=['hexagons', 'triangles'],
+                            sides=[6, 3],
+                            uv_ratio=1.0/sqrt(3.0))
+
+
+class HexTriTile(Tile):
+    #    ....o....
+    #    .../.\...
+    #  ^ --o---o--
+    #  | ./.....\.
+    #  | o.......o
+    #  | .\...../.
+    #  | --o---o--
+    #    ...\./...
+    #  V ....o ...
+    #
+    #     U ------>
+
+    def __init__(self, tessagon, **kwargs):
+        super().__init__(tessagon, **kwargs)
+        self.u_symmetric = True
+        self.v_symmetric = True
+
+    def init_verts(self):
+        return {'top': None,
+                'left': {'top': None,
+                         'middle': None,
+                         'bottom': None},
+                'right':  {'top': None,
+                           'middle': None,
+                           'bottom': None},
+                'bottom': None}
+
+    def init_faces(self):
+        return {'center': {'top': None,
+                           'middle': None,
+                           'bottom': None},
+                'left': {'top': {'triangle': None, 'hexagon': None},
+                         'bottom': {'triangle': None, 'hexagon': None}},
+                'right': {'top': {'triangle': None, 'hexagon': None},
+                          'bottom': {'triangle': None, 'hexagon': None}}}
+
+    def calculate_verts(self):
+        # top left verts
+        self.add_vert('top', 0.5, 1, v_boundary=True)
+        self.add_vert(['left', 'top'], 0.25, 0.75)
+        self.add_vert(['left', 'middle'], 0, 0.5, u_boundary=True)
+
+    def calculate_faces(self):
+        # Middle hexagon
+        self.add_face(['center', 'middle'],
+                      [['left', 'top'],
+                       ['left', 'middle'],
+                       ['left', 'bottom'],
+                       ['right', 'bottom'],
+                       ['right', 'middle'],
+                       ['right', 'top']],
+                      face_type='hexagon')
+        # Interior top triangle
+        self.add_face(['center', 'top'],
+                      [['top'],
+                       ['left', 'top'],
+                       ['right', 'top']],
+                      face_type='triangle')
+
+        # Exterior left triangle
+        self.add_face(['left', 'top', 'triangle'],
+                      [['left', 'top'],
+                       ['left', 'middle'],
+                       # Verts on neighbor tiles
+                       left_tile(['right', 'top'])],
+                      face_type='triangle', u_boundary=True)
+
+        # Exterior top-left hexagon
+        self.add_face(['left', 'top', 'hexagon'],
+                      [['top'],
+                       ['left', 'top'],
+                       # Verts on neighbor tiles
+                       left_tile(['right', 'top']),
+                       left_tile('top'),
+                       left_top_tile(['right', 'bottom']),
+                       top_tile(['left', 'bottom'])],
+                      face_type='hexagon', corner=True)
+
+    def color_pattern1(self):
+        # Color the hexagons
+        self.color_face(['center', 'middle'], 1)
+        self.color_face(['left', 'top', 'hexagon'], 1)
+
+
+class HexTriTessagon(Tessagon):
+    tile_class = HexTriTile
+    metadata = metadata

add_mesh_extra_objects/tessagon/types/islamic_hex_stars_tessagon.py

@@ -0,0 +1,127 @@
+from math import sqrt
+from tessagon.core.tile import Tile
+from tessagon.core.tessagon import Tessagon
+from tessagon.core.tessagon_metadata import TessagonMetadata
+from tessagon.core.tile_utils import left_tile, top_left_tile, top_tile
+
+metadata = TessagonMetadata(name='Islamic Hexagons and Stars',
+                            num_color_patterns=1,
+                            classification='non_convex',
+                            shapes=['hexagons', 'stars'],
+                            sides=[6, 12],
+                            uv_ratio=sqrt(3.0))
+
+
+class IslamicHexStarsTile(Tile):
+    # See page 3 of "Islamic Design" by Daud Sutton
+    # See the SVG for decomposition:
+    # https://raw.githubusercontent.com/cwant/tessagon/master/documentation/code/islamic_hex_stars.svg
+
+    def __init__(self, tessagon, **kwargs):
+        super().__init__(tessagon, **kwargs)
+        self.u_symmetric = True
+        self.v_symmetric = True
+
+    def init_verts(self):
+        return {'left': {'top': {'boundary': None,
+                                 'mid': {'outer': None,
+                                         'mid': None,
+                                         'inner': None}},
+                         'middle': {'inner': None,
+                                    'outer': None},
+                         'bottom': {'boundary': None,
+                                    'mid': {'outer': None,
+                                            'mid': None,
+                                            'inner': None}}},
+                'center': {'top': None,
+                           'bottom': None},
+                'right': {'top': {'boundary': None,
+                                  'mid': {'outer': None,
+                                          'mid': None,
+                                          'inner': None}},
+                          'middle': {'inner': None,
+                                     'outer': None},
+                          'bottom': {'boundary': None,
+                                     'mid': {'outer': None,
+                                             'mid': None,
+                                             'inner': None}}},
+                }
+
+    def init_faces(self):
+        return {'left': {'top': {'star': None, 'hexagon': None},
+                         'middle': {'hexagon': None},
+                         'bottom': {'star': None, 'hexagon': None}},
+                'center': {'star': None},
+                'right': {'top': {'star': None, 'hexagon': None},
+                          'middle': {'hexagon': None},
+                          'bottom': {'star': None, 'hexagon': None}}}
+
+    def calculate_verts(self):
+        # left verts
+        self.add_vert(['left', 'top', 'boundary'], 2/12.0, 1, v_boundary=True)
+        self.add_vert(['left', 'top', 'mid', 'outer'], 1/12.0, 0.75)
+        self.add_vert(['left', 'top', 'mid', 'mid'], 3/12.0, 0.75)
+        self.add_vert(['left', 'top', 'mid', 'inner'], 5/12.0, 0.75)
+        self.add_vert(['left', 'middle', 'outer'], 0, 0.5, u_boundary=True)
+        self.add_vert(['left', 'middle', 'inner'], 4/12, 0.5)
+
+        # center vert
+        self.add_vert(['center', 'top'], 0.5, 1, v_boundary=True)
+
+    def calculate_faces(self):
+        self.add_face(['left', 'top', 'star'],
+                      [['left', 'top', 'boundary'],
+                       ['left', 'top', 'mid', 'mid'],
+                       ['left', 'top', 'mid', 'outer'],
+                       ['left', 'middle', 'outer'],
+                       left_tile(['right', 'top', 'mid', 'outer']),
+                       left_tile(['right', 'top', 'mid', 'mid']),
+                       left_tile(['right', 'top', 'boundary']),
+                       top_left_tile(['right', 'bottom', 'mid', 'mid']),
+                       top_left_tile(['right', 'bottom', 'mid', 'outer']),
+                       top_tile(['left', 'middle', 'outer']),
+                       top_tile(['left', 'bottom', 'mid', 'outer']),
+                       top_tile(['left', 'bottom', 'mid', 'mid'])],
+                      face_type='star', corner=True)
+
+        self.add_face(['left', 'top', 'hexagon'],
+                      [['center', 'top'],
+                       ['left', 'top', 'mid', 'inner'],
+                       ['left', 'top', 'mid', 'mid'],
+                       ['left', 'top', 'boundary'],
+                       top_tile(['left', 'bottom', 'mid', 'mid']),
+                       top_tile(['left', 'bottom', 'mid', 'inner'])],
+                      face_type='hexagon', v_boundary=True)
+
+        self.add_face(['left', 'middle', 'hexagon'],
+                      [['left', 'middle', 'outer'],
+                       ['left', 'top', 'mid', 'outer'],
+                       ['left', 'top', 'mid', 'mid'],
+                       ['left', 'middle', 'inner'],
+                       ['left', 'bottom', 'mid', 'mid'],
+                       ['left', 'bottom', 'mid', 'outer']],
+                      face_type='hexagon')
+
+        self.add_face(['center', 'star'],
+                      [['center', 'top'],
+                       ['right', 'top', 'mid', 'inner'],
+                       ['right', 'top', 'mid', 'mid'],
+                       ['right', 'middle', 'inner'],
+                       ['right', 'bottom', 'mid', 'mid'],
+                       ['right', 'bottom', 'mid', 'inner'],
+                       ['center', 'bottom'],
+                       ['left', 'bottom', 'mid', 'inner'],
+                       ['left', 'bottom', 'mid', 'mid'],
+                       ['left', 'middle', 'inner'],
+                       ['left', 'top', 'mid', 'mid'],
+                       ['left', 'top', 'mid', 'inner']],
+                      face_type='star')
+
+    def color_pattern1(self):
+        self.color_face(['left', 'top', 'star'], 1)
+        self.color_face(['center', 'star'], 1)
+
+
+class IslamicHexStarsTessagon(Tessagon):
+    tile_class = IslamicHexStarsTile
+    metadata = metadata

