703 lines
19 KiB
Python
703 lines
19 KiB
Python
# SPDX-License-Identifier: GPL-2.0-or-later
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"""Geometry classes and operations.
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Also, vector file representation (Art).
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"""
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__author__ = "howard.trickey@gmail.com"
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import math
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# distances less than about DISTTOL will be considered
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# essentially zero
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DISTTOL = 1e-3
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INVDISTTOL = 1e3
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class Points(object):
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"""Container of points without duplication, each mapped to an int.
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Points are either have dimension at least 2, maybe more.
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Implementation:
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In order to efficiently find duplicates, we quantize the points
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to triples of ints and map from quantized triples to vertex
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index.
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Attributes:
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pos: list of tuple of float - coordinates indexed by
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vertex number
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invmap: dict of (int, int, int) to int - quantized coordinates
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to vertex number map
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"""
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def __init__(self, initlist=[]):
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self.pos = []
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self.invmap = dict()
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for p in initlist:
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self.AddPoint(p)
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@staticmethod
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def Quantize(p):
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"""Quantize the float tuple into an int tuple.
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Args:
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p: tuple of float
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Returns:
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tuple of int - scaled by INVDISTTOL and rounded p
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"""
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return tuple([int(round(v * INVDISTTOL)) for v in p])
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def AddPoint(self, p, allowdups = False):
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"""Add point p to the Points set and return vertex number.
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If there is an existing point which quantizes the same,,
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don't add a new one but instead return existing index.
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Except if allowdups is True, don't do that deduping.
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Args:
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p: tuple of float - coordinates (2-tuple or 3-tuple)
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Returns:
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int - the vertex number of added (or existing) point
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"""
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qp = Points.Quantize(p)
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if qp in self.invmap and not allowdups:
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return self.invmap[qp]
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else:
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self.invmap[qp] = len(self.pos)
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self.pos.append(p)
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return len(self.pos) - 1
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def AddPoints(self, points, allowdups = False):
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"""Add another set of points to this set.
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We need to return a mapping from indices
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in the argument points space into indices
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in this point space.
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Args:
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points: Points - to union into this set
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Returns:
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list of int: maps added indices to new ones
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"""
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vmap = [0] * len(points.pos)
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for i in range(len(points.pos)):
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vmap[i] = self.AddPoint(points.pos[i], allowdups)
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return vmap
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def AddZCoord(self, z):
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"""Change this in place to have a z coordinate, with value z.
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Assumes the coordinates are currently 2d.
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Args:
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z: the value of the z coordinate to add
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Side Effect:
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self now has a z-coordinate added
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"""
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assert(len(self.pos) == 0 or len(self.pos[0]) == 2)
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newinvmap = dict()
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for i, (x, y) in enumerate(self.pos):
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newp = (x, y, z)
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self.pos[i] = newp
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newinvmap[self.Quantize(newp)] = i
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self.invmap = newinvmap
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def AddToZCoord(self, i, delta):
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"""Change the z-coordinate of point with index i to add delta.
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Assumes the coordinates are currently 3d.
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Args:
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i: int - index of a point
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delta: float - value to add to z-coord
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"""
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(x, y, z) = self.pos[i]
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self.pos[i] = (x, y, z + delta)
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class PolyArea(object):
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"""Contains a Polygonal Area (polygon with possible holes).
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A polygon is a list of vertex ids, each an index given by
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a Points object. The list represents a CCW-oriented
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outer boundary (implicitly closed).
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If there are holes, they are lists of CW-oriented vertices
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that should be contained in the outer boundary.
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(So the left face of both the poly and the holes is
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the filled part.)
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Attributes:
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points: Points
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poly: list of vertex ids
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holes: list of lists of vertex ids (each a hole in poly)
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data: any - application data (can hold color, e.g.)
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"""
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def __init__(self, points=None, poly=None, holes=None, data=None):
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self.points = points if points else Points()
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self.poly = poly if poly else []
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self.holes = holes if holes else []
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self.data = data
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def AddHole(self, holepa):
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"""Add a PolyArea's poly as a hole of self.
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Need to reverse the contour and
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adjust the the point indexes and self.points.
