Assert that texture is valid before binding it.

# Conflicts:
#	source/blender/nodes/geometry/nodes/node_geo_input_normal.cc

source/blender/blenkernel/BKE_attribute_access.hh

@@ -26,9 +26,8 @@
 #include "BKE_attribute.h"
 
 #include "BLI_color.hh"
-#include "BLI_float2.hh"
-#include "BLI_float3.hh"
 #include "BLI_function_ref.hh"
+#include "BLI_math_vec_types.hh"
 
 /**
  * This file defines classes that help to provide access to attribute data on a #GeometryComponent.

source/blender/blenkernel/BKE_attribute_math.hh

@@ -18,8 +18,7 @@
 
 #include "BLI_array.hh"
 #include "BLI_color.hh"
-#include "BLI_float2.hh"
-#include "BLI_float3.hh"
+#include "BLI_math_vec_types.hh"
 
 #include "DNA_customdata_types.h"
 
@@ -160,12 +159,12 @@ template<> inline float mix2(const float factor, const float &a, const float &b)
 
 template<> inline float2 mix2(const float factor, const float2 &a, const float2 &b)
 {
-  return float2::interpolate(a, b, factor);
+  return math::interpolate(a, b, factor);
 }
 
 template<> inline float3 mix2(const float factor, const float3 &a, const float3 &b)
 {
-  return float3::interpolate(a, b, factor);
+  return math::interpolate(a, b, factor);
 }
 
 template<>

source/blender/blenkernel/BKE_geometry_set.hh

@@ -23,11 +23,11 @@
 #include <atomic>
 #include <iostream>
 
-#include "BLI_float3.hh"
 #include "BLI_float4x4.hh"
 #include "BLI_function_ref.hh"
 #include "BLI_hash.hh"
 #include "BLI_map.hh"
+#include "BLI_math_vec_types.hh"
 #include "BLI_set.hh"
 #include "BLI_user_counter.hh"
 #include "BLI_vector_set.hh"

source/blender/blenkernel/BKE_mesh_sample.hh

@@ -22,7 +22,7 @@
 
 #include "FN_generic_virtual_array.hh"
 
-#include "BLI_float3.hh"
+#include "BLI_math_vec_types.hh"
 
 #include "BKE_attribute.h"
 

source/blender/blenkernel/BKE_spline.hh

@@ -24,8 +24,8 @@
 
 #include "FN_generic_virtual_array.hh"
 
-#include "BLI_float3.hh"
 #include "BLI_float4x4.hh"
+#include "BLI_math_vec_types.hh"
 #include "BLI_vector.hh"
 
 #include "BKE_attribute_access.hh"

source/blender/blenkernel/BKE_volume.h

@@ -163,8 +163,8 @@ bool BKE_volume_save(const struct Volume *volume,
  * file or copy shared grids to make them writeable. */
 
 #ifdef __cplusplus
-#  include "BLI_float3.hh"
 #  include "BLI_float4x4.hh"
+#  include "BLI_math_vec_types.hh"
 #  include "BLI_string_ref.hh"
 
 bool BKE_volume_min_max(const Volume *volume, blender::float3 &r_min, blender::float3 &r_max);

source/blender/blenkernel/intern/DerivedMesh.cc

@@ -38,9 +38,9 @@
 #include "BLI_array.h"
 #include "BLI_bitmap.h"
 #include "BLI_blenlib.h"
-#include "BLI_float2.hh"
 #include "BLI_linklist.h"
 #include "BLI_math.h"
+#include "BLI_math_vec_types.hh"
 #include "BLI_task.h"
 #include "BLI_task.hh"
 #include "BLI_utildefines.h"

source/blender/blenkernel/intern/attribute_access.cc

@@ -30,7 +30,7 @@
 #include "DNA_pointcloud_types.h"
 
 #include "BLI_color.hh"
-#include "BLI_float2.hh"
+#include "BLI_math_vec_types.hh"
 #include "BLI_span.hh"
 
 #include "BLT_translation.h"

source/blender/blenkernel/intern/geometry_component_mesh.cc

@@ -217,9 +217,8 @@ VArray<float3> mesh_normals_varray(const MeshComponent &mesh_component,
        * calculating unnecessary values and to allow normalizing the result much more simply. */
       for (const int i : mask) {
         const MEdge &edge = edges[i];
-        edge_normals[i] = float3::interpolate(
-                              vert_normals_span[edge.v1], vert_normals_span[edge.v2], 0.5f)
-                              .normalized();
+        edge_normals[i] = math::normalize(
+            math::interpolate(vert_normals_span[edge.v1], vert_normals_span[edge.v2], 0.5f));
       }
 
       return VArray<float3>::ForContainer(std::move(edge_normals));

source/blender/blenkernel/intern/gpencil_geom.cc

@@ -33,10 +33,10 @@
 
 #include "BLI_array_utils.h"
 #include "BLI_blenlib.h"
-#include "BLI_float3.hh"
 #include "BLI_ghash.h"
 #include "BLI_hash.h"
 #include "BLI_heap.h"
+#include "BLI_math_vec_types.hh"
 #include "BLI_math_vector.h"
 #include "BLI_polyfill_2d.h"
 #include "BLI_span.hh"

source/blender/blenkernel/intern/hair.cc

@@ -28,9 +28,9 @@
 #include "DNA_material_types.h"
 #include "DNA_object_types.h"
 
-#include "BLI_float3.hh"
 #include "BLI_listbase.h"
 #include "BLI_math_base.h"
+#include "BLI_math_vec_types.hh"
 #include "BLI_rand.h"
 #include "BLI_string.h"
 #include "BLI_utildefines.h"

source/blender/blenkernel/intern/mesh.cc

@@ -36,13 +36,13 @@
 #include "BLI_bitmap.h"
 #include "BLI_edgehash.h"
 #include "BLI_endian_switch.h"
-#include "BLI_float3.hh"
 #include "BLI_ghash.h"
 #include "BLI_hash.h"
 #include "BLI_index_range.hh"
 #include "BLI_linklist.h"
 #include "BLI_listbase.h"
 #include "BLI_math.h"
+#include "BLI_math_vec_types.hh"
 #include "BLI_memarena.h"
 #include "BLI_string.h"
 #include "BLI_task.hh"
@@ -1597,16 +1597,16 @@ bool BKE_mesh_minmax(const Mesh *me, float r_min[3], float r_max[3])
       [&](IndexRange range, const Result &init) {
         Result result = init;
         for (const int i : range) {
-          float3::min_max(me->mvert[i].co, result.min, result.max);
+          math::min_max(float3(me->mvert[i].co), result.min, result.max);
         }
         return result;
       },
       [](const Result &a, const Result &b) {
-        return Result{float3::min(a.min, b.min), float3::max(a.max, b.max)};
+        return Result{math::min(a.min, b.min), math::max(a.max, b.max)};
       });
 
-  copy_v3_v3(r_min, float3::min(minmax.min, r_min));
-  copy_v3_v3(r_max, float3::max(minmax.max, r_max));
+  copy_v3_v3(r_min, math::min(minmax.min, float3(r_min)));
+  copy_v3_v3(r_max, math::max(minmax.max, float3(r_max)));
 
   return true;
 }

source/blender/blenkernel/intern/mesh_boolean_convert.cc

@@ -32,9 +32,9 @@
 
 #include "BLI_alloca.h"
 #include "BLI_array.hh"
-#include "BLI_float2.hh"
 #include "BLI_float4x4.hh"
 #include "BLI_math.h"
+#include "BLI_math_vec_types.hh"
 #include "BLI_mesh_boolean.hh"
 #include "BLI_mesh_intersect.hh"
 #include "BLI_span.hh"

source/blender/blenkernel/intern/mesh_remesh_voxel.cc

@@ -31,8 +31,8 @@
 #include "MEM_guardedalloc.h"
 
 #include "BLI_array.hh"
-#include "BLI_float3.hh"
 #include "BLI_index_range.hh"
+#include "BLI_math_vec_types.hh"
 #include "BLI_span.hh"
 
 #include "DNA_mesh_types.h"

source/blender/blenkernel/intern/object_dupli.cc

@@ -31,9 +31,9 @@
 #include "BLI_string_utf8.h"
 
 #include "BLI_array.hh"
-#include "BLI_float3.hh"
 #include "BLI_float4x4.hh"
 #include "BLI_math.h"
+#include "BLI_math_vec_types.hh"
 #include "BLI_rand.h"
 #include "BLI_span.hh"
 #include "BLI_vector.hh"
@@ -1026,6 +1026,8 @@ static void get_dupliface_transform_from_coords(Span<float3> coords,
                                                 const float scale_fac,
                                                 float r_mat[4][4])
 {
+  using namespace blender::math;
+
   /* Location. */
   float3 location(0);
   for (const float3 &coord : coords) {
@@ -1036,9 +1038,7 @@ static void get_dupliface_transform_from_coords(Span<float3> coords,
   /* Rotation. */
   float quat[4];
 
-  float3 f_no;
-  cross_poly_v3(f_no, (const float(*)[3])coords.data(), (uint)coords.size());
-  f_no.normalize();
+  float3 f_no = normalize(cross_poly(coords));
   tri_to_quat_ex(quat, coords[0], coords[1], coords[2], f_no);
 
   /* Scale. */

source/blender/blenkernel/intern/pointcloud.cc

@@ -25,9 +25,9 @@
 #include "DNA_object_types.h"
 #include "DNA_pointcloud_types.h"
 