add_mesh_extra_objects/tessagon/types/islamic_stars_crosses_tessagon.py

@@ -0,0 +1,121 @@
+from math import sqrt
+from tessagon.core.tile import Tile
+from tessagon.core.tessagon import Tessagon
+from tessagon.core.tessagon_metadata import TessagonMetadata
+from tessagon.core.tile_utils import left_tile, top_left_tile, top_tile
+
+metadata = TessagonMetadata(name='Islamic Stars and Crosses',
+                            num_color_patterns=1,
+                            classification='non_convex',
+                            shapes=['stars', 'crosses'],
+                            sides=[16],
+                            uv_ratio=1.0)
+
+
+class IslamicStarsCrossesTile(Tile):
+    # See page 9 of "Islamic Design" by Daud Sutton
+    #
+    # ......o......
+    # ...../.\.....
+    # ..o-o...o-o..
+    # ..|.......|..
+    # ..o.......o..
+    # ./.........\.
+    # o...........o
+    # .\........./.
+    # ..o.......o..
+    # ..|.......|..
+    # ..o-o...o-o..
+    # .....\./.....
+    # ......o......
+
+    def __init__(self, tessagon, **kwargs):
+        super().__init__(tessagon, **kwargs)
+        self.u_symmetric = True
+        self.v_symmetric = True
+
+    def init_verts(self):
+        return {'left': {'top': {'v_dominant': None,
+                                 'point': None,
+                                 'u_dominant': None},
+                         'middle': None,
+                         'bottom': {'v_dominant': None,
+                                    'point': None,
+                                    'u_dominant': None}},
+                'center': {'top': None,
+                           'bottom': None},
+                'right': {'top': {'v_dominant': None,
+                                  'point': None,
+                                  'u_dominant': None},
+                          'middle': None,
+                          'bottom': {'v_dominant': None,
+                                     'point': None,
+                                     'u_dominant': None}}}
+
+    def init_faces(self):
+        return {'left': {'top': None,
+                         'bottom': None},
+                'center': None,
+                'right': {'top': None,
+                          'bottom': None}}
+
+    def calculate_verts(self):
+        c = 1.0 / (2 * (sqrt(2) + 1))
+        a = c / sqrt(2)
+
+        # left top corner
+        self.add_vert(['left', 'middle'], 0.0, 0.5, u_boundary=True)
+        self.add_vert(['left', 'top', 'u_dominant'], a, 0.5 + a)
+        self.add_vert(['left', 'top', 'point'], a, 1.0 - a)
+        self.add_vert(['left', 'top', 'v_dominant'], 0.5 - a, 1.0 - a)
+        self.add_vert(['center', 'top'], 0.5, 1.0, v_boundary=True)
+
+    def calculate_faces(self):
+        # Middle star
+        self.add_face(['center'],
+                      [['left', 'middle'],
+                       ['left', 'top', 'u_dominant'],
+                       ['left', 'top', 'point'],
+                       ['left', 'top', 'v_dominant'],
+                       ['center', 'top'],
+                       ['right', 'top', 'v_dominant'],
+                       ['right', 'top', 'point'],
+                       ['right', 'top', 'u_dominant'],
+                       ['right', 'middle'],
+                       ['right', 'bottom', 'u_dominant'],
+                       ['right', 'bottom', 'point'],
+                       ['right', 'bottom', 'v_dominant'],
+                       ['center', 'bottom'],
+                       ['left', 'bottom', 'v_dominant'],
+                       ['left', 'bottom', 'point'],
+                       ['left', 'bottom', 'u_dominant']],
+                      face_type='star')
+
+        # Top left cross
+        self.add_face(['left', 'top'],
+                      [['center', 'top'],
+                       ['left', 'top', 'v_dominant'],
+                       ['left', 'top', 'point'],
+                       ['left', 'top', 'u_dominant'],
+                       ['left', 'middle'],
+                       left_tile(['right', 'top', 'u_dominant']),
+                       left_tile(['right', 'top', 'point']),
+                       left_tile(['right', 'top', 'v_dominant']),
+                       left_tile(['center', 'top']),
+                       top_left_tile(['right', 'bottom', 'v_dominant']),
+                       top_left_tile(['right', 'bottom', 'point']),
+                       top_left_tile(['right', 'bottom', 'u_dominant']),
+                       top_left_tile(['right', 'middle']),
+                       top_tile(['left', 'bottom', 'u_dominant']),
+                       top_tile(['left', 'bottom', 'point']),
+                       top_tile(['left', 'bottom', 'v_dominant'])],
+                      face_type='cross', corner=True)
+
+    def color_pattern1(self):
+        self.color_face(['left', 'top'], 1)
+        self.color_face(['center'], 0)
+
+
+class IslamicStarsCrossesTessagon(Tessagon):
+    tile_class = IslamicStarsCrossesTile
+    metadata = metadata

add_mesh_extra_objects/tessagon/types/octo_tessagon.py

@@ -0,0 +1,84 @@
+from math import sqrt
+from tessagon.core.tile import Tile
+from tessagon.core.tessagon import Tessagon
+from tessagon.core.tessagon_metadata import TessagonMetadata
+from tessagon.core.tile_utils import left_tile, top_tile
+
+# TODO: gulp, 'octagon' does not begin with 'octo'
+
+metadata = TessagonMetadata(name='Octagons and Squares',
+                            num_color_patterns=1,
+                            classification='archimedean',
+                            shapes=['octagons', 'squares'],
+                            sides=[8, 4],
+                            uv_ratio=1.0)
+
+
+class OctoTile(Tile):
+    # ^  ..o-o..
+    # |  ./...\.
+    # |  o.....o
+    # |  |.....|
+    # |  o.....o
+    # |  .\.../.
+    #    ..o-o..
+    # V
+    #    U ---->
+
+    CORNER_TO_VERT_RATIO = 1.0 / (2.0 + sqrt(2))
+
+    def __init__(self, tessagon, **kwargs):
+        super().__init__(tessagon, **kwargs)
+        self.u_symmetric = True
+        self.v_symmetric = True
+
+    def init_verts(self):
+        return {'left': {'top': {'u_boundary': None,
+                                 'v_boundary': None},
+                         'bottom': {'u_boundary': None,
+                                    'v_boundary': None}},
+                'right': {'top': {'u_boundary': None,
+                                  'v_boundary': None},
+                          'bottom': {'u_boundary': None,
+                                     'v_boundary': None}}}
+
+    def init_faces(self):
+        return {'middle': None,
+                'left': {'top': None,
+                         'bottom': None},
+                'right': {'top': None,
+                          'bottom': None}}
+
+    def calculate_verts(self):
+        self.add_vert(['left', 'top', 'v_boundary'],
+                      self.CORNER_TO_VERT_RATIO, 1, v_boundary=True)
+        self.add_vert(['left', 'top', 'u_boundary'],
+                      0, 1.0 - self.CORNER_TO_VERT_RATIO, u_boundary=True)
+
+    def calculate_faces(self):
+        # Middle interior face
+        self.add_face('middle', [['left', 'top', 'v_boundary'],
+                                 ['left', 'top', 'u_boundary'],
+                                 ['left', 'bottom', 'u_boundary'],
+                                 ['left', 'bottom', 'v_boundary'],
+                                 ['right', 'bottom', 'v_boundary'],
+                                 ['right', 'bottom', 'u_boundary'],
+                                 ['right', 'top', 'u_boundary'],
+                                 ['right', 'top', 'v_boundary']])
+
+        # Four faces, define top left corner, others via symmetry
+        self.add_face(['left', 'top'],
+                      [['left', 'top', 'v_boundary'],
+                       ['left', 'top', 'u_boundary'],
+                       # Verts on neighbor tiles
+                       left_tile(['right', 'top', 'v_boundary']),
+                       top_tile(['left', 'bottom', 'u_boundary'])],
+                      corner=True)
+
+    def color_pattern1(self):
+        self.color_face(['middle'], 1)
+
+
+class OctoTessagon(Tessagon):
+    tile_class = OctoTile
+    metadata = metadata

add_mesh_extra_objects/tessagon/types/penta2_tessagon.py

@@ -0,0 +1,97 @@
+from math import sqrt
+from tessagon.core.tile import Tile
+from tessagon.core.tessagon import Tessagon
+from tessagon.core.tessagon_metadata import TessagonMetadata
+from tessagon.core.tile_utils import left_tile
+
+metadata = TessagonMetadata(name='Other Pentagons',
+                            num_color_patterns=1,
+                            classification='laves',
+                            shapes=['pentagons'],
+                            sides=[5],
+                            uv_ratio=1.0/(2.0+sqrt(3.0)))
+
+
+class Penta2Tile(Tile):
+    # 11 verts, 6 faces (2 internal, 4 on boundary)
+    #
+    #     O---O
+    #     |...|
+    #     O...O
+    #     .\./.
+    #  ^  ..O..
+    #  |  ..|..
+    #  |  --O--
+    #  |  ..|..
+    #     ..O..
+    #  V  ./.\.
+    #     O...O
+    #     |...|
+    #     O---O
+    #
+    #    U ----->
+
+    def __init__(self, tessagon, **kwargs):
+        super().__init__(tessagon, **kwargs)
+        self.u_symmetric = True
+        self.v_symmetric = True
+
+    def init_verts(self):
+        return {'left': {'top': {'corner': None,
+                                 'u_boundary': None},
+                         'bottom': {'corner': None,
+                                    'u_boundary': None}},
+                'right': {'top': {'corner': None,
+                                  'u_boundary': None},
+                          'bottom': {'corner': None,
+                                     'u_boundary': None}},
+                'center': {'top': None,
+                           'middle': None,
+                           'bottom': None}}
+
+    def init_faces(self):
+        return {'left': {'top': None,
+                         'bottom': None},
+                'right': {'top': None,
+                          'bottom': None},
+                'center': {'top': None,
+                           'bottom': None}}
+
+    def calculate_verts(self):
+        v_unit = 1.0 / (2.0 + sqrt(3.0))
+        v0 = 0
+        v1 = v_unit * 0.5 * (1.0 + 1.0 / sqrt(3.0))
+        v2 = 0.5 - v1
+
+        self.add_vert(['left', 'bottom', 'corner'], 0, v0, corner=True)
+        self.add_vert(['left', 'bottom', 'u_boundary'], 0, v1,
+                      u_boundary=True)
+        self.add_vert(['center', 'bottom'], 0.5, v2)
+        self.add_vert(['center', 'middle'], 0.5, 0.5)
+
+    def calculate_faces(self):
+        self.add_face(['center', 'bottom'],
+                      [['left', 'bottom', 'corner'],
+                       ['left', 'bottom', 'u_boundary'],
+                       ['center', 'bottom'],
+                       ['right', 'bottom', 'u_boundary'],
+                       ['right', 'bottom', 'corner']])
+        self.add_face(['left', 'bottom'],
+                      [['center', 'middle'],
+                       ['center', 'bottom'],
+                       ['left', 'bottom', 'u_boundary'],
+                       left_tile(['center', 'bottom']),
+                       left_tile(['center', 'middle'])],
+                      u_boundary=True)
+
+    def color_pattern1(self):
+        self.color_paths([
+            ['center', 'top'],
+            ['left', 'bottom'],
+            ['right', 'bottom']
+        ], 1, 0)
+
+
+class Penta2Tessagon(Tessagon):
+    tile_class = Penta2Tile
+    metadata = metadata