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Args:
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holepa: PolyArea
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"""
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vmap = self.points.AddPoints(holepa.points)
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holepoly = [vmap[i] for i in holepa.poly]
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holepoly.reverse()
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self.holes.append(holepoly)
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def ContainsPoly(self, poly, points):
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"""Tests if poly is contained within self.poly.
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Args:
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poly: list of int - indices into points
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points: Points - maps to coords
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Returns:
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bool - True if poly is fully contained within self.poly
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"""
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for v in poly:
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if PointInside(points.pos[v], self.poly, self.points) == -1:
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return False
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return True
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def Normal(self):
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"""Returns the normal of the polyarea's main poly."""
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pos = self.points.pos
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poly = self.poly
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if len(pos) == 0 or len(pos[0]) == 2 or len(poly) == 0:
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print("whoops, not enough info to calculate normal")
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return (0.0, 0.0, 1.0)
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return Newell(poly, self.points)
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class PolyAreas(object):
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"""Contains a list of PolyAreas and a shared Points.
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Attributes:
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polyareas: list of PolyArea
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points: Points
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"""
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def __init__(self):
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self.polyareas = []
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self.points = Points()
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def scale_and_center(self, scaled_side_target):
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"""Adjust the coordinates of the polyareas so that
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it is centered at the origin and has its longest
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dimension scaled to be scaled_side_target."""
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if len(self.points.pos) == 0:
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return
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(minv, maxv) = self.bounds()
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maxside = max([maxv[i] - minv[i] for i in range(2)])
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if maxside > 0.0:
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scale = scaled_side_target / maxside
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else:
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scale = 1.0
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translate = [-0.5 * (maxv[i] + minv[i]) for i in range(2)]
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dim = len(self.points.pos[0])
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if dim == 3:
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translate.append([0.0])
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for v in range(len(self.points.pos)):
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self.points.pos[v] = tuple([scale * (self.points.pos[v][i] + \
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translate[i]) for i in range(dim)])
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def bounds(self):
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"""Find bounding box of polyareas in xy.
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Returns:
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([minx,miny],[maxx,maxy]) - all floats
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"""
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huge = 1e100
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minv = [huge, huge]
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maxv = [-huge, -huge]
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for pa in self.polyareas:
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for face in [pa.poly] + pa.holes:
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for v in face:
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vcoords = self.points.pos[v]
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for i in range(2):
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if vcoords[i] < minv[i]:
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minv[i] = vcoords[i]
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if vcoords[i] > maxv[i]:
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maxv[i] = vcoords[i]
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if minv[0] == huge:
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minv = [0.0, 0.0]
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if maxv[0] == huge:
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maxv = [0.0, 0.0]
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return (minv, maxv)
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class Model(object):
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"""Contains a generic 3d model.
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A generic 3d model has vertices with 3d coordinates.
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Each vertex gets a 'vertex id', which is an index that
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can be used to refer to the vertex and can be used
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to retrieve the 3d coordinates of the point.
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The actual visible part of the geometry are the faces,
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which are n-gons (n>2), specified by a vector of the
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n corner vertices.
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Faces may also have data associated with them,
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and the data will be copied into newly created faces
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from the most likely neighbor faces..
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Attributes:
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points: geom.Points - the 3d vertices
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faces: list of list of indices (each a CCW traversal of a face)
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face_data: list of any - if present, is parallel to
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faces list and holds arbitrary data
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"""
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def __init__(self):
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self.points = Points()
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self.faces = []
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self.face_data = []
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class Art(object):
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"""Contains a vector art diagram.
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Attributes:
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paths: list of Path objects
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"""
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def __init__(self):
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self.paths = []
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class Paint(object):
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"""A color or pattern to fill or stroke with.
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For now, just do colors, but could later do
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patterns or images too.
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Attributes:
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color: (r,g,b) triple of floats, 0.0=no color, 1.0=max color
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"""
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def __init__(self, r=0.0, g=0.0, b=0.0):
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self.color = (r, g, b)
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@staticmethod
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def CMYK(c, m, y, k):
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"""Return Paint specified in CMYK model.
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Uses formula from 6.2.4 of PDF Reference.