-#include "BLI_float3.hh"
 #include "BLI_index_range.hh"
 #include "BLI_listbase.h"
+#include "BLI_math_vec_types.hh"
 #include "BLI_rand.h"
 #include "BLI_span.hh"
 #include "BLI_string.h"
@@ -275,6 +275,8 @@ struct MinMaxResult {
 
 static MinMaxResult min_max_no_radii(Span<float3> positions)
 {
+  using namespace blender::math;
+
   return blender::threading::parallel_reduce(
       positions.index_range(),
       1024,
@@ -282,17 +284,19 @@ static MinMaxResult min_max_no_radii(Span<float3> positions)
       [&](IndexRange range, const MinMaxResult &init) {
         MinMaxResult result = init;
         for (const int i : range) {
-          float3::min_max(positions[i], result.min, result.max);
+          min_max(positions[i], result.min, result.max);
         }
         return result;
       },
       [](const MinMaxResult &a, const MinMaxResult &b) {
-        return MinMaxResult{float3::min(a.min, b.min), float3::max(a.max, b.max)};
+        return MinMaxResult{min(a.min, b.min), max(a.max, b.max)};
       });
 }
 
 static MinMaxResult min_max_with_radii(Span<float3> positions, Span<float> radii)
 {
+  using namespace blender::math;
+
   return blender::threading::parallel_reduce(
       positions.index_range(),
       1024,
@@ -300,18 +304,20 @@ static MinMaxResult min_max_with_radii(Span<float3> positions, Span<float> radii
       [&](IndexRange range, const MinMaxResult &init) {
         MinMaxResult result = init;
         for (const int i : range) {
-          result.min = float3::min(positions[i] - radii[i], result.min);
-          result.max = float3::max(positions[i] + radii[i], result.max);
+          result.min = min(positions[i] - radii[i], result.min);
+          result.max = max(positions[i] + radii[i], result.max);
         }
         return result;
       },
       [](const MinMaxResult &a, const MinMaxResult &b) {
-        return MinMaxResult{float3::min(a.min, b.min), float3::max(a.max, b.max)};
+        return MinMaxResult{min(a.min, b.min), max(a.max, b.max)};
       });
 }
 
 bool BKE_pointcloud_minmax(const PointCloud *pointcloud, float r_min[3], float r_max[3])
 {
+  using namespace blender::math;
+
   if (!pointcloud->totpoint) {
     return false;
   }
@@ -322,8 +328,8 @@ bool BKE_pointcloud_minmax(const PointCloud *pointcloud, float r_min[3], float r
                                                       {pointcloud->radius, pointcloud->totpoint}) :
                                    min_max_no_radii(positions);
 
-  copy_v3_v3(r_min, float3::min(min_max.min, r_min));
-  copy_v3_v3(r_max, float3::max(min_max.max, r_max));
+  copy_v3_v3(r_min, min(min_max.min, float3(r_min)));
+  copy_v3_v3(r_max, max(min_max.max, float3(r_max)));
 
   return true;
 }
@@ -340,7 +346,7 @@ BoundBox *BKE_pointcloud_boundbox_get(Object *ob)
     ob->runtime.bb = static_cast<BoundBox *>(MEM_callocN(sizeof(BoundBox), "pointcloud boundbox"));
   }
 
-  blender::float3 min, max;
+  float3 min, max;
   INIT_MINMAX(min, max);
   if (ob->runtime.geometry_set_eval != nullptr) {
     ob->runtime.geometry_set_eval->compute_boundbox_without_instances(&min, &max);

source/blender/blenkernel/intern/simulation.cc

@@ -28,9 +28,9 @@
 #include "DNA_simulation_types.h"
 
 #include "BLI_compiler_compat.h"
-#include "BLI_float3.hh"
 #include "BLI_listbase.h"
 #include "BLI_math.h"
+#include "BLI_math_vec_types.hh"
 #include "BLI_rand.h"
 #include "BLI_span.hh"
 #include "BLI_string.h"

source/blender/blenkernel/intern/spline_base.cc

@@ -166,13 +166,15 @@ static void accumulate_lengths(Span<float3> positions,
                                const bool is_cyclic,
                                MutableSpan<float> lengths)
 {
+  using namespace blender::math;
+
   float length = 0.0f;
   for (const int i : IndexRange(positions.size() - 1)) {
-    length += float3::distance(positions[i], positions[i + 1]);
+    length += distance(positions[i], positions[i + 1]);
     lengths[i] = length;
   }
   if (is_cyclic) {
-    lengths.last() = length + float3::distance(positions.last(), positions.first());
+    lengths.last() = length + distance(positions.last(), positions.first());
   }
 }
 
@@ -200,11 +202,13 @@ Span<float> Spline::evaluated_lengths() const
 
 static float3 direction_bisect(const float3 &prev, const float3 &middle, const float3 &next)
 {
-  const float3 dir_prev = (middle - prev).normalized();
-  const float3 dir_next = (next - middle).normalized();
+  using namespace blender::math;
 
-  const float3 result = (dir_prev + dir_next).normalized();
-  if (UNLIKELY(result.is_zero())) {
+  const float3 dir_prev = normalize(middle - prev);
+  const float3 dir_next = normalize(next - middle);
+
+  const float3 result = normalize(dir_prev + dir_next);
+  if (UNLIKELY(is_zero(result))) {
     return float3(0.0f, 0.0f, 1.0f);
   }
   return result;
@@ -214,6 +218,8 @@ static void calculate_tangents(Span<float3> positions,
                                const bool is_cyclic,
                                MutableSpan<float3> tangents)
 {
+  using namespace blender::math;
+
   if (positions.size() == 1) {
     tangents.first() = float3(0.0f, 0.0f, 1.0f);
     return;
@@ -232,8 +238,8 @@ static void calculate_tangents(Span<float3> positions,
     tangents.last() = direction_bisect(second_to_last, last, first);
   }
   else {
-    tangents.first() = (positions[1] - positions[0]).normalized();
-    tangents.last() = (positions.last() - positions[positions.size() - 2]).normalized();
+    tangents.first() = normalize(positions[1] - positions[0]);
+    tangents.last() = normalize(positions.last() - positions[positions.size() - 2]);
   }
 }
 
@@ -264,18 +270,22 @@ static float3 rotate_direction_around_axis(const float3 &direction,
                                            const float3 &axis,
                                            const float angle)
 {
+  using namespace blender::math;
+
   BLI_ASSERT_UNIT_V3(direction);
   BLI_ASSERT_UNIT_V3(axis);
 
-  const float3 axis_scaled = axis * float3::dot(direction, axis);
+  const float3 axis_scaled = axis * dot(direction, axis);
   const float3 diff = direction - axis_scaled;
-  const float3 cross = float3::cross(axis, diff);
+  const float3 cross = blender::math::cross(axis, diff);
 
   return axis_scaled + diff * std::cos(angle) + cross * std::sin(angle);
 }
 
 static void calculate_normals_z_up(Span<float3> tangents, MutableSpan<float3> r_normals)
 {
+  using namespace blender::math;
+
   BLI_assert(r_normals.size() == tangents.size());
 
   /* Same as in `vec_to_quat`. */
@@ -286,7 +296,7 @@ static void calculate_normals_z_up(Span<float3> tangents, MutableSpan<float3> r_
       r_normals[i] = {1.0f, 0.0f, 0.0f};
     }
     else {
-      r_normals[i] = float3(tangent.y, -tangent.x, 0.0f).normalized();
+      r_normals[i] = normalize(float3(tangent.y, -tangent.x, 0.0f));
     }
   }
 }
@@ -298,12 +308,14 @@ static float3 calculate_next_normal(const float3 &last_normal,
                                     const float3 &last_tangent,
                                     const float3 &current_tangent)
 {
-  if (last_tangent.is_zero() || current_tangent.is_zero()) {
+  using namespace blender::math;
+
+  if (is_zero(last_tangent) || is_zero(current_tangent)) {
     return last_normal;
   }
   const float angle = angle_normalized_v3v3(last_tangent, current_tangent);
   if (angle != 0.0) {
-    const float3 axis = float3::cross(last_tangent, current_tangent).normalized();
+    const float3 axis = normalize(cross(last_tangent, current_tangent));
     return rotate_direction_around_axis(last_normal, axis, angle);
   }
   return last_normal;
@@ -313,6 +325,7 @@ static void calculate_normals_minimum(Span<float3> tangents,
                                       const bool cyclic,
                                       MutableSpan<float3> r_normals)
 {
+  using namespace blender::math;
   BLI_assert(r_normals.size() == tangents.size());
 
   if (r_normals.is_empty()) {
@@ -327,7 +340,7 @@ static void calculate_normals_minimum(Span<float3> tangents,
     r_normals[0] = {1.0f, 0.0f, 0.0f};
   }
   else {
-    r_normals[0] = float3(first_tangent.y, -first_tangent.x, 0.0f).normalized();
+    r_normals[0] = normalize(float3(first_tangent.y, -first_tangent.x, 0.0f));
   }
 
   /* Forward normal with minimum twist along the entire spline. */

source/blender/blenkernel/intern/spline_bezier.cc

@@ -199,11 +199,13 @@ void BezierSpline::ensure_auto_handles() const
   }
 
   for (const int i : IndexRange(this->size())) {
+    using namespace blender;
+
     if (ELEM(HandleType::Auto, handle_types_left_[i], handle_types_right_[i])) {
       const float3 prev_diff = positions_[i] - previous_position(positions_, is_cyclic_, i);
       const float3 next_diff = next_position(positions_, is_cyclic_, i) - positions_[i];
-      float prev_len = prev_diff.length();
-      float next_len = next_diff.length();
+      float prev_len = math::length(prev_diff);
+      float next_len = math::length(next_diff);
       if (prev_len == 0.0f) {
         prev_len = 1.0f;
       }
@@ -213,7 +215,7 @@ void BezierSpline::ensure_auto_handles() const
       const float3 dir = next_diff / next_len + prev_diff / prev_len;
 