add_mesh_extra_objects/tessagon/types/penta_tessagon.py

@@ -0,0 +1,137 @@
+from math import sqrt
+from tessagon.core.tile import Tile
+from tessagon.core.tessagon import Tessagon
+from tessagon.core.tessagon_metadata import TessagonMetadata
+from tessagon.core.tile_utils import left_tile, bottom_tile
+
+metadata = TessagonMetadata(name='Pentagons',
+                            num_color_patterns=1,
+                            classification='laves',
+                            shapes=['pentagons'],
+                            sides=[5],
+                            uv_ratio=1.0)
+
+
+class PentaTile(Tile):
+    # 16 verts, 12 faces (4 internal, 8 on boundaries)
+    #
+    #  +              O+++++++++O              +
+    #  +             +           +             +
+    #  O            +             +            O
+    #     ++       +               +       ++
+    #        ++   +                 +   ++
+    #            O+                 +O
+    #          ++   ++           ++   ++
+    #         +         +     +         +
+    #        +             O             +
+    #       +              +              +
+    #  ++++O               +               O++++
+    #       +              +              +
+    #        +             O             +
+    #         +         +     +         +
+    #          ++   ++           ++   ++
+    #            O+                 +O
+    #        ++   +                 +   ++
+    #     ++       +               +       ++
+    #  O            +             +            O
+    #  +             +           +             +
+    #  +              O+++++++++O              +
+
+    def __init__(self, tessagon, **kwargs):
+        super().__init__(tessagon, **kwargs)
+        self.u_symmetric = True
+        self.v_symmetric = True
+
+    def init_verts(self):
+        return {'left': {'top': {'u_boundary': None,
+                                 'v_boundary': None,
+                                 'interior': None},
+                         'middle': None,
+                         'bottom': {'u_boundary': None,
+                                    'v_boundary': None,
+                                    'interior': None}},
+                'center': {'top': None,
+                           'bottom': None},
+                'right': {'top': {'u_boundary': None,
+                                  'v_boundary': None,
+                                  'interior': None},
+                          'middle': None,
+                          'bottom': {'u_boundary': None,
+                                     'v_boundary': None,
+                                     'interior': None}}}
+
+    def init_faces(self):
+        return {'left': {'top': {'u_boundary': None,
+                                 'v_boundary': None},
+                         'middle': None,
+                         'bottom': {'u_boundary': None,
+                                    'v_boundary': None}},
+                'center': {'top': None,
+                           'bottom': None},
+                'right': {'top': {'u_boundary': None,
+                                  'v_boundary': None},
+                          'middle': None,
+                          'bottom': {'u_boundary': None,
+                                     'v_boundary': None}}}
+
+    def calculate_verts(self):
+        # u_unit is the length of the edges expressed as a
+        # proportion of the tile
+        u_unit = 1.0 / (1.0 + sqrt(3))
+        u0 = v0 = 0
+        u1 = v1 = u_unit/(2*sqrt(3))
+        u3 = v3 = (0.5 + 1/sqrt(3)) * u_unit
+        u2 = v2 = 0.5*(u1 + u3)
+        u4 = v4 = 0.5
+
+        self.add_vert(['left', 'bottom', 'u_boundary'], u0, v1,
+                      u_boundary=True)
+        self.add_vert(['left', 'bottom', 'v_boundary'], u3, v0,
+                      v_boundary=True)
+        self.add_vert(['left', 'bottom', 'interior'], u2, v2)
+        self.add_vert(['left', 'middle'], u1, v4)
+        self.add_vert(['center', 'bottom'], u4, v3)
+
+    def calculate_faces(self):
+        self.add_face(['left', 'bottom', 'u_boundary'],
+                      [['left', 'bottom', 'u_boundary'],
+                       ['left', 'bottom', 'interior'],
+                       ['left', 'middle'],
+                       left_tile(['right', 'middle']),
+                       left_tile(['right', 'bottom', 'interior'])],
+                      u_boundary=True)
+
+        self.add_face(['left', 'bottom', 'v_boundary'],
+                      [['left', 'bottom', 'u_boundary'],
+                       ['left', 'bottom', 'interior'],
+                       ['left', 'bottom', 'v_boundary'],
+                       bottom_tile(['left', 'top', 'interior']),
+                       bottom_tile(['left', 'top', 'u_boundary'])],
+                      v_boundary=True)
+
+        self.add_face(['left', 'middle'],
+                      [['left', 'middle'],
+                       ['left', 'bottom', 'interior'],
+                       ['center', 'bottom'],
+                       ['center', 'top'],
+                       ['left', 'top', 'interior']])
+
+        self.add_face(['center', 'bottom'],
+                      [['left', 'bottom', 'interior'],
+                       ['center', 'bottom'],
+                       ['right', 'bottom', 'interior'],
+                       ['right', 'bottom', 'v_boundary'],
+                       ['left', 'bottom', 'v_boundary']])
+
+    def color_pattern1(self):
+        self.color_paths([
+            ['right', 'middle'],
+            ['center', 'bottom'],
+            ['right', 'bottom', 'v_boundary'],
+            ['right', 'bottom', 'u_boundary'],
+        ], 1, 0)
+
+
+class PentaTessagon(Tessagon):
+    tile_class = PentaTile
+    metadata = metadata

add_mesh_extra_objects/tessagon/types/pythagorean_tessagon.py

@@ -0,0 +1,194 @@
+from tessagon.core.tile import Tile
+from tessagon.core.tessagon import Tessagon
+from tessagon.core.tessagon_metadata import TessagonMetadata
+from tessagon.core.tile_utils import top_tile, bottom_tile, \
+    left_tile, right_tile, left_bottom_tile, left_top_tile, \
+    right_bottom_tile, right_top_tile
+
+metadata = TessagonMetadata(name='Pythagorean',
+                            num_color_patterns=1,
+                            classification='non_edge',
+                            shapes=['squares'],
+                            sides=[4],
+                            uv_ratio=1.0)
+
+
+class PythagoreanTile(Tile):
+    # 29 verts in six rows, six columns
+    # 12 faces (2 sets shared with neighbors)
+    #
+    #    o...o-o-o-o  row6  o.1.o-o-o-o
+    #    |...|.|...|        |...|2|...|
+    #    o-o-o-o...o  row5  o-o-o-o.3.o
+    # ^  |.|...|...|        |4|...|...|
+    # |  o-o...o-o-o  row4  o-o.5.o-o-o
+    # |  ..|...|.|..        ..|...|7|..
+    # |  ..o-o-o-o..  row3  6.o-o-o-o.8
+    #    ..|.|...|..        ..|9|...|..
+    # V  o-o-o...o-o  row2  o-o-o10.o-o
+    #    |...|...|.|        |...|...12|
+    #    o...o-o-o-o  row1  o11.o-o-o-o
+    #
+    #    1 2 3 4 5 6 <-cols
+    #
+    #      U ------>
+
+    def init_verts(self):
+        # [col, row], these read like columns
+        return {1: {1: None, 2: None, 4: None, 5: None, 6: None},
+                2: {2: None, 3: None, 4: None, 5: None},
+                3: {1: None, 2: None, 3: None, 5: None, 6: None},
+                4: {1: None, 3: None, 4: None, 5: None, 6: None},
+                5: {1: None, 2: None, 3: None, 4: None, 6: None},
+                6: {1: None, 2: None, 4: None, 5: None, 6: None}}
+
+    def calculate_verts(self):
+        c = {1: 0.0,
+             2: 1/5.0,
+             3: 2/5.0,
+             4: 3/5.0,
+             5: 4/5.0,
+             6: 1.0}
+        for col in self.verts.keys():
+            for row in self.verts[col].keys():
+                # Some verts only get created if neighbors exist
+                if col == 1:
+                    if not self.get_neighbor_tile(['left']):
+                        if row == 6 and not self.get_neighbor_tile(['top']):
+                            continue
+                        if not self.get_neighbor_tile(['bottom']):
+                            if row == 1 or row == 2:
+                                continue
+
+                vert = self.add_vert([col, row], c[col], c[row])
+                if col == 1:
+                    self.set_equivalent_vert(*left_tile([6, row]), vert)
+                    if row == 6:
+                        self.set_equivalent_vert(*left_top_tile([6, 1]), vert)
+                    elif row == 1:
+                        self.set_equivalent_vert(*left_bottom_tile([6, 6]),
+                                                 vert)
+                elif col == 6:
+                    self.set_equivalent_vert(*right_tile([1, row]), vert)
+                    if row == 6:
+                        self.set_equivalent_vert(*right_top_tile([1, 1]),
+                                                 vert)
+                    elif row == 1:
+                        self.set_equivalent_vert(*right_bottom_tile([1, 6]),
+                                                 vert)
+                if row == 6:
+                    self.set_equivalent_vert(*top_tile([col, 1]), vert)
+                elif row == 1:
+                    self.set_equivalent_vert(*bottom_tile([col, 6]), vert)
+
+    def init_faces(self):
+        return {1: None, 2: None, 3: None, 4: None, 5: None, 6: None,
+                7: None, 8: None, 9: None, 10: None, 11: None, 12: None}
+
+    def calculate_faces(self):
+        face = self.add_face(1, [[1, 6],
+                                 [1, 5],
+                                 [2, 5],
+                                 [3, 5],
+                                 [3, 6],
+                                 top_tile([3, 2]),
+                                 top_tile([2, 2]),
+                                 top_tile([1, 2])])
+        self.set_equivalent_face(*top_tile(11), face)
+
+        self.add_face(2, [[3, 6],
+                          [4, 6],
+                          [4, 5],
+                          [3, 5]])
+
+        self.add_face(3, [[4, 6],
+                          [5, 6],
+                          [6, 6],
+                          [6, 5],
+                          [6, 4],
+                          [5, 4],
+                          [4, 4],
+                          [4, 5]])
+
+        self.add_face(4, [[1, 5],
+                          [2, 5],
+                          [2, 4],
+                          [1, 4]])
+
+        self.add_face(5, [[2, 5],
+                          [3, 5],
+                          [4, 5],
+                          [4, 4],
+                          [4, 3],
+                          [3, 3],
+                          [2, 3],
+                          [2, 4]])
+
+        face = self.add_face(6, [[1, 4],
+                                 [2, 4],
+                                 [2, 3],
+                                 [2, 2],
+                                 [1, 2],
+                                 left_tile([5, 2]),
+                                 left_tile([5, 3]),
+                                 left_tile([5, 4])])
+        self.set_equivalent_face(*left_tile(8), face)
+
+        self.add_face(7, [[4, 4],
+                          [5, 4],
+                          [5, 3],
+                          [4, 3]])
+
+        face = self.add_face(8, [[6, 4],
+                                 [5, 4],
+                                 [5, 3],
+                                 [5, 2],
+                                 [6, 2],
+                                 right_tile([2, 2]),
+                                 right_tile([2, 3]),
+                                 right_tile([2, 4])])
+        self.set_equivalent_face(*right_tile(6), face)
+
+        self.add_face(9, [[2, 3],
+                          [3, 3],
+                          [3, 2],
+                          [2, 2]])
+
+        self.add_face(10, [[3, 3],
+                           [4, 3],
+                           [5, 3],
+                           [5, 2],
+                           [5, 1],
+                           [4, 1],
+                           [3, 1],
+                           [3, 2]])
+
+        face = self.add_face(11, [[1, 1],
+                                  [1, 2],
+                                  [2, 2],
+                                  [3, 2],
+                                  [3, 1],
+                                  bottom_tile([3, 5]),
+                                  bottom_tile([2, 5]),
+                                  bottom_tile([1, 5])])
+        self.set_equivalent_face(*bottom_tile(1), face)
+
+        self.add_face(12, [[5, 2],
+                           [6, 2],
+                           [6, 1],
+                           [5, 1]])
+
+    def color_pattern1(self):
+        # Color the big ones
+        self.color_face([1], 1)
+        self.color_face([3], 1)
+        self.color_face([5], 1)
+        self.color_face([6], 1)
+        self.color_face([8], 1)
+        self.color_face([10], 1)
+        self.color_face([11], 1)
+
+
+class PythagoreanTessagon(Tessagon):
+    tile_class = PythagoreanTile
+    metadata = metadata