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Args:
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c, m, y, k: float - in range [0, 1]
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Returns:
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Paint - with components in rgb form now
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"""
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return Paint(1.0 - min(1.0, c + k),
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1.0 - min(1.0, m + k), 1.0 - min(1.0, y + k))
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black_paint = Paint()
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white_paint = Paint(1.0, 1.0, 1.0)
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ColorDict = {
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'aqua': Paint(0.0, 1.0, 1.0),
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'black': Paint(0.0, 0.0, 0.0),
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'blue': Paint(0.0, 0.0, 1.0),
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'fuchsia': Paint(1.0, 0.0, 1.0),
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'gray': Paint(0.5, 0.5, 0.5),
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'green': Paint(0.0, 0.5, 0.0),
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'lime': Paint(0.0, 1.0, 0.0),
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'maroon': Paint(0.5, 0.0, 0.0),
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'navy': Paint(0.0, 0.0, 0.5),
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'olive': Paint(0.5, 0.5, 0.0),
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'purple': Paint(0.5, 0.0, 0.5),
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'red': Paint(1.0, 0.0, 0.0),
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'silver': Paint(0.75, 0.75, 0.75),
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'teal': Paint(0.0, 0.5, 0.5),
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'white': Paint(1.0, 1.0, 1.0),
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'yellow': Paint(1.0, 1.0, 0.0)
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}
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class Path(object):
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"""Represents a path in the PDF sense, with painting instructions.
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Attributes:
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subpaths: list of Subpath objects
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filled: True if path is to be filled
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fillevenodd: True if use even-odd rule to fill (else non-zero winding)
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stroked: True if path is to be stroked
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fillpaint: Paint to fill with
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strokepaint: Paint to stroke with
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"""
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def __init__(self):
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self.subpaths = []
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self.filled = False
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self.fillevenodd = False
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self.stroked = False
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self.fillpaint = black_paint
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self.strokepaint = black_paint
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def AddSubpath(self, subpath):
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""""Add a subpath."""
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self.subpaths.append(subpath)
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def Empty(self):
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"""Returns True if this Path as no subpaths."""
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return not self.subpaths
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class Subpath(object):
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"""Represents a subpath in PDF sense, either open or closed.
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We'll represent lines, bezier pieces, circular arc pieces
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as tuples with letters giving segment type in first position
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and coordinates (2-tuples of floats) in the other positions.
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Segment types:
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('L', a, b) - line from a to b
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('B', a, b, c, d) - cubic bezier from a to b, with control points c,d
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('Q', a, b, c) - quadratic bezier from a to b, with 1 control point c
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('A', a, b, rad, xrot, large-arc, ccw) - elliptical arc from a to b,
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with rad=(rx, ry) as radii, xrot is x-axis rotation in degrees,
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large-arc is True if arc should be >= 180 degrees,
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ccw is True if start->end follows counter-clockwise direction
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(see SVG spec); note that after rad,
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the rest are floats or bools, not coordinate pairs
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Note that s[1] and s[2] are the start and end points for any segment s.
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Attributes:
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segments: list of segment tuples (see above)
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closed: True if closed
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"""
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def __init__(self):
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self.segments = []
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self.closed = False
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def Empty(self):
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"""Returns True if this subpath as no segments."""
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return not self.segments
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def AddSegment(self, seg):
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"""Add a segment."""
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self.segments.append(seg)
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@staticmethod
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def SegStart(s):
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"""Return start point for segment.
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Args:
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s: a segment tuple
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Returns:
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(float, float): the coordinates of the segment's start point
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"""
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return s[1]
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@staticmethod
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def SegEnd(s):
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"""Return end point for segment.
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Args:
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s: a segment tuple
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Returns:
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(float, float): the coordinates of the segment's end point
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"""
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return s[2]
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class TransformMatrix(object):
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"""Transformation matrix for 2d coordinates.