       /* This magic number is unfortunate, but comes from elsewhere in Blender. */
-      const float len = dir.length() * 2.5614f;
+      const float len = math::length(dir) * 2.5614f;
       if (len != 0.0f) {
         if (handle_types_left_[i] == HandleType::Auto) {
           const float prev_len_clamped = std::min(prev_len, next_len * 5.0f);
@@ -228,12 +230,12 @@ void BezierSpline::ensure_auto_handles() const
 
     if (handle_types_left_[i] == HandleType::Vector) {
       const float3 prev = previous_position(positions_, is_cyclic_, i);
-      handle_positions_left_[i] = float3::interpolate(positions_[i], prev, 1.0f / 3.0f);
+      handle_positions_left_[i] = math::interpolate(positions_[i], prev, 1.0f / 3.0f);
     }
 
     if (handle_types_right_[i] == HandleType::Vector) {
       const float3 next = next_position(positions_, is_cyclic_, i);
-      handle_positions_right_[i] = float3::interpolate(positions_[i], next, 1.0f / 3.0f);
+      handle_positions_right_[i] = math::interpolate(positions_[i], next, 1.0f / 3.0f);
     }
   }
 
@@ -275,6 +277,8 @@ static void set_handle_position(const float3 &position,
                                 float3 &handle,
                                 float3 &handle_other)
 {
+  using namespace blender::math;
+
   /* Don't bother when the handle positions are calculated automatically anyway. */
   if (ELEM(type, BezierSpline::HandleType::Auto, BezierSpline::HandleType::Vector)) {
     return;
@@ -283,9 +287,9 @@ static void set_handle_position(const float3 &position,
   handle = new_value;
   if (type_other == BezierSpline::HandleType::Align) {
     /* Keep track of the old length of the opposite handle. */
-    const float length = float3::distance(handle_other, position);
+    const float length = distance(handle_other, position);
     /* Set the other handle to directly opposite from the current handle. */
-    const float3 dir = (handle - position).normalized();
+    const float3 dir = normalize(handle - position);
     handle_other = position - dir * length;
   }
 }
@@ -353,6 +357,7 @@ int BezierSpline::evaluated_points_size() const
 
 void BezierSpline::correct_end_tangents() const
 {
+  using namespace blender::math;
   if (is_cyclic_) {
     return;
   }
@@ -360,10 +365,10 @@ void BezierSpline::correct_end_tangents() const
   MutableSpan<float3> tangents(evaluated_tangents_cache_);
 
   if (handle_positions_right_.first() != positions_.first()) {
-    tangents.first() = (handle_positions_right_.first() - positions_.first()).normalized();
+    tangents.first() = normalize(handle_positions_right_.first() - positions_.first());
   }
   if (handle_positions_left_.last() != positions_.last()) {
-    tangents.last() = (positions_.last() - handle_positions_left_.last()).normalized();
+    tangents.last() = normalize(positions_.last() - handle_positions_left_.last());
   }
 }
 
@@ -371,20 +376,22 @@ BezierSpline::InsertResult BezierSpline::calculate_segment_insertion(const int i
                                                                      const int next_index,
                                                                      const float parameter)
 {
+  using namespace blender::math;
+
   BLI_assert(parameter <= 1.0f && parameter >= 0.0f);
   BLI_assert(next_index == 0 || next_index == index + 1);
   const float3 &point_prev = positions_[index];
   const float3 &handle_prev = handle_positions_right_[index];
   const float3 &handle_next = handle_positions_left_[next_index];
   const float3 &point_next = positions_[next_index];
-  const float3 center_point = float3::interpolate(handle_prev, handle_next, parameter);
+  const float3 center_point = interpolate(handle_prev, handle_next, parameter);
 
   BezierSpline::InsertResult result;
-  result.handle_prev = float3::interpolate(point_prev, handle_prev, parameter);
-  result.handle_next = float3::interpolate(handle_next, point_next, parameter);
-  result.left_handle = float3::interpolate(result.handle_prev, center_point, parameter);
-  result.right_handle = float3::interpolate(center_point, result.handle_next, parameter);
-  result.position = float3::interpolate(result.left_handle, result.right_handle, parameter);
+  result.handle_prev = interpolate(point_prev, handle_prev, parameter);
+  result.handle_next = interpolate(handle_next, point_next, parameter);
+  result.left_handle = interpolate(result.handle_prev, center_point, parameter);
+  result.right_handle = interpolate(center_point, result.handle_next, parameter);
+  result.position = interpolate(result.left_handle, result.right_handle, parameter);
   return result;
 }
 

source/blender/blenkernel/intern/tracking_test.cc

@@ -5,7 +5,7 @@
 #include "DNA_tracking_types.h"
 
 #include "BKE_tracking.h"
-#include "BLI_float2.hh"
+#include "BLI_math_vec_types.hh"
 
 namespace blender {
 

source/blender/blenkernel/intern/type_conversions.cc

@@ -19,8 +19,7 @@
 #include "FN_multi_function_builder.hh"
 
 #include "BLI_color.hh"
-#include "BLI_float2.hh"
-#include "BLI_float3.hh"
+#include "BLI_math_vec_types.hh"
 
 namespace blender::bke {
 

source/blender/blenkernel/intern/volume.cc

@@ -28,12 +28,12 @@
 
 #include "BLI_compiler_compat.h"
 #include "BLI_fileops.h"
-#include "BLI_float3.hh"
 #include "BLI_float4x4.hh"
 #include "BLI_ghash.h"
 #include "BLI_index_range.hh"
 #include "BLI_map.hh"
 #include "BLI_math.h"
+#include "BLI_math_vec_types.hh"
 #include "BLI_path_util.h"
 #include "BLI_string.h"
 #include "BLI_string_ref.hh"

source/blender/blenkernel/intern/volume_render.cc

@@ -21,8 +21,8 @@
 #include "MEM_guardedalloc.h"
 
 #include "BLI_array.hh"
-#include "BLI_float3.hh"
 #include "BLI_math_matrix.h"
+#include "BLI_math_vec_types.hh"
 #include "BLI_math_vector.h"
 #include "BLI_vector.hh"
 

source/blender/blenkernel/intern/volume_to_mesh.cc

@@ -16,7 +16,7 @@
 
 #include <vector>
 
-#include "BLI_float3.hh"
+#include "BLI_math_vec_types.hh"
 #include "BLI_span.hh"
 #include "BLI_utildefines.h"
 

source/blender/blenlib/BLI_delaunay_2d.h

@@ -215,9 +215,9 @@ void BLI_delaunay_2d_cdt_free(CDT_result *result);
 /* C++ Interface. */
 
 #  include "BLI_array.hh"
-#  include "BLI_double2.hh"
 #  include "BLI_math_mpq.hh"
-#  include "BLI_mpq2.hh"
+#  include "BLI_math_vec_mpq_types.hh"
+#  include "BLI_math_vec_types.hh"
 #  include "BLI_vector.hh"
 
 namespace blender::meshintersect {

source/blender/blenlib/BLI_double2.hh

@@ -1,143 +0,0 @@
-/*
- * This program is free software; you can redistribute it and/or
- * modify it under the terms of the GNU General Public License
- * as published by the Free Software Foundation; either version 2
- * of the License, or (at your option) any later version.
- *
- * This program is distributed in the hope that it will be useful,
- * but WITHOUT ANY WARRANTY; without even the implied warranty of
- * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
- * GNU General Public License for more details.
- *
- * You should have received a copy of the GNU General Public License
- * along with this program; if not, write to the Free Software Foundation,
- * Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
- */
-
-#pragma once
-
-/** \file
- * \ingroup bli
- */
-
-#include "BLI_double3.hh"
-
-namespace blender {
-
-struct double2 {
-  double x, y;
-
-  double2() = default;
-
-  double2(const double *ptr) : x{ptr[0]}, y{ptr[1]}
-  {
-  }
-
-  double2(double x, double y) : x(x), y(y)
-  {
-  }
-
-  double2(const double3 &other) : x(other.x), y(other.y)
-  {
-  }
-
-  operator double *()
-  {
-    return &x;
-  }
-
-  operator const double *() const
-  {
-    return &x;
-  }
-
-  double length() const
-  {
-    return len_v2_db(*this);
-  }
-
-  friend double2 operator+(const double2 &a, const double2 &b)
-  {
-    return {a.x + b.x, a.y + b.y};
-  }
-
-  friend double2 operator-(const double2 &a, const double2 &b)
-  {
-    return {a.x - b.x, a.y - b.y};
-  }
-
-  friend double2 operator*(const double2 &a, double b)
-  {
-    return {a.x * b, a.y * b};
-  }
-
-  friend double2 operator/(const double2 &a, double b)
-  {
-    BLI_assert(b != 0.0);
-    return {a.x / b, a.y / b};
-  }
-
-  friend double2 operator*(double a, const double2 &b)
-  {
-    return b * a;
-  }
-
-  friend bool operator==(const double2 &a, const double2 &b)
-  {
-    return a.x == b.x && a.y == b.y;
-  }
-
-  friend bool operator!=(const double2 &a, const double2 &b)
-  {
-    return a.x != b.x || a.y != b.y;
-  }
-
-  friend std::ostream &operator<<(std::ostream &stream, const double2 &v)
-  {
-    stream << "(" << v.x << ", " << v.y << ")";
-    return stream;
-  }
-
-  static double dot(const double2 &a, const double2 &b)
-  {
-    return a.x * b.x + a.y * b.y;
-  }
-
-  static double2 interpolate(const double2 &a, const double2 &b, double t)
-  {
-    return a * (1 - t) + b * t;
-  }
-
-  static double2 abs(const double2 &a)
-  {
-    return double2(fabs(a.x), fabs(a.y));
-  }
-
-  static double distance(const double2 &a, const double2 &b)
-  {
-    return (a - b).length();
-  }
-
-  static double distance_squared(const double2 &a, const double2 &b)
-  {
-    double2 diff = a - b;
-    return double2::dot(diff, diff);
-  }
-
-  struct isect_result {
-    enum {
-      LINE_LINE_COLINEAR = -1,
-      LINE_LINE_NONE = 0,
-      LINE_LINE_EXACT = 1,
-      LINE_LINE_CROSS = 2,
-    } kind;
-    double lambda;
-  };
-
-  static isect_result isect_seg_seg(const double2 &v1,
-                                    const double2 &v2,
-                                    const double2 &v3,
-                                    const double2 &v4);
-};
-
-}  // namespace blender