add_mesh_extra_objects/tessagon/types/rhombus_tessagon.py

@@ -0,0 +1,93 @@
+from math import sqrt
+from tessagon.core.tile import Tile
+from tessagon.core.tessagon import Tessagon
+from tessagon.core.tessagon_metadata import TessagonMetadata
+from tessagon.core.tile_utils import left_tile, top_tile
+
+metadata = TessagonMetadata(name='Rhombuses',
+                            num_color_patterns=2,
+                            classification='laves',
+                            shapes=['rhombuses'],
+                            sides=[4],
+                            uv_ratio=1.0/sqrt(3.0))
+
+
+class RhombusTile(Tile):
+    #    ..o..
+    #    ./|\.
+    #    o.|.o
+    # ^  |.o.|
+    # |  |/.\|
+    # |  o...o
+    # |  |\./|
+    # |  |.o.|
+    # |  o.|.o
+    #    .\|/.
+    # V  ..o..
+    #
+    #   U --->
+
+    def __init__(self, tessagon, **kwargs):
+        super().__init__(tessagon, **kwargs)
+        self.u_symmetric = True
+        self.v_symmetric = True
+
+    def init_verts(self):
+        return {'left': {'top': None, 'middle': None, 'bottom': None},
+                'center': {'top': {'boundary': None, 'interior': None},
+                           'bottom': {'boundary': None, 'interior': None}},
+                'right': {'top': None, 'middle': None, 'bottom': None}}
+
+    def init_faces(self):
+        return {'middle': None,
+                'left': {'top': {'interior': None, 'exterior': None},
+                         'bottom': {'interior': None, 'exterior': None}},
+                'right': {'top': {'interior': None, 'exterior': None},
+                          'bottom': {'interior': None, 'exterior': None}}}
+
+    def calculate_verts(self):
+        # 10 verts, do top left quadrant, others via symmetry
+        self.add_vert(['center', 'top', 'boundary'], 0.5, 1, v_boundary=True)
+        self.add_vert(['left', 'top'], 0, 5.0/6.0, u_boundary=True)
+        self.add_vert(['center', 'top', 'interior'], 0.5, 2.0/3.0)
+        self.add_vert(['left', 'middle'], 0, 1.0/2.0, u_boundary=True)
+
+    def calculate_faces(self):
+        # One middle face
+        self.add_face('middle',
+                      [['center', 'top', 'interior'],
+                       ['left', 'middle'],
+                       ['center', 'bottom', 'interior'],
+                       ['right', 'middle']], face_type='horizontal')
+        # Eight others, define only left top, others by symmetry
+        self.add_face(['left', 'top', 'interior'],
+                      [['center', 'top', 'boundary'],
+                       ['left', 'top'],
+                       ['left', 'middle'],
+                       ['center', 'top', 'interior']], face_type='upward')
+        self.add_face(['left', 'top', 'exterior'],
+                      [['center', 'top', 'boundary'],
+                       ['left', 'top'],
+                       # Verts on neighbor tile
+                       left_tile(['center', 'top', 'boundary']),
+                       top_tile(['left', 'bottom'])],
+                      face_type='horizontal', corner=True)
+
+    def color_pattern1(self):
+        self.color_face(['middle'], 1)
+        self.color_face(['left', 'top', 'exterior'], 1)
+
+        self.color_face(['left', 'top', 'interior'], 2)
+        self.color_face(['right', 'bottom', 'interior'], 2)
+
+    def color_pattern2(self):
+        self.color_face(['left', 'top', 'interior'], 1)
+        self.color_face(['right', 'top', 'interior'], 1)
+
+        self.color_face(['left', 'bottom', 'interior'], 2)
+        self.color_face(['right', 'bottom', 'interior'], 2)
+
+
+class RhombusTessagon(Tessagon):
+    tile_class = RhombusTile
+    metadata = metadata

add_mesh_extra_objects/tessagon/types/square_tessagon.py

@@ -0,0 +1,104 @@
+from tessagon.core.tessagon import Tessagon
+from tessagon.core.tile import Tile
+from tessagon.core.tessagon_metadata import TessagonMetadata
+
+metadata = TessagonMetadata(name='Regular Squares',
+                            num_color_patterns=8,
+                            classification='regular',
+                            shapes=['squares'],
+                            sides=[4],
+                            uv_ratio=1.0)
+
+
+class SquareTile(Tile):
+
+    def __init__(self, tessagon, **kwargs):
+        super().__init__(tessagon, **kwargs)
+        self.u_symmetric = True
+        self.v_symmetric = True
+
+    def init_verts(self):
+        return {'top': {'left': None, 'right': None},
+                'bottom': {'left': None, 'right': None}}
+
+    def init_faces(self):
+        return {'middle': None}
+
+    def calculate_verts(self):
+        self.add_vert(['top', 'left'], 0, 1, corner=True)
+
+    def calculate_faces(self):
+        self.add_face('middle', [['top', 'left'],
+                                 ['top', 'right'],
+                                 ['bottom', 'right'],
+                                 ['bottom', 'left']])
+
+    def color_pattern1(self):
+        if (self.fingerprint[0] + self.fingerprint[1]) % 2 == 0:
+            self.color_face(['middle'], 0)
+        else:
+            self.color_face(['middle'], 1)
+
+    def color_pattern2(self):
+        if (self.fingerprint[0] + self.fingerprint[1]) % 2 == 0:
+            self.color_face(['middle'], 0)
+        elif self.fingerprint[0] % 2 == 0:
+            self.color_face(['middle'], 1)
+        else:
+            self.color_face(['middle'], 2)
+
+    def color_pattern3(self):
+        if (self.fingerprint[0] * self.fingerprint[1]) % 2 == 0:
+            self.color_face(['middle'], 0)
+        else:
+            self.color_face(['middle'], 1)
+
+    def color_pattern4(self):
+        if self.fingerprint[1] % 2 == 0:
+            self.color_face(['middle'], 0)
+        else:
+            if ((self.fingerprint[1] // 2) + self.fingerprint[0]) % 2 == 0:
+                self.color_face(['middle'], 0)
+            else:
+                self.color_face(['middle'], 1)
+
+    def color_pattern5(self):
+        if self.fingerprint[1] % 2 == 0:
+            self.color_face(['middle'], 0)
+        else:
+            self.color_face(['middle'], 1)
+
+    def color_pattern6(self):
+        if self.fingerprint[1] % 2 == 0:
+            self.color_face(['middle'], 0)
+        else:
+            if self.fingerprint[0] % 2 == 0:
+                self.color_face(['middle'], 1)
+            else:
+                self.color_face(['middle'], 2)
+
+    def color_pattern7(self):
+        if self.fingerprint[1] % 2 == 0:
+            self.color_face(['middle'], 0)
+        else:
+            if ((self.fingerprint[1] // 2) + self.fingerprint[0]) % 2 == 0:
+                self.color_face(['middle'], 1)
+            else:
+                self.color_face(['middle'], 2)
+
+    def color_pattern8(self):
+        if self.fingerprint[1] % 2 == 0:
+            if self.fingerprint[0] % 2 == 0:
+                self.color_face(['middle'], 0)
+            else:
+                self.color_face(['middle'], 1)
+        else:
+            if self.fingerprint[0] % 2 == 0:
+                self.color_face(['middle'], 2)
+            else:
+                self.color_face(['middle'], 3)
+
+
+class SquareTessagon(Tessagon):
+    tile_class = SquareTile
+    metadata = metadata