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The transform matrix is:
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[ a b 0 ]
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[ c d 0 ]
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[ e f 1 ]
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and coordinate transformation is defined by:
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[x' y' 1] = [x y 1] x TransformMatrix
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Attributes:
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a, b, c, d, e, f: floats
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"""
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def __init__(self, a=1.0, b=0.0, c=0.0, d=1.0, e=0.0, f=0.0):
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self.a = a
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self.b = b
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self.c = c
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self.d = d
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self.e = e
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self.f = f
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def __str__(self):
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return str([self.a, self.b, self.c, self.d, self.e, self.f])
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def Copy(self):
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"""Return a copy of this matrix."""
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return TransformMatrix(self.a, self.b, self.c, self.d, self.e, self.f)
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def ComposeTransform(self, a, b, c, d, e, f):
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"""Apply the transform given the the arguments on top of this one.
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This is accomplished by returning t x sel
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where t is the transform matrix that would be formed from the args.
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Arguments:
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a, b, c, d, e, f: float - defines a composing TransformMatrix
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"""
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newa = a * self.a + b * self.c
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newb = a * self.b + b * self.d
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newc = c * self.a + d * self.c
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newd = c * self.b + d * self.d
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newe = e * self.a + f * self.c + self.e
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newf = e * self.b + f * self.d + self.f
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self.a = newa
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self.b = newb
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self.c = newc
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self.d = newd
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self.e = newe
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self.f = newf
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def Apply(self, pt):
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"""Return the result of applying this transform to pt = (x,y).
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Arguments:
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(x, y) : (float, float)
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Returns:
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(x', y'): 2-tuple of floats, the result of [x y 1] x self
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"""
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(x, y) = pt
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return (self.a * x + self.c * y + self.e, \
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self.b * x + self.d * y + self.f)
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def ApproxEqualPoints(p, q):
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"""Return True if p and q are approximately the same points.
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Args:
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p: n-tuple of float
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q: n-tuple of float
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Returns:
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bool - True if the 1-norm <= DISTTOL
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"""
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for i in range(len(p)):
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if abs(p[i] - q[i]) > DISTTOL:
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return False
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return True
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def PointInside(v, a, points):
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"""Return 1, 0, or -1 as v is inside, on, or outside polygon.
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Cf. Eric Haines ptinpoly in Graphics Gems IV.
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Args:
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v : (float, float) or (float, float, float) - coordinates of a point
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a : list of vertex indices defining polygon (assumed CCW)
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points: Points - to get coordinates for polygon
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Returns:
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1, 0, -1: as v is inside, on, or outside polygon a
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"""
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(xv, yv) = (v[0], v[1])
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vlast = points.pos[a[-1]]
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(x0, y0) = (vlast[0], vlast[1])
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if x0 == xv and y0 == yv:
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return 0
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yflag0 = y0 > yv
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inside = False
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n = len(a)
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for i in range(0, n):
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vi = points.pos[a[i]]
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(x1, y1) = (vi[0], vi[1])
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if x1 == xv and y1 == yv:
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return 0
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yflag1 = y1 > yv
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if yflag0 != yflag1:
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xflag0 = x0 > xv
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xflag1 = x1 > xv
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if xflag0 == xflag1:
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if xflag0:
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inside = not inside
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else:
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z = x1 - (y1 - yv) * (x0 - x1) / (y0 - y1)
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|
if z >= xv:
|
|
inside = not inside
|
|
x0 = x1
|
|
y0 = y1
|
|
yflag0 = yflag1
|
|
if inside:
|
|
return 1
|
|
else:
|
|
return -1
|
|
|
|
|
|
def SignedArea(polygon, points):
|
|
"""Return the area of the polygon, positive if CCW, negative if CW.
|
|
|
|
Args:
|
|
polygon: list of vertex indices
|
|
points: Points
|
|
Returns:
|
|
float - area of polygon, positive if it was CCW, else negative
|
|
"""
|
|
|
|
a = 0.0
|
|
n = len(polygon)
|
|
for i in range(0, n):
|
|
u = points.pos[polygon[i]]
|
|
v = points.pos[polygon[(i + 1) % n]]
|
|
a += u[0] * v[1] - u[1] * v[0]
|
|
return 0.5 * a
|
|
|
|
|
|
def VecAdd(a, b):
|
|
"""Return vector a-b.