source/blender/blenlib/BLI_double3.hh

@@ -1,246 +0,0 @@
-/*
- * This program is free software; you can redistribute it and/or
- * modify it under the terms of the GNU General Public License
- * as published by the Free Software Foundation; either version 2
- * of the License, or (at your option) any later version.
- *
- * This program is distributed in the hope that it will be useful,
- * but WITHOUT ANY WARRANTY; without even the implied warranty of
- * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
- * GNU General Public License for more details.
- *
- * You should have received a copy of the GNU General Public License
- * along with this program; if not, write to the Free Software Foundation,
- * Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
- */
-
-#pragma once
-
-/** \file
- * \ingroup bli
- */
-
-#include <iostream>
-
-#include "BLI_math_vector.h"
-#include "BLI_span.hh"
-
-namespace blender {
-
-struct double3 {
-  double x, y, z;
-
-  double3() = default;
-
-  double3(const double *ptr) : x{ptr[0]}, y{ptr[1]}, z{ptr[2]}
-  {
-  }
-
-  double3(const double (*ptr)[3]) : double3((const double *)ptr)
-  {
-  }
-
-  explicit double3(double value) : x(value), y(value), z(value)
-  {
-  }
-
-  explicit double3(int value) : x(value), y(value), z(value)
-  {
-  }
-
-  double3(double x, double y, double z) : x{x}, y{y}, z{z}
-  {
-  }
-
-  operator const double *() const
-  {
-    return &x;
-  }
-
-  operator double *()
-  {
-    return &x;
-  }
-
-  double normalize_and_get_length()
-  {
-    return normalize_v3_db(*this);
-  }
-
-  double3 normalized() const
-  {
-    double3 result;
-    normalize_v3_v3_db(result, *this);
-    return result;
-  }
-
-  double length() const
-  {
-    return len_v3_db(*this);
-  }
-
-  double length_squared() const
-  {
-    return len_squared_v3_db(*this);
-  }
-
-  void reflect(const double3 &normal)
-  {
-    *this = this->reflected(normal);
-  }
-
-  double3 reflected(const double3 &normal) const
-  {
-    double3 result;
-    reflect_v3_v3v3_db(result, *this, normal);
-    return result;
-  }
-
-  static double3 safe_divide(const double3 &a, const double3 &b)
-  {
-    double3 result;
-    result.x = (b.x == 0.0) ? 0.0 : a.x / b.x;
-    result.y = (b.y == 0.0) ? 0.0 : a.y / b.y;
-    result.z = (b.z == 0.0) ? 0.0 : a.z / b.z;
-    return result;
-  }
-
-  void invert()
-  {
-    x = -x;
-    y = -y;
-    z = -z;
-  }
-
-  friend double3 operator+(const double3 &a, const double3 &b)
-  {
-    return {a.x + b.x, a.y + b.y, a.z + b.z};
-  }
-
-  void operator+=(const double3 &b)
-  {
-    this->x += b.x;
-    this->y += b.y;
-    this->z += b.z;
-  }
-
-  friend double3 operator-(const double3 &a, const double3 &b)
-  {
-    return {a.x - b.x, a.y - b.y, a.z - b.z};
-  }
-
-  friend double3 operator-(const double3 &a)
-  {
-    return {-a.x, -a.y, -a.z};
-  }
-
-  void operator-=(const double3 &b)
-  {
-    this->x -= b.x;
-    this->y -= b.y;
-    this->z -= b.z;
-  }
-
-  void operator*=(const double &scalar)
-  {
-    this->x *= scalar;
-    this->y *= scalar;
-    this->z *= scalar;
-  }
-
-  void operator*=(const double3 &other)
-  {
-    this->x *= other.x;
-    this->y *= other.y;
-    this->z *= other.z;
-  }
-
-  friend double3 operator*(const double3 &a, const double3 &b)
-  {
-    return {a.x * b.x, a.y * b.y, a.z * b.z};
-  }
-
-  friend double3 operator*(const double3 &a, const double &b)
-  {
-    return {a.x * b, a.y * b, a.z * b};
-  }
-
-  friend double3 operator*(const double &a, const double3 &b)
-  {
-    return b * a;
-  }
-
-  friend double3 operator/(const double3 &a, const double &b)
-  {
-    BLI_assert(b != 0.0);
-    return {a.x / b, a.y / b, a.z / b};
-  }
-
-  friend bool operator==(const double3 &a, const double3 &b)
-  {
-    return a.x == b.x && a.y == b.y && a.z == b.z;
-  }
-
-  friend bool operator!=(const double3 &a, const double3 &b)
-  {
-    return a.x != b.x || a.y != b.y || a.z != b.z;
-  }
-
-  friend std::ostream &operator<<(std::ostream &stream, const double3 &v)
-  {
-    stream << "(" << v.x << ", " << v.y << ", " << v.z << ")";
-    return stream;
-  }
-
-  static double dot(const double3 &a, const double3 &b)
-  {
-    return a.x * b.x + a.y * b.y + a.z * b.z;
-  }
-
-  static double3 cross_high_precision(const double3 &a, const double3 &b)
-  {
-    double3 result;
-    cross_v3_v3v3_db(result, a, b);
-    return result;
-  }
-
-  static double3 project(const double3 &a, const double3 &b)
-  {
-    double3 result;
-    project_v3_v3v3_db(result, a, b);
-    return result;
-  }
-
-  static double distance(const double3 &a, const double3 &b)
-  {
-    return (a - b).length();
-  }
-
-  static double distance_squared(const double3 &a, const double3 &b)
-  {
-    double3 diff = a - b;
-    return double3::dot(diff, diff);
-  }
-
-  static double3 interpolate(const double3 &a, const double3 &b, double t)
-  {
-    return a * (1 - t) + b * t;
-  }
-
-  static double3 abs(const double3 &a)
-  {
-    return double3(fabs(a.x), fabs(a.y), fabs(a.z));
-  }
-
-  static int dominant_axis(const double3 &a)
-  {
-    double x = (a.x >= 0) ? a.x : -a.x;
-    double y = (a.y >= 0) ? a.y : -a.y;
-    double z = (a.z >= 0) ? a.z : -a.z;
-    return ((x > y) ? ((x > z) ? 0 : 2) : ((y > z) ? 1 : 2));
-  }
-
-  static double3 cross_poly(Span<double3> poly);
-};
-
-}  // namespace blender

source/blender/blenlib/BLI_float2.hh

@@ -1,218 +0,0 @@
-/*
- * This program is free software; you can redistribute it and/or
- * modify it under the terms of the GNU General Public License
- * as published by the Free Software Foundation; either version 2
- * of the License, or (at your option) any later version.
- *
- * This program is distributed in the hope that it will be useful,
- * but WITHOUT ANY WARRANTY; without even the implied warranty of
- * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
- * GNU General Public License for more details.
- *
- * You should have received a copy of the GNU General Public License
- * along with this program; if not, write to the Free Software Foundation,
- * Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
- */
-
-#pragma once
-
-#include "BLI_float3.hh"
-
-namespace blender {
-
-struct float2 {
-  float x, y;
-
-  float2() = default;
-
-  float2(const float *ptr) : x{ptr[0]}, y{ptr[1]}
-  {
-  }
-
-  explicit float2(float value) : x(value), y(value)
-  {
-  }
-
-  explicit float2(int value) : x(value), y(value)
-  {
-  }
-
-  float2(float x, float y) : x(x), y(y)
-  {
-  }
-
-  float2(const float3 &other) : x(other.x), y(other.y)
-  {
-  }
-
-  operator float *()
-  {
-    return &x;
-  }
-
-  operator const float *() const
-  {
-    return &x;
-  }
-
-  float length() const
-  {
-    return len_v2(*this);
-  }
-
-  float length_squared() const
-  {
-    return len_squared_v2(*this);
-  }
-
-  bool is_zero() const
-  {
-    return this->x == 0.0f && this->y == 0.0f;
-  }
-
-  float2 &operator+=(const float2 &other)
-  {
-    x += other.x;
-    y += other.y;
-    return *this;
-  }
-
-  float2 &operator-=(const float2 &other)
-  {
-    x -= other.x;
-    y -= other.y;
-    return *this;
-  }
-
-  float2 &operator*=(float factor)
-  {
-    x *= factor;
-    y *= factor;
-    return *this;
-  }
-
-  float2 &operator/=(float divisor)
-  {
-    x /= divisor;
-    y /= divisor;
-    return *this;
-  }
-
-  uint64_t hash() const
-  {
-    uint64_t x1 = *reinterpret_cast<const uint32_t *>(&x);
-    uint64_t x2 = *reinterpret_cast<const uint32_t *>(&y);
-    return (x1 * 812519) ^ (x2 * 707951);
-  }
-
-  friend float2 operator+(const float2 &a, const float2 &b)
-  {
-    return {a.x + b.x, a.y + b.y};
-  }
-
-  friend float2 operator-(const float2 &a, const float2 &b)
-  {
-    return {a.x - b.x, a.y - b.y};
-  }
-
-  friend float2 operator-(const float2 &a, const float &b)
-  {
-    return {a.x - b, a.y - b};
-  }
-
-  friend float2 operator*(const float2 &a, float b)
-  {
-    return {a.x * b, a.y * b};
-  }
-
-  friend float2 operator/(const float2 &a, float b)
-  {
-    BLI_assert(b != 0.0f);
-    return {a.x / b, a.y / b};
-  }
-
-  friend float2 operator*(float a, const float2 &b)
-  {
-    return b * a;
-  }
-
-  friend std::ostream &operator<<(std::ostream &stream, const float2 &v)
-  {
-    stream << "(" << v.x << ", " << v.y << ")";
-    return stream;
-  }
-
-  static float2 safe_divide(const float2 &a, const float b)
-  {
-    return (b != 0.0f) ? a / b : float2(0.0f);
-  }
-
-  static float2 floor(const float2 &a)
-  {
-    return float2(floorf(a.x), floorf(a.y));
-  }
-
-  /**
-   * Returns a normalized vector. The original vector is not changed.
-   */
-  float2 normalized() const
-  {
-    float2 result;
-    normalize_v2_v2(result, *this);
-    return result;
-  }
-
-  static float dot(const float2 &a, const float2 &b)
-  {
-    return a.x * b.x + a.y * b.y;
-  }
-
-  static float2 interpolate(const float2 &a, const float2 &b, float t)
-  {
-    return a * (1 - t) + b * t;
-  }
-
-  static float2 abs(const float2 &a)
-  {
-    return float2(fabsf(a.x), fabsf(a.y));
-  }
-
-  static float distance(const float2 &a, const float2 &b)
-  {
-    return (a - b).length();
-  }
-
-  static float distance_squared(const float2 &a, const float2 &b)
-  {
-    float2 diff = a - b;
-    return float2::dot(diff, diff);
-  }
-
-  struct isect_result {
-    enum {
-      LINE_LINE_COLINEAR = -1,
-      LINE_LINE_NONE = 0,
-      LINE_LINE_EXACT = 1,
-      LINE_LINE_CROSS = 2,
-    } kind;
-    float lambda;
-    float mu;
-  };
-
-  static isect_result isect_seg_seg(const float2 &v1,
-                                    const float2 &v2,
-                                    const float2 &v3,
-                                    const float2 &v4);
-
-  friend bool operator==(const float2 &a, const float2 &b)
-  {
-    return a.x == b.x && a.y == b.y;
-  }
-
-  friend bool operator!=(const float2 &a, const float2 &b)
-  {
-    return !(a == b);
-  }
-};
-
-}  // namespace blender