add_mesh_extra_objects/tessagon/types/square_tri2_tessagon.py

@@ -0,0 +1,98 @@
+from math import sqrt
+from tessagon.core.tile import Tile
+from tessagon.core.tessagon import Tessagon
+from tessagon.core.tessagon_metadata import TessagonMetadata
+
+metadata = TessagonMetadata(name='Other Squares and Triangles',
+                            num_color_patterns=1,
+                            classification='archimedean',
+                            shapes=['squares', 'triangles'],
+                            sides=[4, 3],
+                            uv_ratio=1.0/(2.0+sqrt(3.0)))
+
+
+class SquareTri2Tile(Tile):
+    # 6 verts, 11 faces (3 internal, 8 on boundary)
+    #
+    #  ^  ..|..
+    #  |  --O--
+    #  |  ./.\.
+    #  |  O---O
+    #     |...|
+    #  V  O---O
+    #     .\./.
+    #     --O--
+    #     ..|..
+    #
+    #      U ----->
+
+    def __init__(self, tessagon, **kwargs):
+        super().__init__(tessagon, **kwargs)
+        self.u_symmetric = True
+        self.v_symmetric = True
+
+    def init_verts(self):
+        return {'left': {'top': {'u_boundary': None},
+                         'bottom': {'u_boundary': None}},
+                'right': {'top': {'u_boundary': None},
+                          'bottom': {'u_boundary': None}},
+                'center': {'top': None,
+                           'bottom': None}}
+
+    def init_faces(self):
+        return {'left': {'top': {'corner': None,
+                                 'u_boundary': None},
+                         'bottom': {'corner': None,
+                                    'u_boundary': None}},
+                'right': {'top': {'corner': None,
+                                  'u_boundary': None},
+                          'bottom': {'corner': None,
+                                     'u_boundary': None}},
+                'center': {'top': None,
+                           'middle': None,
+                           'bottom': None}}
+
+    def calculate_verts(self):
+        v_unit = 1.0 / (2 + sqrt(3))
+        v1 = v_unit * 0.5
+        v2 = 0.5 - v1
+
+        # Other verts defined through symmetry
+        self.add_vert(['center', 'bottom'], 0.5, v1)
+        self.add_vert(['left', 'bottom', 'u_boundary'], 0, v2, u_boundary=True)
+
+    def calculate_faces(self):
+        self.add_face(['left', 'bottom', 'corner'],
+                      [['center', 'bottom'],
+                       [['left'], ['center', 'bottom']],
+                       [['left', 'bottom'], ['center', 'top']],
+                       [['bottom'], ['center', 'top']]],
+                      face_type='square', corner=True)
+
+        self.add_face(['left', 'bottom', 'u_boundary'],
+                      [['center', 'bottom'],
+                       ['left', 'bottom', 'u_boundary'],
+                       [['left'], ['center', 'bottom']]],
+                      face_type='triangle', u_boundary=True)
+
+        self.add_face(['center', 'bottom'],
+                      [['left', 'bottom', 'u_boundary'],
+                       ['center', 'bottom'],
+                       ['right', 'bottom', 'u_boundary']],
+                      face_type='triangle')
+
+        self.add_face(['center', 'middle'],
+                      [['left', 'bottom', 'u_boundary'],
+                       ['right', 'bottom', 'u_boundary'],
+                       ['right', 'top', 'u_boundary'],
+                       ['left', 'top', 'u_boundary']],
+                      face_type='square')
+
+    def color_pattern1(self):
+        self.color_paths([['left', 'bottom', 'corner'],
+                          ['center', 'middle']], 1, 0)
+
+
+class SquareTri2Tessagon(Tessagon):
+    tile_class = SquareTri2Tile
+    metadata = metadata

add_mesh_extra_objects/tessagon/types/square_tri_tessagon.py

@@ -0,0 +1,145 @@
+from math import sqrt
+from tessagon.core.tile import Tile
+from tessagon.core.tessagon import Tessagon
+from tessagon.core.tessagon_metadata import TessagonMetadata
+
+metadata = TessagonMetadata(name='Squares and Triangles',
+                            num_color_patterns=2,
+                            classification='archimedean',
+                            shapes=['squares', 'triangles'],
+                            sides=[4, 3],
+                            uv_ratio=1.0)
+
+
+class SquareTriTile(Tile):
+    # 12 verts, 16 faces (8 internal, 8 on boundary)
+    # The angles make it hard to draw all edges, some excluded
+    #
+    #
+    #  ^  ..o..|..o..    3.o.3|3.o.3
+    #  |  ./...o...\.    ./...o...\.
+    #  |  o.../.\...o    o.4./3\.4.o
+    #  |  ...o---o...    .3.o---o.3.
+    #     o...\./...o    o.4.\3/.4.o
+    #  V  .\...o.../.    .\...o.../.
+    #     ..o..|..o..    3.o.3|3.o.3
+    #      U ----->
+
+    def __init__(self, tessagon, **kwargs):
+        super().__init__(tessagon, **kwargs)
+        self.u_symmetric = True
+        self.v_symmetric = True
+
+    def init_verts(self):
+        # u_square means on the square that is on the U-boundary
+        return {'top': {'left': {'u_boundary': None,
+                                 'v_boundary': None},
+                        'right': {'u_boundary': None,
+                                  'v_boundary': None},
+                        'center': None},
+                'bottom': {'left': {'u_boundary': None,
+                                    'v_boundary': None},
+                           'right': {'u_boundary': None,
+                                     'v_boundary': None},
+                           'center': None},
+                'middle': {'left': None,
+                           'right': None}}
+
+    def init_faces(self):
+        return {'tri': {'top': {'left': {'u_boundary': None,
+                                         'v_boundary': None},
+                                'right': {'u_boundary': None,
+                                          'v_boundary': None},
+                                'center': None},
+                        'bottom': {'left': {'u_boundary': None,
+                                            'v_boundary': None},
+                                   'right': {'u_boundary': None,
+                                             'v_boundary': None},
+                                   'center': None},
+                        'middle': {'left': None,
+                                   'right': None}},
+                'square': {'top': {'left': None,
+                                   'right': None},
+                           'bottom': {'left': None,
+                                      'right': None}}}
+
+    def calculate_verts(self):
+        # u_unit is the length of the edges expressed as a
+        # proportion of the tile
+        u_unit = 1.0 / (1.0 + sqrt(3))
+
+        u0 = 0
+        u1 = 0.5*u_unit
+        u2 = 0.5*(1.0-u_unit)
+        u3 = 0.5
+
+        v_unit = 1.0 / (1.0 + sqrt(3))
+        v0 = 0.5
+        v1 = 0.5 * (1.0 + v_unit)
+        v2 = 1.0 - 0.5*v_unit
+        v3 = 1.0
+
+        # Define top left square, other verts defined through symmetry
+        self.add_vert(['top', 'left', 'u_boundary'], u0, v1, u_boundary=True)
+        self.add_vert(['top', 'left', 'v_boundary'], u1, v3, v_boundary=True)
+        self.add_vert(['top', 'center'], u3, v2)
+        self.add_vert(['middle', 'left'], u2, v0)
+
+    def calculate_faces(self):
+        # 4 internal squares (others via symmetry)
+        self.add_face(['square', 'top', 'left'],
+                      [['top', 'left', 'u_boundary'],
+                       ['top', 'left', 'v_boundary'],
+                       ['top', 'center'],
+                       ['middle', 'left']],
+                      face_type='square')
+
+        # 4 u-boundary triangles
+        self.add_face(['tri', 'top', 'left', 'u_boundary'],
+                      [['top', 'left', 'v_boundary'],
+                       ['top', 'left', 'u_boundary'],
+                       [['left'], ['top', 'right', 'v_boundary']]],
+                      face_type='triangle', u_boundary=True)
+
+        # 4 v-boundary triangles
+        self.add_face(['tri', 'top', 'left', 'v_boundary'],
+                      [['top', 'left', 'v_boundary'],
+                       ['top', 'center'],
+                       [['top'], ['bottom', 'center']]],
+                      face_type='triangle', v_boundary=True)
+
+        # 2 internal center triangles
+        self.add_face(['tri', 'top', 'center'],
+                      [['top', 'center'],
+                       ['middle', 'right'],
+                       ['middle', 'left']],
+                      face_type='triangle')
+
+        # 2 internal middle triangles
+        self.add_face(['tri', 'middle', 'left'],
+                      [['middle', 'left'],
+                       ['bottom', 'left', 'u_boundary'],
+                       ['top', 'left', 'u_boundary']],
+                      face_type='triangle')
+
+    def color_pattern1(self):
+        self.color_face(['square', 'top', 'left'], 1)
+        self.color_face(['square', 'top', 'right'], 1)
+        self.color_face(['square', 'bottom', 'left'], 1)
+        self.color_face(['square', 'bottom', 'right'], 1)
+
+    def color_pattern2(self):
+        self.color_face(['square', 'top', 'left'], 1)
+        self.color_face(['square', 'top', 'right'], 1)
+        self.color_face(['square', 'bottom', 'left'], 1)
+        self.color_face(['square', 'bottom', 'right'], 1)
+
+        self.color_face(['tri', 'middle', 'left'], 2)
+        self.color_face(['tri', 'middle', 'right'], 2)
+        self.color_face(['tri', 'top', 'left', 'v_boundary'], 2)
+        self.color_face(['tri', 'top', 'right', 'v_boundary'], 2)
+
+
+class SquareTriTessagon(Tessagon):
+    tile_class = SquareTriTile
+    metadata = metadata