|
|
|
|
Args:
|
|
a: n-tuple of floats
|
|
b: n-tuple of floats
|
|
Returns:
|
|
n-tuple of floats - pairwise addition a+b
|
|
"""
|
|
|
|
n = len(a)
|
|
assert(n == len(b))
|
|
return tuple([a[i] + b[i] for i in range(n)])
|
|
|
|
|
|
def VecSub(a, b):
|
|
"""Return vector a-b.
|
|
|
|
Args:
|
|
a: n-tuple of floats
|
|
b: n-tuple of floats
|
|
Returns:
|
|
n-tuple of floats - pairwise subtraction a-b
|
|
"""
|
|
|
|
n = len(a)
|
|
assert(n == len(b))
|
|
return tuple([a[i] - b[i] for i in range(n)])
|
|
|
|
|
|
def VecDot(a, b):
|
|
"""Return the dot product of two vectors.
|
|
|
|
Args:
|
|
a: n-tuple of floats
|
|
b: n-tuple of floats
|
|
Returns:
|
|
n-tuple of floats - dot product of a and b
|
|
"""
|
|
|
|
n = len(a)
|
|
assert(n == len(b))
|
|
sum = 0.0
|
|
for i in range(n):
|
|
sum += a[i] * b[i]
|
|
return sum
|
|
|
|
|
|
def VecLen(a):
|
|
"""Return the Euclidean length of the argument vector.
|
|
|
|
Args:
|
|
a: n-tuple of floats
|
|
Returns:
|
|
float: the 2-norm of a
|
|
"""
|
|
|
|
s = 0.0
|
|
for v in a:
|
|
s += v * v
|
|
return math.sqrt(s)
|
|
|
|
|
|
def Newell(poly, points):
|
|
"""Use Newell method to find polygon normal.
|
|
|
|
Assume poly has length at least 3 and points are 3d.
|
|
|
|
Args:
|
|
poly: list of int - indices into points.pos
|
|
points: Points - assumed 3d
|
|
Returns:
|
|
(float, float, float) - the average normal
|
|
"""
|
|
|
|
sumx = 0.0
|
|
sumy = 0.0
|
|
sumz = 0.0
|
|
n = len(poly)
|
|
pos = points.pos
|
|
for i, ai in enumerate(poly):
|
|
bi = poly[(i + 1) % n]
|
|
a = pos[ai]
|
|
b = pos[bi]
|
|
sumx += (a[1] - b[1]) * (a[2] + b[2])
|
|
sumy += (a[2] - b[2]) * (a[0] + b[0])
|
|
sumz += (a[0] - b[0]) * (a[1] + b[1])
|
|
return Norm3(sumx, sumy, sumz)
|
|
|
|
|
|
def Norm3(x, y, z):
|
|
"""Return vector (x,y,z) normalized by dividing by squared length.
|
|
Return (0.0, 0.0, 1.0) if the result is undefined."""
|
|
sqrlen = x * x + y * y + z * z
|
|
if sqrlen < 1e-100:
|
|
return (0.0, 0.0, 1.0)
|
|
else:
|
|
try:
|
|
d = math.sqrt(sqrlen)
|
|
return (x / d, y / d, z / d)
|
|
except:
|
|
return (0.0, 0.0, 1.0)
|
|
|
|
|
|
# We're using right-hand coord system, where
|
|
# forefinger=x, middle=y, thumb=z on right hand.
|
|
# Then, e.g., (1,0,0) x (0,1,0) = (0,0,1)
|
|
def Cross3(a, b):
|
|
"""Return the cross product of two vectors, a x b."""
|
|
|
|
(ax, ay, az) = a
|
|
(bx, by, bz) = b
|
|
return (ay * bz - az * by, az * bx - ax * bz, ax * by - ay * bx)
|
|
|
|
|
|
def MulPoint3(p, m):
|
|
"""Return matrix multiplication of p times m
|
|
where m is a 4x3 matrix and p is a 3d point, extended with 1."""
|
|
|
|
(x, y, z) = p
|
|
return (x * m[0] + y * m[3] + z * m[6] + m[9],
|
|
x * m[1] + y * m[4] + z * m[7] + m[10],
|
|
x * m[2] + y * m[5] + z * m[8] + m[11])
|