source/blender/blenlib/BLI_float3.hh

@@ -1,320 +0,0 @@
-/*
- * This program is free software; you can redistribute it and/or
- * modify it under the terms of the GNU General Public License
- * as published by the Free Software Foundation; either version 2
- * of the License, or (at your option) any later version.
- *
- * This program is distributed in the hope that it will be useful,
- * but WITHOUT ANY WARRANTY; without even the implied warranty of
- * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
- * GNU General Public License for more details.
- *
- * You should have received a copy of the GNU General Public License
- * along with this program; if not, write to the Free Software Foundation,
- * Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
- */
-
-#pragma once
-
-#include <iostream>
-
-#include "BLI_math_vector.h"
-
-namespace blender {
-
-struct float3 {
-  float x, y, z;
-
-  float3() = default;
-
-  float3(const float *ptr) : x{ptr[0]}, y{ptr[1]}, z{ptr[2]}
-  {
-  }
-
-  float3(const float (*ptr)[3]) : float3(static_cast<const float *>(ptr[0]))
-  {
-  }
-
-  explicit float3(float value) : x(value), y(value), z(value)
-  {
-  }
-
-  explicit float3(int value) : x(value), y(value), z(value)
-  {
-  }
-
-  float3(float x, float y, float z) : x{x}, y{y}, z{z}
-  {
-  }
-
-  operator const float *() const
-  {
-    return &x;
-  }
-
-  operator float *()
-  {
-    return &x;
-  }
-
-  friend float3 operator+(const float3 &a, const float3 &b)
-  {
-    return {a.x + b.x, a.y + b.y, a.z + b.z};
-  }
-
-  friend float3 operator+(const float3 &a, const float &b)
-  {
-    return {a.x + b, a.y + b, a.z + b};
-  }
-
-  float3 &operator+=(const float3 &b)
-  {
-    this->x += b.x;
-    this->y += b.y;
-    this->z += b.z;
-    return *this;
-  }
-
-  friend float3 operator-(const float3 &a, const float3 &b)
-  {
-    return {a.x - b.x, a.y - b.y, a.z - b.z};
-  }
-
-  friend float3 operator-(const float3 &a)
-  {
-    return {-a.x, -a.y, -a.z};
-  }
-
-  friend float3 operator-(const float3 &a, const float &b)
-  {
-    return {a.x - b, a.y - b, a.z - b};
-  }
-
-  float3 &operator-=(const float3 &b)
-  {
-    this->x -= b.x;
-    this->y -= b.y;
-    this->z -= b.z;
-    return *this;
-  }
-
-  float3 &operator*=(float scalar)
-  {
-    this->x *= scalar;
-    this->y *= scalar;
-    this->z *= scalar;
-    return *this;
-  }
-
-  float3 &operator*=(const float3 &other)
-  {
-    this->x *= other.x;
-    this->y *= other.y;
-    this->z *= other.z;
-    return *this;
-  }
-
-  friend float3 operator*(const float3 &a, const float3 &b)
-  {
-    return {a.x * b.x, a.y * b.y, a.z * b.z};
-  }
-
-  friend float3 operator*(const float3 &a, float b)
-  {
-    return {a.x * b, a.y * b, a.z * b};
-  }
-
-  friend float3 operator*(float a, const float3 &b)
-  {
-    return b * a;
-  }
-
-  friend float3 operator/(const float3 &a, float b)
-  {
-    BLI_assert(b != 0.0f);
-    return {a.x / b, a.y / b, a.z / b};
-  }
-
-  friend std::ostream &operator<<(std::ostream &stream, const float3 &v)
-  {
-    stream << "(" << v.x << ", " << v.y << ", " << v.z << ")";
-    return stream;
-  }
-
-  friend bool operator==(const float3 &a, const float3 &b)
-  {
-    return a.x == b.x && a.y == b.y && a.z == b.z;
-  }
-
-  friend bool operator!=(const float3 &a, const float3 &b)
-  {
-    return !(a == b);
-  }
-
-  float normalize_and_get_length()
-  {
-    return normalize_v3(*this);
-  }
-
-  /**
-   * Normalizes the vector in place.
-   */
-  void normalize()
-  {
-    normalize_v3(*this);
-  }
-
-  /**
-   * Returns a normalized vector. The original vector is not changed.
-   */
-  float3 normalized() const
-  {
-    float3 result;
-    normalize_v3_v3(result, *this);
-    return result;
-  }
-
-  float length() const
-  {
-    return len_v3(*this);
-  }
-
-  float length_squared() const
-  {
-    return len_squared_v3(*this);
-  }
-
-  bool is_zero() const
-  {
-    return this->x == 0.0f && this->y == 0.0f && this->z == 0.0f;
-  }
-
-  void reflect(const float3 &normal)
-  {
-    *this = this->reflected(normal);
-  }
-
-  float3 reflected(const float3 &normal) const
-  {
-    float3 result;
-    reflect_v3_v3v3(result, *this, normal);
-    return result;
-  }
-
-  static float3 refract(const float3 &incident, const float3 &normal, const float eta)
-  {
-    float3 result;
-    float k = 1.0f - eta * eta * (1.0f - dot(normal, incident) * dot(normal, incident));
-    if (k < 0.0f) {
-      result = float3(0.0f);
-    }
-    else {
-      result = eta * incident - (eta * dot(normal, incident) + sqrt(k)) * normal;
-    }
-    return result;
-  }
-
-  static float3 faceforward(const float3 &vector, const float3 &incident, const float3 &reference)
-  {
-    return dot(reference, incident) < 0.0f ? vector : -vector;
-  }
-
-  static float3 safe_divide(const float3 &a, const float3 &b)
-  {
-    float3 result;
-    result.x = (b.x == 0.0f) ? 0.0f : a.x / b.x;
-    result.y = (b.y == 0.0f) ? 0.0f : a.y / b.y;
-    result.z = (b.z == 0.0f) ? 0.0f : a.z / b.z;
-    return result;
-  }
-
-  static float3 min(const float3 &a, const float3 &b)
-  {
-    return {a.x < b.x ? a.x : b.x, a.y < b.y ? a.y : b.y, a.z < b.z ? a.z : b.z};
-  }
-
-  static float3 max(const float3 &a, const float3 &b)
-  {
-    return {a.x > b.x ? a.x : b.x, a.y > b.y ? a.y : b.y, a.z > b.z ? a.z : b.z};
-  }
-
-  static void min_max(const float3 &vector, float3 &min, float3 &max)
-  {
-    min = float3::min(vector, min);
-    max = float3::max(vector, max);
-  }
-
-  static float3 safe_divide(const float3 &a, const float b)
-  {
-    return (b != 0.0f) ? a / b : float3(0.0f);
-  }
-
-  static float3 floor(const float3 &a)
-  {
-    return float3(floorf(a.x), floorf(a.y), floorf(a.z));
-  }
-
-  void invert()
-  {
-    x = -x;
-    y = -y;
-    z = -z;
-  }
-
-  uint64_t hash() const
-  {
-    uint64_t x1 = *reinterpret_cast<const uint32_t *>(&x);
-    uint64_t x2 = *reinterpret_cast<const uint32_t *>(&y);
-    uint64_t x3 = *reinterpret_cast<const uint32_t *>(&z);
-    return (x1 * 435109) ^ (x2 * 380867) ^ (x3 * 1059217);
-  }
-
-  static float dot(const float3 &a, const float3 &b)
-  {
-    return a.x * b.x + a.y * b.y + a.z * b.z;
-  }
-
-  static float3 cross_high_precision(const float3 &a, const float3 &b)
-  {
-    float3 result;
-    cross_v3_v3v3_hi_prec(result, a, b);
-    return result;
-  }
-
-  static float3 cross(const float3 &a, const float3 &b)
-  {
-    float3 result;
-    cross_v3_v3v3(result, a, b);
-    return result;
-  }
-
-  static float3 project(const float3 &a, const float3 &b)
-  {
-    float3 result;
-    project_v3_v3v3(result, a, b);
-    return result;
-  }
-
-  static float distance(const float3 &a, const float3 &b)
-  {
-    return (a - b).length();
-  }
-
-  static float distance_squared(const float3 &a, const float3 &b)
-  {
-    float3 diff = a - b;
-    return float3::dot(diff, diff);
-  }
-
-  static float3 interpolate(const float3 &a, const float3 &b, float t)
-  {
-    return a * (1 - t) + b * t;
-  }
-
-  static float3 abs(const float3 &a)
-  {
-    return float3(fabsf(a.x), fabsf(a.y), fabsf(a.z));
-  }
-};
-
-}  // namespace blender