add_mesh_extra_objects/tessagon/types/stanley_park_tessagon.py

@@ -0,0 +1,142 @@
+from math import sqrt
+from tessagon.core.tessagon import Tessagon
+from tessagon.core.tile import Tile
+from tessagon.core.tessagon_metadata import TessagonMetadata
+from tessagon.core.tile_utils import top_tile, bottom_tile, \
+    top_left_tile, left_tile
+
+metadata = TessagonMetadata(name='Stanley Park',
+                            num_color_patterns=2,
+                            classification='non_convex',
+                            sides=[12],
+                            uv_ratio=sqrt(3.0))
+
+# Non-convex pattern. Might work better for 2D than 3D
+# Also, the ASCII art below is a bit hard to visualize,
+# so check out preview images linked from README.md
+
+
+class StanleyParkTile(Tile):
+    #    VERTS:
+    #   ....a...b....  a = ['top', 'left']
+    # ^ .../.....\...  b = ['top', 'right']
+    # | ..c.......d..  c = ['mid1', 'left']
+    # | ..|.......|..  d = ['mid1', 'right']
+    # | ..e...f...g .  e = ['mid2', 'left']
+    # | ./.\./.\./.\.  f = ['mid2', 'center']
+    #   h...i...j...k  g = ['mid2', 'right']
+    # V ....|...|....  h = ['mid3', 'left', 'outer']
+    #   ....l...m....  i = ['mid3', 'left', 'inner']
+    #                  j = ['mid3', 'right', 'inner']
+    #     U --->       k = ['mid3', 'right', 'outer']
+    #                  l = ['bottom', 'left']
+    #                  m = ['bottom', 'right']
+
+    #    FACES:
+    #   ....o...o....
+    # ^ .A./.....\.C.  A = ['top', 'left']
+    # | ..o...B...o..  B = ['top', 'middle']
+    # | ..|.......|..  C = ['top', 'right']
+    # | ..o...o...o .  D = ['bottom', 'left']
+    # | ./.\./.\./.\.  E = ['bottom', 'middle']
+    #   o...o...o...o  F = ['bottom', 'right']
+    # V ..D.|.E.|.F..
+    #   ....o...o....
+    #
+    #     U --->
+
+    def __init__(self, tessagon, **kwargs):
+        super().__init__(tessagon, **kwargs)
+        self.u_symmetric = True
+        self.v_symmetric = False
+
+    def init_verts(self):
+        return {'top': {'left': None,
+                        'right': None},
+                'mid1': {'left': None,
+                         'right': None},
+                'mid2': {'left': None,
+                         'center': None,
+                         'right': None},
+                'mid3': {'left': {'outer': None,
+                                  'inner': None},
+                         'right': {'inner': None,
+                                   'outer': None}},
+                'bottom': {'left': None,
+                           'right': None}}
+
+    def init_faces(self):
+        return {'top': {'left': None,
+                        'center': None,
+                        'right': None},
+                'bottom': {'left': None,
+                           'center': None,
+                           'right': None}}
+
+    def calculate_verts(self):
+        vert = self.add_vert(['top', 'left'], 2.0/6.0, 1.0)
+        self.set_equivalent_vert(*top_tile(['bottom', 'left']), vert)
+        # Reflection doesn't handle 'set_equivalent_vert' so ...
+        vert = self.add_vert(['top', 'right'], 4.0/6.0, 1.0)
+        self.set_equivalent_vert(*top_tile(['bottom', 'right']), vert)
+
+        self.add_vert(['mid1', 'left'], 1.0/6.0, 5.0/6.0)
+        self.add_vert(['mid2', 'left'], 1.0/6.0, 3.0/6.0)
+        self.add_vert(['mid2', 'center'], 3.0/6.0, 3.0/6.0)
+        self.add_vert(['mid3', 'left', 'outer'], 0.0, 2.0/6.0,
+                      u_boundary=True)
+        self.add_vert(['mid3', 'left', 'inner'], 2.0/6.0, 2.0/6.0)
+
+        vert = self.add_vert(['bottom', 'left'], 2.0/6.0, 0.0)
+        self.set_equivalent_vert(*bottom_tile(['top', 'left']), vert)
+        vert = self.add_vert(['bottom', 'right'], 4.0/6.0, 0.0)
+        self.set_equivalent_vert(*bottom_tile(['top', 'right']), vert)
+
+    def calculate_faces(self):
+        face = self.add_face(['top', 'left'],
+                             [['mid3', 'left', 'outer'],
+                              ['mid2', 'left'],
+                              ['mid1', 'left'],
+                              ['top', 'left'],
+                              top_tile(['mid3', 'left', 'inner']),
+                              top_tile(['mid2', 'left']),
+                              top_tile(['mid3', 'left', 'outer']),
+                              top_left_tile(['mid2', 'right']),
+                              top_left_tile(['mid3', 'right', 'inner']),
+                              left_tile(['top', 'right']),
+                              left_tile(['mid1', 'right']),
+                              left_tile(['mid2', 'right'])],
+                             u_boundary=True)
+        self.set_equivalent_face(*top_tile(['bottom', 'left']), face)
+        self.set_equivalent_face(*top_left_tile(['bottom', 'right']), face)
+        self.set_equivalent_face(*left_tile(['top', 'right']), face)
+
+        face = self.add_face(['top', 'center'],
+                             [['top', 'left'],
+                              ['mid1', 'left'],
+                              ['mid2', 'left'],
+                              ['mid3', 'left', 'inner'],
+                              ['mid2', 'center'],
+                              ['mid3', 'right', 'inner'],
+                              ['mid2', 'right'],
+                              ['mid1', 'right'],
+                              ['top', 'right'],
+                              top_tile(['mid3', 'right', 'inner']),
+                              top_tile(['mid2', 'center']),
+                              top_tile(['mid3', 'left', 'inner'])])
+        self.set_equivalent_face(*top_tile(['bottom', 'center']), face)
+
+    def color_pattern1(self):
+        self.color_face(['top', 'center'], 1)
+        self.color_face(['bottom', 'center'], 1)
+
+    def color_pattern2(self):
+        if self.fingerprint[1] % 2 == 0:
+            self.color_face(['top', 'left'], 1)
+            self.color_face(['top', 'center'], 1)
+            self.color_face(['top', 'right'], 1)
+
+
+class StanleyParkTessagon(Tessagon):
+    tile_class = StanleyParkTile
+    metadata = metadata

add_mesh_extra_objects/tessagon/types/tri_tessagon.py

@@ -0,0 +1,152 @@
+from math import sqrt
+from tessagon.core.tessagon import Tessagon
+from tessagon.core.tile import Tile
+from tessagon.core.tessagon_metadata import TessagonMetadata
+from tessagon.core.tile_utils import top_tile
+
+metadata = TessagonMetadata(name='Regular Triangles',
+                            num_color_patterns=3,
+                            classification='regular',
+                            shapes=['triangles'],
+                            sides=[3],
+                            uv_ratio=sqrt(3.0))
+
+
+class TriTile(Tile):
+
+    #  ^  0.|.1   This is the topology of the tile.
+    #  |  |\|/|   (Not a Dead Kennedy's logo ...).
+    #  |  |.2.|
+    #  |  |/|\|
+    #  V  3.|.4
+    #
+    #  U ----->
+
+    def __init__(self, tessagon, **kwargs):
+        super().__init__(tessagon, **kwargs)
+        self.u_symmetric = True
+        self.v_symmetric = True
+
+    def init_verts(self):
+        return {'left': {'top': None, 'bottom': None},
+                'middle': None,
+                'right': {'top': None, 'bottom': None}}
+
+    def init_faces(self):
+        return {'left': {'top': None, 'middle': None, 'bottom': None},
+                'right': {'top': None, 'middle': None, 'bottom': None}}
+
+    def calculate_verts(self):
+        # Four corners, via symmetry
+        self.add_vert(['left', 'top'], 0, 1, corner=True)
+        # The middle vert
+        self.add_vert('middle', 0.5, 0.5)
+
+    def calculate_faces(self):
+        # Four corners, via symmetry
+        self.add_face(['left', 'top'],
+                      [['left', 'top'],
+                       ['middle'],
+                       # Vert on neighboring tile
+                       top_tile(['middle'])], v_boundary=True)
+        # Two interior faces, via symmetry
+        self.add_face(['left', 'middle'],
+                      [['left', 'top'],
+                       ['left', 'bottom'],
+                       ['middle']])
+
+    def color_pattern1(self):
+        # two colors for triangles pointing in different directions
+        self.color_face(['left', 'top'], 0)
+        self.color_face(['right', 'top'], 1)
+        self.color_face(['left', 'middle'], 1)
+        self.color_face(['right', 'middle'], 0)
+        self.color_face(['left', 'bottom'], 0)
+        self.color_face(['right', 'bottom'], 1)
+
+    def color_pattern2(self):
+        # Two colors, this one is awesome, but complicated
+        if not self.fingerprint:
+            return
+        if self.fingerprint[1] % 3 == 0:
+            if self.fingerprint[0] % 3 == 0:
+                self.color_0_0()
+            elif self.fingerprint[0] % 3 == 1:
+                self.color_0_1()
+        elif self.fingerprint[1] % 3 == 1:
+            if self.fingerprint[0] % 3 == 0:
+                self.color_1_0()
+            elif self.fingerprint[0] % 3 == 1:
+                self.color_1_1()
+            else:
+                self.color_1_2()
+        else:
+            if self.fingerprint[0] % 3 == 0:
+                self.color_2_0()
+            elif self.fingerprint[0] % 3 == 1:
+                self.color_2_1()
+            else:
+                self.color_2_2()
+
+    def color_pattern3(self):
+        if not self.fingerprint:
+            return
+        if self.fingerprint[1] % 3 == 2:
+            self.color_paths([['left', 'middle'],
+                              ['right', 'bottom']], 1, 0)
+        elif self.fingerprint[1] % 3 == 1:
+            self.color_paths([['right', 'top'],
+                              ['right', 'bottom']], 1, 0)
+        else:
+            self.color_paths([['left', 'middle'],
+                              ['right', 'top']], 1, 0)
+
+    def color_0_0(self):
+        self.color_paths([], 0, 1)
+
+    def color_0_1(self):
+        paths = [['left', 'top'],
+                 ['left', 'bottom'],
+                 ['right', 'middle']]
+        self.color_paths(paths, 1, 0)
+
+    def color_1_0(self):
+        paths = [['left', 'top'],
+                 ['left', 'bottom'],
+                 ['right', 'bottom']]
+        self.color_paths(paths, 1, 0)
+
+    def color_1_1(self):
+        paths = [['left', 'bottom'],
+                 ['right', 'top'],
+                 ['right', 'middle']]
+        self.color_paths(paths, 1, 0)
+
+    def color_1_2(self):
+        paths = [['left', 'top'],
+                 ['left', 'middle'],
+                 ['right', 'middle']]
+        self.color_paths(paths, 1, 0)
+
+    def color_2_0(self):
+        paths = [['left', 'top'],
+                 ['left', 'bottom'],
+                 ['right', 'top']]
+        self.color_paths(paths, 1, 0)
+
+    def color_2_1(self):
+        paths = [['left', 'top'],
+                 ['right', 'middle'],
+                 ['right', 'bottom']]
+        self.color_paths(paths, 1, 0)
+
+    def color_2_2(self):
+        paths = [['left', 'middle'],
+                 ['left', 'bottom'],
+                 ['right', 'middle']]
+        self.color_paths(paths, 1, 0)
+
+
+class TriTessagon(Tessagon):
+    tile_class = TriTile
+    metadata = metadata

add_mesh_extra_objects/tessagon/types/valemount_tessagon.py

@@ -0,0 +1,133 @@
+from tessagon.core.tile import Tile
+from tessagon.core.tessagon import Tessagon
+from tessagon.core.tessagon_metadata import TessagonMetadata
+from tessagon.core.tile_utils import left_tile, right_tile, \
+    top_tile, top_left_tile, top_right_tile, \
+    bottom_tile, bottom_left_tile, bottom_right_tile
+
+metadata = TessagonMetadata(name='Valemount',
+                            num_color_patterns=1,
+                            classification='non_edge',
+                            shapes=['rectangles', 'squares'],
+                            sides=[4],
+                            uv_ratio=1.0)
+
+
+class ValemountTile(Tile):
+    #    o--o--o--o    1,2,3,4
+    #    |..|.....|
+    #    o..o--o--o    5,6,7,8
+    # ^  |..|..|..|
+    # |  o--o--o..o    9,10,11,12
+    # |  |.....|..|
+    # |  o--o--o--o    13,14,15,16
+    # V
+    #   U --->
+
+    def __init__(self, tessagon, **kwargs):
+        super().__init__(tessagon, **kwargs)
+        self.u_symmetric = False
+        self.v_symmetric = False
+
+    def init_verts(self):
+        # Naming stuff is hard ...
+        return {1: None,
+                2: None,
+                3: None,
+                4: None,
+                5: None,
+                6: None,
+                7: None,
+                8: None,
+                9: None,
+                10: None,
+                11: None,
+                12: None,
+                13: None,
+                14: None,
+                15: None,
+                16: None}
+
+    def init_faces(self):
+        return {'top_left': None,
+                'top_right': None,
+                'bottom_left': None,
+                'bottom_right': None,
+                'center': None}
+
+    def calculate_verts(self):
+        # Top row
+        vert = self.add_vert([1], 0, 1)
+        self.set_equivalent_vert(*left_tile(4), vert)
+        self.set_equivalent_vert(*top_tile(13), vert)
+        self.set_equivalent_vert(*top_left_tile(16), vert)
+
+        vert = self.add_vert([2], 1/3.0, 1)
+        self.set_equivalent_vert(*top_tile(14), vert)
+
+        vert = self.add_vert([3], 2/3.0, 1)
+        self.set_equivalent_vert(*top_tile(15), vert)
+
+        vert = self.add_vert([4], 1, 1)
+        self.set_equivalent_vert(*right_tile(1), vert)
+        self.set_equivalent_vert(*top_tile(16), vert)
+        self.set_equivalent_vert(*top_right_tile(13), vert)
+
+        # Next row
+        vert = self.add_vert([5], 0, 2/3.0)
+        self.set_equivalent_vert(*left_tile(8), vert)
+
+        self.add_vert([6], 1/3.0, 2/3.0)
+        self.add_vert([7], 2/3.0, 2/3.0)
+
+        vert = self.add_vert([8], 1, 2/3.0)
+        self.set_equivalent_vert(*right_tile(5), vert)
+
+        # Next row
+        vert = self.add_vert([9], 0, 1/3.0)
+        self.set_equivalent_vert(*left_tile(12), vert)
+
+        self.add_vert([10], 1/3.0, 1/3.0)
+        self.add_vert([11], 2/3.0, 1/3.0)
+
+        vert = self.add_vert([12], 1, 1/3.0)
+        self.set_equivalent_vert(*right_tile(9), vert)
+
+        # Bottom row
+        vert = self.add_vert([13], 0, 0)
+        self.set_equivalent_vert(*left_tile(16), vert)
+        self.set_equivalent_vert(*bottom_tile(1), vert)
+        self.set_equivalent_vert(*bottom_left_tile(4), vert)
+
+        vert = self.add_vert([14], 1/3.0, 0)
+        self.set_equivalent_vert(*bottom_tile(2), vert)
+
+        vert = self.add_vert([15], 2/3.0, 0)
+        self.set_equivalent_vert(*bottom_tile(3), vert)
+
+        vert = self.add_vert([16], 1, 0)
+        self.set_equivalent_vert(*right_tile(13), vert)
+        self.set_equivalent_vert(*bottom_tile(4), vert)
+        self.set_equivalent_vert(*bottom_right_tile(1), vert)
+
+    def calculate_faces(self):
+        self.add_face('top_left',
+                      [1, 2, 6, 10, 9, 5])
+        self.add_face('top_right',
+                      [2, 3, 4, 8, 7, 6])
+        self.add_face('bottom_left',
+                      [9, 10, 11, 15, 14, 13])
+        self.add_face('bottom_right',
+                      [7, 8, 12, 16, 15, 11])
+        self.add_face('center',
+                      [6, 7, 11, 10])
+
+    def color_pattern1(self):
+        self.color_paths([
+            ['center']
+        ], 1, 0)
+
+
+class ValemountTessagon(Tessagon):
+    tile_class = ValemountTile
+    metadata = metadata

add_mesh_extra_objects/tessagon/types/weave_tessagon.py

@@ -0,0 +1,162 @@
+from tessagon.core.tile import Tile
+from tessagon.core.tessagon import Tessagon
+from tessagon.core.tessagon_metadata import TessagonMetadata
+from tessagon.core.tile_utils import left_tile, top_tile, left_top_tile
+
+metadata = TessagonMetadata(name='Weave',
+                            num_color_patterns=1,
+                            classification='non_edge',
+                            shapes=['quads', 'rectangles'],
+                            sides=[4],
+                            uv_ratio=1.0,
+                            extra_parameters={
+                                'square_ratio': {
+                                    'type': 'float',
+                                    'min': 0.0,
+                                    'max': 1.0,
+                                    'default': 0.5,
+                                    'description':
+                                    'Control the size of the squares'
+                                }
+                            })
+
+
+class WeaveTile(Tile):
+    # 16 verts, 13 faces (5 internal, 8 on boundary)
+    #
+    #      ....|..|....  .8..|.8|.8..
+    #      -o--o..o--o-  -o--o..o--o-
+    #   ^  .|..|..|..|.  .|4.|..|4.|.
+    #   |  .o--o--o--o.  .o--o--o--o.
+    #   |  .|........|.  8|...8....|8
+    #   |  .o--o--o--o.  .o--o--o--o.
+    #      .|..|..|..|.  .|4.|..|4.|.
+    #   V  -o--o..o--o.  -o--o..o--o.
+    #      ....|..|....  8...|8.|...8
+    #
+    #        U ----->
+
+    def __init__(self, tessagon, **kwargs):
+        super().__init__(tessagon, **kwargs)
+        self.u_symmetric = True
+        self.v_symmetric = True
+        self.square_ratio = kwargs.get('square_ratio', 0.5)
+
+    def init_verts(self):
+        # u_square means on the square that is on the U-boundary
+        return {'top': {'left': {'u_inner': {'v_inner': None,
+                                             'v_outer': None},
+                                 'u_outer': {'v_inner': None,
+                                             'v_outer': None}},
+                        'right': {'u_inner': {'v_inner': None,
+                                              'v_outer': None},
+                                  'u_outer': {'v_inner': None,
+                                              'v_outer': None}}},
+                'bottom': {'left': {'u_inner': {'v_inner': None,
+                                                'v_outer': None},
+                                    'u_outer': {'v_inner': None,
+                                                'v_outer': None}},
+                           'right': {'u_inner': {'v_inner': None,
+                                                 'v_outer': None},
+                                     'u_outer': {'v_inner': None,
+                                                 'v_outer': None}}}}
+
+    def init_faces(self):
+        return {'square': {'top': {'left': None,
+                                   'right': None},
+                           'bottom': {'left': None,
+                                      'right': None}},
+                'oct': {'top': {'left': None,
+                                'center': None,
+                                'right': None},
+                        'middle': {'left': None,
+                                   'center': None,
+                                   'right': None},
+                        'bottom': {'left': None,
+                                   'center': None,
+                                   'right': None}}}
+
+    def calculate_verts(self):
+        half_square_size = 0.25 * self.square_ratio
+        u0 = 0.25 - half_square_size
+        u1 = 0.25 + half_square_size
+
+        v0 = 0.75 - half_square_size
+        v1 = 0.75 + half_square_size
+
+        # Define top left square, other verts defined through symmetry
+        self.add_vert(['top', 'left', 'u_inner', 'v_inner'], u1, v0)
+        self.add_vert(['top', 'left', 'u_inner', 'v_outer'], u1, v1)
+        self.add_vert(['top', 'left', 'u_outer', 'v_inner'], u0, v0)
+        self.add_vert(['top', 'left', 'u_outer', 'v_outer'], u0, v1)
+
+    def calculate_faces(self):
+        # 4 internal squares (via symmetry)
+        self.add_face(['square', 'top', 'left'],
+                      [['top', 'left', 'u_outer', 'v_outer'],
+                       ['top', 'left', 'u_inner', 'v_outer'],
+                       ['top', 'left', 'u_inner', 'v_inner'],
+                       ['top', 'left', 'u_outer', 'v_inner']],
+                      face_type='square')
+
+        # 1 interior strip
+        self.add_face(['oct', 'middle', 'center'],
+                      [['top', 'left', 'u_outer', 'v_inner'],
+                       ['top', 'left', 'u_inner', 'v_inner'],
+                       ['top', 'right', 'u_inner', 'v_inner'],
+                       ['top', 'right', 'u_outer', 'v_inner'],
+                       ['bottom', 'right', 'u_outer', 'v_inner'],
+                       ['bottom', 'right', 'u_inner', 'v_inner'],
+                       ['bottom', 'left', 'u_inner', 'v_inner'],
+                       ['bottom', 'left', 'u_outer', 'v_inner']],
+                      face_type='oct')
+
+        # 4 corner strips
+        self.add_face(['oct', 'top', 'left'],
+                      [['top', 'left', 'u_inner', 'v_outer'],
+                       ['top', 'left', 'u_outer', 'v_outer'],
+                       left_tile(['top', 'right', 'u_outer', 'v_outer']),
+                       left_tile(['top', 'right', 'u_inner', 'v_outer']),
+                       left_top_tile(['bottom', 'right',
+                                      'u_inner', 'v_outer']),
+                       left_top_tile(['bottom', 'right',
+                                      'u_outer', 'v_outer']),
+                       top_tile(['bottom', 'left', 'u_outer', 'v_outer']),
+                       top_tile(['bottom', 'left', 'u_inner', 'v_outer'])],
+                      face_type='oct', corner=True)
+
+        # 2 side strips
+        self.add_face(['oct', 'middle', 'left'],
+                      [['top', 'left', 'u_outer', 'v_outer'],
+                       ['top', 'left', 'u_outer', 'v_inner'],
+                       ['bottom', 'left', 'u_outer', 'v_inner'],
+                       ['bottom', 'left', 'u_outer', 'v_outer'],
+                       left_tile(['bottom', 'right', 'u_outer', 'v_outer']),
+                       left_tile(['bottom', 'right', 'u_outer', 'v_inner']),
+                       left_tile(['top', 'right', 'u_outer', 'v_inner']),
+                       left_tile(['top', 'right', 'u_outer', 'v_outer'])],
+                      face_type='oct', u_boundary=True)
+
+        # 2 top/bottom strips
+        self.add_face(['oct', 'top', 'center'],
+                      [['top', 'left', 'u_inner', 'v_outer'],
+                       ['top', 'left', 'u_inner', 'v_inner'],
+                       ['top', 'right', 'u_inner', 'v_inner'],
+                       ['top', 'right', 'u_inner', 'v_outer'],
+                       top_tile(['bottom', 'right', 'u_inner', 'v_outer']),
+                       top_tile(['bottom', 'right', 'u_inner', 'v_inner']),
+                       top_tile(['bottom', 'left', 'u_inner', 'v_inner']),
+                       top_tile(['bottom', 'left', 'u_inner', 'v_outer'])],
+                      face_type='oct', v_boundary=True)
+
+    def color_pattern1(self):
+        self.color_face(['oct', 'top', 'center'], 1)
+        self.color_face(['oct', 'middle', 'left'], 1)
+
+        self.color_face(['oct', 'top', 'left'], 2)
+        self.color_face(['oct', 'middle', 'center'], 2)
+
+
+class WeaveTessagon(Tessagon):
+    tile_class = WeaveTile
+    metadata = metadata