source/blender/blenlib/BLI_float4.hh

@@ -1,138 +0,0 @@
-/*
- * This program is free software; you can redistribute it and/or
- * modify it under the terms of the GNU General Public License
- * as published by the Free Software Foundation; either version 2
- * of the License, or (at your option) any later version.
- *
- * This program is distributed in the hope that it will be useful,
- * but WITHOUT ANY WARRANTY; without even the implied warranty of
- * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
- * GNU General Public License for more details.
- *
- * You should have received a copy of the GNU General Public License
- * along with this program; if not, write to the Free Software Foundation,
- * Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
- */
-
-#pragma once
-
-namespace blender {
-
-struct float4 {
-  float x, y, z, w;
-
-  float4() = default;
-
-  float4(const float *ptr) : x{ptr[0]}, y{ptr[1]}, z{ptr[2]}, w{ptr[3]}
-  {
-  }
-
-  explicit float4(float value) : x(value), y(value), z(value), w(value)
-  {
-  }
-
-  explicit float4(int value) : x(value), y(value), z(value), w(value)
-  {
-  }
-
-  float4(float x, float y, float z, float w) : x(x), y(y), z(z), w(w)
-  {
-  }
-
-  operator float *()
-  {
-    return &x;
-  }
-
-  friend float4 operator+(const float4 &a, const float &b)
-  {
-    return {a.x + b, a.y + b, a.z + b, a.w + b};
-  }
-
-  operator const float *() const
-  {
-    return &x;
-  }
-
-  float4 &operator+=(const float4 &other)
-  {
-    x += other.x;
-    y += other.y;
-    z += other.z;
-    w += other.w;
-    return *this;
-  }
-
-  friend float4 operator-(const float4 &a, const float4 &b)
-  {
-    return {a.x - b.x, a.y - b.y, a.z - b.z, a.w - b.w};
-  }
-
-  friend float4 operator-(const float4 &a, const float &b)
-  {
-    return {a.x - b, a.y - b, a.z - b, a.w - b};
-  }
-
-  friend float4 operator+(const float4 &a, const float4 &b)
-  {
-    return {a.x + b.x, a.y + b.y, a.z + b.z, a.w + b.w};
-  }
-
-  friend float4 operator/(const float4 &a, float f)
-  {
-    BLI_assert(f != 0.0f);
-    return a * (1.0f / f);
-  }
-
-  float4 &operator*=(float factor)
-  {
-    x *= factor;
-    y *= factor;
-    z *= factor;
-    w *= factor;
-    return *this;
-  }
-
-  friend float4 operator*(const float4 &a, float b)
-  {
-    return {a.x * b, a.y * b, a.z * b, a.w * b};
-  }
-
-  friend float4 operator*(float a, const float4 &b)
-  {
-    return b * a;
-  }
-
-  float length() const
-  {
-    return len_v4(*this);
-  }
-
-  static float distance(const float4 &a, const float4 &b)
-  {
-    return (a - b).length();
-  }
-
-  static float4 safe_divide(const float4 &a, const float b)
-  {
-    return (b != 0.0f) ? a / b : float4(0.0f);
-  }
-
-  static float4 interpolate(const float4 &a, const float4 &b, float t)
-  {
-    return a * (1 - t) + b * t;
-  }
-
-  static float4 floor(const float4 &a)
-  {
-    return float4(floorf(a.x), floorf(a.y), floorf(a.z), floorf(a.w));
-  }
-
-  static float4 normalize(const float4 &a)
-  {
-    const float t = len_v4(a);
-    return (t != 0.0f) ? a / t : float4(0.0f);
-  }
-};
-
-}  // namespace blender

source/blender/blenlib/BLI_float4x4.hh

@@ -16,8 +16,9 @@
 
 #pragma once
 
-#include "BLI_float3.hh"
 #include "BLI_math_matrix.h"
+#include "BLI_math_vec_types.hh"
+#include "BLI_math_vector.h"
 
 namespace blender {
 
@@ -63,7 +64,7 @@ struct float4x4 {
      * Without the negation, the result would be a so called improper rotation. That means it
      * contains a reflection. Such an improper rotation matrix could not be converted to another
      * representation of a rotation such as euler angles. */
-    const float3 cross = -float3::cross(forward, up);
+    const float3 cross = -math::cross(forward, up);
 
     float4x4 matrix;
     matrix.values[0][0] = forward.x;

source/blender/blenlib/BLI_math_boolean.hh

@@ -21,13 +21,11 @@
  * \brief Math vector functions needed specifically for mesh intersect and boolean.
  */
 
-#include "BLI_double2.hh"
-#include "BLI_double3.hh"
+#include "BLI_math_vec_types.hh"
 
 #ifdef WITH_GMP
 #  include "BLI_math_mpq.hh"
-#  include "BLI_mpq2.hh"
-#  include "BLI_mpq3.hh"
+#  include "BLI_math_vec_mpq_types.hh"
 #endif
 
 namespace blender {

source/blender/blenlib/BLI_math_vec_mpq_types.hh

@@ -0,0 +1,91 @@
+/*
+ * This program is free software; you can redistribute it and/or
+ * modify it under the terms of the GNU General Public License
+ * as published by the Free Software Foundation; either version 2
+ * of the License, or (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software Foundation,
+ * Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#pragma once
+
+/** \file
+ * \ingroup bli
+ */
+
+#ifdef WITH_GMP
+
+#  include "BLI_math_mpq.hh"
+#  include "BLI_math_vec_types.hh"
+
+namespace blender {
+
+using mpq2 = vec_base<mpq_class, 2>;
+using mpq3 = vec_base<mpq_class, 3>;
+
+namespace math {
+
+uint64_t hash_mpq_class(const mpq_class &value);
+
+template<> inline uint64_t vector_hash(const mpq2 &vec)
+{
+  return hash_mpq_class(vec.x) ^ (hash_mpq_class(vec.y) * 33);
+}
+
+template<> inline uint64_t vector_hash(const mpq3 &vec)
+{
+  return hash_mpq_class(vec.x) ^ (hash_mpq_class(vec.y) * 33) ^ (hash_mpq_class(vec.z) * 33 * 37);
+}
+
+/**
+ * Cannot do this exactly in rational arithmetic!
+ * Approximate by going in and out of doubles.
+ */
+template<> inline mpq_class length(const mpq2 &a)
+{
+  return mpq_class(sqrt(length_squared(a).get_d()));
+}
+
+/**
+ * Cannot do this exactly in rational arithmetic!
+ * Approximate by going in and out of doubles.
+ */
+template<> inline mpq_class length(const mpq3 &a)
+{
+  return mpq_class(sqrt(length_squared(a).get_d()));
+}
+
+/**
+ * The buffer avoids allocating a temporary variable.
+ */
+inline mpq_class distance_squared_with_buffer(const mpq3 &a, const mpq3 &b, mpq3 &buffer)
+{
+  buffer = a;
+  buffer -= b;
+  return dot(buffer, buffer);
+}
+
+/**
+ * The buffer avoids allocating a temporary variable.
+ */
+inline mpq_class dot_with_buffer(const mpq3 &a, const mpq3 &b, mpq3 &buffer)
+{
+  buffer = a;
+  buffer *= b;
+  buffer.x += buffer.y;
+  buffer.x += buffer.z;
+  return buffer.x;
+}
+
+}  // namespace math
+
+}  // namespace blender
+
+#endif /* WITH_GMP */