add_mesh_extra_objects/tessagon/types/zig_zag_tessagon.py

@@ -0,0 +1,171 @@
+from tessagon.core.tile import Tile
+from tessagon.core.tessagon import Tessagon
+from tessagon.core.tessagon_metadata import TessagonMetadata
+from tessagon.core.tile_utils import left_tile, right_tile, \
+    top_tile, bottom_tile, left_top_tile, left_bottom_tile, \
+    right_bottom_tile, right_top_tile
+
+metadata = TessagonMetadata(name='Zig-Zag',
+                            num_color_patterns=1,
+                            classification='non_edge',
+                            shapes=['rectangles'],
+                            sides=[4],
+                            uv_ratio=1.0)
+
+
+class ZigZagTile(Tile):
+    # 25 verts in five rows, five columns
+    # 10 faces (2 sets shared with neighbors)
+    #
+    #    o-o-o-o.o  row5  o-o-o-o.o
+    # ^  |...|.|.|        |.1.|.|3|
+    # |  o-o-o.o-o  row4  o-o-o2o-o
+    # |  ..|.|.|..        4.|.|.|.6
+    # |  o-o.o-o-o  row3  o-o5o-o-o
+    #    |.|.|...|        |.|.|.8.|
+    # V  o.o-o-o-o  row2  o7o-o-o-o
+    #    |.|.|.|.|        |.|.9.|10
+    #    o-o-o-o.o  row5  o-o-o-o.o
+    #
+    #    1 2 3 4 5 <-cols
+    #
+    #      U ------>
+
+    def init_verts(self):
+        # [col, row], these read like columns
+        return {1: {1: None, 2: None, 3: None, 4: None, 5: None},
+                2: {1: None, 2: None, 3: None, 4: None, 5: None},
+                3: {1: None, 2: None, 3: None, 4: None, 5: None},
+                4: {1: None, 2: None, 3: None, 4: None, 5: None},
+                5: {1: None, 2: None, 3: None, 4: None, 5: None}}
+
+    def init_faces(self):
+        return {1: None, 2: None, 3: None, 4: None, 5: None, 6: None,
+                7: None, 8: None, 9: None, 10: None}
+
+    def calculate_verts(self):
+        c = {1: 0.0,
+             2: 1/4.0,
+             3: 2/4.0,
+             4: 3/4.0,
+             5: 1.0}
+        for col in self.verts.keys():
+            for row in self.verts[col].keys():
+                # Some verts only get created if neighbors exist
+                if col == 5:
+                    if not self.get_neighbor_tile(['right']):
+                        if not self.get_neighbor_tile(['top']):
+                            if row == 5:
+                                continue
+                            if row == 4:
+                                continue
+                        if not self.get_neighbor_tile(['bottom']):
+                            if row == 1:
+                                continue
+                vert = self.add_vert([col, row], c[col], c[row])
+                if col == 1:
+                    self.set_equivalent_vert(*left_tile([5, row]), vert)
+                    if row == 5:
+                        self.set_equivalent_vert(*left_top_tile([5, 1]),
+                                                 vert)
+                    elif row == 1:
+                        self.set_equivalent_vert(*left_bottom_tile([5, 5]),
+                                                 vert)
+                elif col == 5:
+                    self.set_equivalent_vert(*right_tile([1, row]), vert)
+                    if row == 5:
+                        self.set_equivalent_vert(*right_top_tile([1, 1]),
+                                                 vert)
+                    elif row == 1:
+                        self.set_equivalent_vert(*right_bottom_tile([1, 5]),
+                                                 vert)
+                if row == 5:
+                    self.set_equivalent_vert(*top_tile([col, 1]), vert)
+                elif row == 1:
+                    self.set_equivalent_vert(*bottom_tile([col, 5]), vert)
+
+    def calculate_faces(self):
+        self.add_face(1, [[1, 5],
+                          [1, 4],
+                          [2, 4],
+                          [3, 4],
+                          [3, 5],
+                          [2, 5]])
+
+        self.add_face(2, [[3, 5],
+                          [3, 4],
+                          [3, 3],
+                          [4, 3],
+                          [4, 4],
+                          [4, 5]])
+
+        face = self.add_face(3, [[4, 5],
+                                 [4, 4],
+                                 [5, 4],
+                                 [5, 5],
+                                 top_tile([5, 2]),
+                                 top_tile([4, 2])])
+        self.set_equivalent_face(*top_tile(10), face)
+
+        face = self.add_face(4, [[1, 3],
+                                 [2, 3],
+                                 [2, 4],
+                                 [1, 4],
+                                 left_tile([4, 4]),
+                                 left_tile([4, 3])])
+        self.set_equivalent_face(*left_tile(6), face)
+
+        self.add_face(5, [[3, 2],
+                          [3, 3],
+                          [3, 4],
+                          [2, 4],
+                          [2, 3],
+                          [2, 2]])
+
+        face = self.add_face(6, [[5, 4],
+                                 [4, 4],
+                                 [4, 3],
+                                 [5, 3],
+                                 right_tile([2, 3]),
+                                 right_tile([2, 4])])
+        self.set_equivalent_face(*right_tile(4), face)
+
+        self.add_face(7, [[2, 1],
+                          [2, 2],
+                          [2, 3],
+                          [1, 3],
+                          [1, 2],
+                          [1, 1]])
+
+        self.add_face(8, [[5, 2],
+                          [5, 3],
+                          [4, 3],
+                          [3, 3],
+                          [3, 2],
+                          [4, 2]])
+
+        self.add_face(9, [[4, 1],
+                          [4, 2],
+                          [3, 2],
+                          [2, 2],
+                          [2, 1],
+                          [3, 1]])
+
+        face = self.add_face(10, [[5, 1],
+                                  [5, 2],
+                                  [4, 2],
+                                  [4, 1],
+                                  bottom_tile([4, 4]),
+                                  bottom_tile([5, 4])])
+        self.set_equivalent_face(*bottom_tile(3), face)
+
+    def color_pattern1(self):
+        self.color_face(1, 1)
+        self.color_face(2, 1)
+        self.color_face(7, 1)
+        self.color_face(8, 1)
+
+
+class ZigZagTessagon(Tessagon):
+    tile_class = ZigZagTile
+    metadata = metadata

add_mesh_extra_objects/tessagon/version.py

@@ -0,0 +1 @@
+__version__ = '0.8'