source/blender/blenlib/BLI_math_vec_types.hh

@@ -0,0 +1,566 @@
+/*
+ * This program is free software; you can redistribute it and/or
+ * modify it under the terms of the GNU General Public License
+ * as published by the Free Software Foundation; either version 2
+ * of the License, or (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software Foundation,
+ * Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ *
+ * Copyright 2022, Blender Foundation.
+ */
+
+#pragma once
+
+/** \file
+ * \ingroup bli
+ */
+
+#include <array>
+#include <cmath>
+#include <iostream>
+#include <type_traits>
+
+#include "BLI_math_vector.hh"
+#include "BLI_utildefines.h"
+
+namespace blender {
+
+/* clang-format off */
+template<typename T>
+using as_uint_type = std::conditional_t<sizeof(T) == sizeof(uint8_t), uint8_t,
+                     std::conditional_t<sizeof(T) == sizeof(uint16_t), uint16_t,
+                     std::conditional_t<sizeof(T) == sizeof(uint32_t), uint32_t,
+                     std::conditional_t<sizeof(T) == sizeof(uint64_t), uint64_t, void>>>>;
+/* clang-format on */
+
+template<typename T, int Size> struct vec_struct_base {
+  std::array<T, Size> values;
+};
+
+template<typename T> struct vec_struct_base<T, 2> {
+  T x, y;
+};
+
+template<typename T> struct vec_struct_base<T, 3> {
+  T x, y, z;
+};
+
+template<typename T> struct vec_struct_base<T, 4> {
+  T x, y, z, w;
+};
+
+template<typename T, int Size> struct vec_base : public vec_struct_base<T, Size> {
+
+  static constexpr int type_length = Size;
+
+  using base_type = T;
+  using uint_type = vec_base<as_uint_type<T>, Size>;
+
+  vec_base() = default;
+
+  explicit vec_base(uint value)
+  {
+    for (int i = 0; i < Size; i++) {
+      (*this)[i] = static_cast<T>(value);
+    }
+  }
+
+  explicit vec_base(int value)
+  {
+    for (int i = 0; i < Size; i++) {
+      (*this)[i] = static_cast<T>(value);
+    }
+  }
+
+  explicit vec_base(float value)
+  {
+    for (int i = 0; i < Size; i++) {
+      (*this)[i] = static_cast<T>(value);
+    }
+  }
+
+  explicit vec_base(double value)
+  {
+    for (int i = 0; i < Size; i++) {
+      (*this)[i] = static_cast<T>(value);
+    }
+  }
+
+/* Workaround issue with template BLI_ENABLE_IF((Size == 2)) not working. */
+#define BLI_ENABLE_IF_VEC(_size, _test) int S = _size, BLI_ENABLE_IF((S _test))
+
+  template<BLI_ENABLE_IF_VEC(Size, == 2)> vec_base(T _x, T _y)
+  {
+    (*this)[0] = _x;
+    (*this)[1] = _y;
+  }
+
+  template<BLI_ENABLE_IF_VEC(Size, == 3)> vec_base(T _x, T _y, T _z)
+  {
+    (*this)[0] = _x;
+    (*this)[1] = _y;
+    (*this)[2] = _z;
+  }
+
+  template<BLI_ENABLE_IF_VEC(Size, == 4)> vec_base(T _x, T _y, T _z, T _w)
+  {
+    (*this)[0] = _x;
+    (*this)[1] = _y;
+    (*this)[2] = _z;
+    (*this)[3] = _w;
+  }
+
+  /** Mixed scalar-vector constructors. */
+
+  template<typename U, BLI_ENABLE_IF_VEC(Size, == 3)>
+  constexpr vec_base(const vec_base<U, 2> &xy, T z)
+      : vec_base(static_cast<T>(xy.x), static_cast<T>(xy.y), z)
+  {
+  }
+
+  template<typename U, BLI_ENABLE_IF_VEC(Size, == 3)>
+  constexpr vec_base(T x, const vec_base<U, 2> &yz)
+      : vec_base(x, static_cast<T>(yz.x), static_cast<T>(yz.y))
+  {
+  }
+
+  template<typename U, BLI_ENABLE_IF_VEC(Size, == 4)>
+  vec_base(vec_base<U, 3> xyz, T w)
+      : vec_base(
+            static_cast<T>(xyz.x), static_cast<T>(xyz.y), static_cast<T>(xyz.z), static_cast<T>(w))
+  {
+  }
+
+  template<typename U, BLI_ENABLE_IF_VEC(Size, == 4)>
+  vec_base(T x, vec_base<U, 3> yzw)
+      : vec_base(
+            static_cast<T>(x), static_cast<T>(yzw.x), static_cast<T>(yzw.y), static_cast<T>(yzw.z))
+  {
+  }
+
+  template<typename U, typename V, BLI_ENABLE_IF_VEC(Size, == 4)>
+  vec_base(vec_base<U, 2> xy, vec_base<V, 2> zw)
+      : vec_base(
+            static_cast<T>(xy.x), static_cast<T>(xy.y), static_cast<T>(zw.x), static_cast<T>(zw.y))
+  {
+  }
+
+  template<typename U, BLI_ENABLE_IF_VEC(Size, == 4)>
+  vec_base(vec_base<U, 2> xy, T z, T w)
+      : vec_base(static_cast<T>(xy.x), static_cast<T>(xy.y), static_cast<T>(z), static_cast<T>(w))
+  {
+  }
+
+  template<typename U, BLI_ENABLE_IF_VEC(Size, == 4)>
+  vec_base(T x, vec_base<U, 2> yz, T w)
+      : vec_base(static_cast<T>(x), static_cast<T>(yz.x), static_cast<T>(yz.y), static_cast<T>(w))
+  {
+  }
+
+  template<typename U, BLI_ENABLE_IF_VEC(Size, == 4)>
+  vec_base(T x, T y, vec_base<U, 2> zw)
+      : vec_base(static_cast<T>(x), static_cast<T>(y), static_cast<T>(zw.x), static_cast<T>(zw.y))
+  {
+  }
+
+  /** Masking. */
+
+  template<typename U, int OtherSize, BLI_ENABLE_IF(OtherSize > Size)>
+  explicit vec_base(const vec_base<U, OtherSize> &other)
+  {
+    for (int i = 0; i < Size; i++) {
+      (*this)[i] = static_cast<T>(other[i]);
+    }
+  }
+
+#undef BLI_ENABLE_IF_VEC
+
+  /** Conversion from pointers (from C-style vectors). */
+
+  vec_base(const T *ptr)
+  {
+    for (int i = 0; i < Size; i++) {
+      (*this)[i] = ptr[i];
+    }
+  }
+
+  vec_base(const T (*ptr)[Size]) : vec_base(static_cast<const T *>(ptr[0]))
+  {
+  }
+
+  /** Conversion from other vector types. */
+
+  template<typename U> explicit vec_base(const vec_base<U, Size> &vec)
+  {
+    for (int i = 0; i < Size; i++) {
+      (*this)[i] = static_cast<T>(vec[i]);
+    }
+  }
+
+  /** C-style pointer dereference. */
+
+  operator const T *() const
+  {
+    return reinterpret_cast<const T *>(this);
+  }
+
+  operator T *()
+  {
+    return reinterpret_cast<T *>(this);
+  }
+
+  /** Array access. */
+
+  const T &operator[](int index) const
+  {
+    BLI_assert(index >= 0);
+    BLI_assert(index < Size);
+    return reinterpret_cast<const T *>(this)[index];
+  }
+
+  T &operator[](int index)
+  {
+    BLI_assert(index >= 0);
+    BLI_assert(index < Size);
+    return reinterpret_cast<T *>(this)[index];
+  }
+
+  /** Internal Operators Macro. */
+
+#define BLI_INT_OP(_T) template<typename U = _T, BLI_ENABLE_IF((std::is_integral_v<U>))>
+
+#define BLI_VEC_OP_IMPL(_result, _i, _op) \
+  vec_base _result; \
+  for (int _i = 0; _i < Size; _i++) { \
+    _op; \
+  } \
+  return _result;
+
+#define BLI_VEC_OP_IMPL_SELF(_i, _op) \
+  for (int _i = 0; _i < Size; _i++) { \
+    _op; \
+  } \
+  return *this;
+
+  /** Arithmetic operators. */
+
+  friend vec_base operator+(const vec_base &a, const vec_base &b)
+  {
+    BLI_VEC_OP_IMPL(ret, i, ret[i] = a[i] + b[i]);
+  }
+
+  friend vec_base operator+(const vec_base &a, const T &b)
+  {
+    BLI_VEC_OP_IMPL(ret, i, ret[i] = a[i] + b);
+  }
+
+  friend vec_base operator+(const T &a, const vec_base &b)
+  {
+    return b + a;
+  }
+
+  vec_base &operator+=(const vec_base &b)
+  {
+    BLI_VEC_OP_IMPL_SELF(i, (*this)[i] += b[i]);
+  }
+
+  vec_base &operator+=(const T &b)
+  {
+    BLI_VEC_OP_IMPL_SELF(i, (*this)[i] += b);
+  }
+
+  friend vec_base operator-(const vec_base &a)
+  {
+    BLI_VEC_OP_IMPL(ret, i, ret[i] = -a[i]);
+  }
+
+  friend vec_base operator-(const vec_base &a, const vec_base &b)
+  {
+    BLI_VEC_OP_IMPL(ret, i, ret[i] = a[i] - b[i]);
+  }
+
+  friend vec_base operator-(const vec_base &a, const T &b)
+  {
+    BLI_VEC_OP_IMPL(ret, i, ret[i] = a[i] - b);
+  }
+
+  friend vec_base operator-(const T &a, const vec_base &b)
+  {
+    BLI_VEC_OP_IMPL(ret, i, ret[i] = a - b[i]);
+  }
+
+  vec_base &operator-=(const vec_base &b)
+  {
+    BLI_VEC_OP_IMPL_SELF(i, (*this)[i] -= b[i]);
+  }
+
+  vec_base &operator-=(const T &b)
+  {
+    BLI_VEC_OP_IMPL_SELF(i, (*this)[i] -= b);
+  }
+
+  friend vec_base operator*(const vec_base &a, const vec_base &b)
+  {
+    BLI_VEC_OP_IMPL(ret, i, ret[i] = a[i] * b[i]);
+  }
+
+  friend vec_base operator*(const vec_base &a, T b)
+  {
+    BLI_VEC_OP_IMPL(ret, i, ret[i] = a[i] * b);
+  }
+
+  friend vec_base operator*(T a, const vec_base &b)
+  {
+    return b * a;
+  }
+
+  vec_base &operator*=(T b)
+  {
+    BLI_VEC_OP_IMPL_SELF(i, (*this)[i] *= b);
+  }
+
+  vec_base &operator*=(const vec_base &b)
+  {
+    BLI_VEC_OP_IMPL_SELF(i, (*this)[i] *= b[i]);
+  }
+
+  friend vec_base operator/(const vec_base &a, const vec_base &b)
+  {
+    BLI_assert(!math::is_any_zero(b));
+    BLI_VEC_OP_IMPL(ret, i, ret[i] = a[i] / b[i]);
+  }
+
+  friend vec_base operator/(const vec_base &a, T b)
+  {
+    BLI_assert(b != T(0));
+    BLI_VEC_OP_IMPL(ret, i, ret[i] = a[i] / b);
+  }
+
+  friend vec_base operator/(T a, const vec_base &b)
+  {
+    BLI_assert(!math::is_any_zero(b));
+    BLI_VEC_OP_IMPL(ret, i, ret[i] = a / b[i]);
+  }
+
+  vec_base &operator/=(T b)
+  {
+    BLI_assert(b != T(0));
+    BLI_VEC_OP_IMPL_SELF(i, (*this)[i] /= b);
+  }
+
+  vec_base &operator/=(const vec_base &b)
+  {
+    BLI_assert(!math::is_any_zero(b));
+    BLI_VEC_OP_IMPL_SELF(i, (*this)[i] /= b[i]);
+  }
+
+  /** Binary operators. */
+
+  BLI_INT_OP(T) friend vec_base operator&(const vec_base &a, const vec_base &b)
+  {
+    BLI_VEC_OP_IMPL(ret, i, ret[i] = a[i] & b[i]);
+  }
+
+  BLI_INT_OP(T) friend vec_base operator&(const vec_base &a, T b)
+  {
+    BLI_VEC_OP_IMPL(ret, i, ret[i] = a[i] & b);
+  }
+
+  BLI_INT_OP(T) friend vec_base operator&(T a, const vec_base &b)
+  {
+    return b & a;
+  }
+
+  BLI_INT_OP(T) vec_base &operator&=(T b)
+  {
+    BLI_VEC_OP_IMPL_SELF(i, (*this)[i] &= b);
+  }
+
+  BLI_INT_OP(T) vec_base &operator&=(const vec_base &b)
+  {
+    BLI_VEC_OP_IMPL_SELF(i, (*this)[i] &= b[i]);
+  }
+
+  BLI_INT_OP(T) friend vec_base operator|(const vec_base &a, const vec_base &b)
+  {
+    BLI_VEC_OP_IMPL(ret, i, ret[i] = a[i] | b[i]);
+  }
+
+  BLI_INT_OP(T) friend vec_base operator|(const vec_base &a, T b)
+  {
+    BLI_VEC_OP_IMPL(ret, i, ret[i] = a[i] | b);
+  }
+
+  BLI_INT_OP(T) friend vec_base operator|(T a, const vec_base &b)
+  {
+    return b | a;
+  }
+
+  BLI_INT_OP(T) vec_base &operator|=(T b)
+  {
+    BLI_VEC_OP_IMPL_SELF(i, (*this)[i] |= b);
+  }
+
+  BLI_INT_OP(T) vec_base &operator|=(const vec_base &b)
+  {
+    BLI_VEC_OP_IMPL_SELF(i, (*this)[i] |= b[i]);
+  }
+
+  BLI_INT_OP(T) friend vec_base operator^(const vec_base &a, const vec_base &b)
+  {
+    BLI_VEC_OP_IMPL(ret, i, ret[i] = a[i] ^ b[i]);
+  }
+
+  BLI_INT_OP(T) friend vec_base operator^(const vec_base &a, T b)
+  {
+    BLI_VEC_OP_IMPL(ret, i, ret[i] = a[i] ^ b);
+  }
+
+  BLI_INT_OP(T) friend vec_base operator^(T a, const vec_base &b)
+  {
+    return b ^ a;
+  }
+
+  BLI_INT_OP(T) vec_base &operator^=(T b)
+  {
+    BLI_VEC_OP_IMPL_SELF(i, (*this)[i] ^= b);
+  }
+
+  BLI_INT_OP(T) vec_base &operator^=(const vec_base &b)
+  {
+    BLI_VEC_OP_IMPL_SELF(i, (*this)[i] ^= b[i]);
+  }
+
+  BLI_INT_OP(T) friend vec_base operator~(const vec_base &a)
+  {
+    BLI_VEC_OP_IMPL(ret, i, ret[i] = ~a[i]);
+  }
+
+  /** Bit-shift operators. */
+
+  BLI_INT_OP(T) friend vec_base operator<<(const vec_base &a, const vec_base &b)
+  {
+    BLI_VEC_OP_IMPL(ret, i, ret[i] = a[i] << b[i]);
+  }
+
+  BLI_INT_OP(T) friend vec_base operator<<(const vec_base &a, T b)
+  {
+    BLI_VEC_OP_IMPL(ret, i, ret[i] = a[i] << b);
+  }
+
+  BLI_INT_OP(T) vec_base &operator<<=(T b)
+  {
+    BLI_VEC_OP_IMPL_SELF(i, (*this)[i] <<= b);
+  }
+
+  BLI_INT_OP(T) vec_base &operator<<=(const vec_base &b)
+  {
+    BLI_VEC_OP_IMPL_SELF(i, (*this)[i] <<= b[i]);
+  }
+
+  BLI_INT_OP(T) friend vec_base operator>>(const vec_base &a, const vec_base &b)
+  {
+    BLI_VEC_OP_IMPL(ret, i, ret[i] = a[i] >> b[i]);
+  }
+
+  BLI_INT_OP(T) friend vec_base operator>>(const vec_base &a, T b)
+  {
+    BLI_VEC_OP_IMPL(ret, i, ret[i] = a[i] >> b);
+  }
+
+  BLI_INT_OP(T) vec_base &operator>>=(T b)
+  {
+    BLI_VEC_OP_IMPL_SELF(i, (*this)[i] >>= b);
+  }
+
+  BLI_INT_OP(T) vec_base &operator>>=(const vec_base &b)
+  {
+    BLI_VEC_OP_IMPL_SELF(i, (*this)[i] >>= b[i]);
+  }
+
+  /** Modulo operators. */
+
+  BLI_INT_OP(T) friend vec_base operator%(const vec_base &a, const vec_base &b)
+  {
+    BLI_assert(!math::is_any_zero(b));
+    BLI_VEC_OP_IMPL(ret, i, ret[i] = a[i] % b[i]);
+  }
+
+  BLI_INT_OP(T) friend vec_base operator%(const vec_base &a, T b)
+  {
+    BLI_assert(b != 0);
+    BLI_VEC_OP_IMPL(ret, i, ret[i] = a[i] % b);
+  }
+
+  BLI_INT_OP(T) friend vec_base operator%(T a, const vec_base &b)
+  {
+    BLI_assert(!math::is_any_zero(b));
+    BLI_VEC_OP_IMPL(ret, i, ret[i] = a % b[i]);
+  }
+
+#undef BLI_INT_OP
+#undef BLI_VEC_OP_IMPL
+#undef BLI_VEC_OP_IMPL_SELF
+
+  /** Compare. */
+
+  friend bool operator==(const vec_base &a, const vec_base &b)
+  {
+    for (int i = 0; i < Size; i++) {
+      if (a[i] != b[i]) {
+        return false;
+      }
+    }
+    return true;
+  }
+
+  friend bool operator!=(const vec_base &a, const vec_base &b)
+  {
+    return !(a == b);
+  }
+
+  /** Misc. */
+
+  uint64_t hash() const
+  {
+    return math::vector_hash(*this);
+  }
+
+  friend std::ostream &operator<<(std::ostream &stream, const vec_base &v)
+  {
+    stream << "(";
+    for (int i = 0; i < Size; i++) {
+      stream << v[i];
+      if (i != Size - 1) {
+        stream << ", ";
+      }
+    }
+    stream << ")";
+    return stream;
+  }
+};
+
+using int2 = vec_base<int32_t, 2>;
+using int3 = vec_base<int32_t, 3>;
+using int4 = vec_base<int32_t, 4>;
+
+using uint2 = vec_base<uint32_t, 2>;
+using uint3 = vec_base<uint32_t, 3>;
+using uint4 = vec_base<uint32_t, 4>;
+
+using float2 = vec_base<float, 2>;
+using float3 = vec_base<float, 3>;
+using float4 = vec_base<float, 4>;
+
+using double2 = vec_base<double, 2>;
+using double3 = vec_base<double, 3>;
+using double4 = vec_base<double, 4>;
+
+}  // namespace blender

source/blender/blenlib/BLI_math_vector.hh

@@ -0,0 +1,399 @@
+/*
+ * This program is free software; you can redistribute it and/or
+ * modify it under the terms of the GNU General Public License
+ * as published by the Free Software Foundation; either version 2
+ * of the License, or (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software Foundation,
+ * Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ *
+ * Copyright 2022, Blender Foundation.
+ */
+
+#pragma once
+
+/** \file
+ * \ingroup bli
+ */
+
+#include <cmath>
+#include <type_traits>
+
+#include "BLI_math_base_safe.h"
+#include "BLI_math_vector.h"
+#include "BLI_span.hh"
+#include "BLI_utildefines.h"
+
+#ifdef WITH_GMP
+#  include "BLI_math_mpq.hh"
+#endif
+
+namespace blender::math {
+
+#ifndef NDEBUG
+#  define BLI_ASSERT_UNIT(v) \
+    { \
+      const float _test_unit = length_squared(v); \
+      BLI_assert(!(std::abs(_test_unit - 1.0f) >= BLI_ASSERT_UNIT_EPSILON) || \
+                 !(std::abs(_test_unit) >= BLI_ASSERT_UNIT_EPSILON)); \
+    } \
+    (void)0
+#else
+#  define BLI_ASSERT_UNIT(v) (void)(v)
+#endif
+
+#define bT typename T::base_type
+
+#ifdef WITH_GMP
+#  define BLI_ENABLE_IF_FLT_VEC(T) \
+    BLI_ENABLE_IF((std::is_floating_point_v<typename T::base_type> || \
+                   std::is_same_v<typename T::base_type, mpq_class>))
+#else
+#  define BLI_ENABLE_IF_FLT_VEC(T) BLI_ENABLE_IF((std::is_floating_point_v<typename T::base_type>))
+#endif
+
+#define BLI_ENABLE_IF_INT_VEC(T) BLI_ENABLE_IF((std::is_integral_v<typename T::base_type>))
+
+template<typename T> inline bool is_zero(const T &a)
+{
+  for (int i = 0; i < T::type_length; i++) {
+    if (a[i] != bT(0)) {
+      return false;
+    }
+  }
+  return true;
+}
+
+template<typename T> inline bool is_any_zero(const T &a)
+{
+  for (int i = 0; i < T::type_length; i++) {
+    if (a[i] == bT(0)) {
+      return true;
+    }
+  }
+  return false;
+}
+
+template<typename T> inline T abs(const T &a)
+{
+  T result;
+  for (int i = 0; i < T::type_length; i++) {
+    result[i] = a[i] >= 0 ? a[i] : -a[i];
+  }
+  return result;
+}
+
+template<typename T> inline T min(const T &a, const T &b)
+{
+  T result;
+  for (int i = 0; i < T::type_length; i++) {
+    result[i] = a[i] < b[i] ? a[i] : b[i];
+  }
+  return result;
+}
+
+template<typename T> inline T max(const T &a, const T &b)
+{
+  T result;
+  for (int i = 0; i < T::type_length; i++) {
+    result[i] = a[i] > b[i] ? a[i] : b[i];
+  }
+  return result;
+}
+
+template<typename T> inline T clamp(const T &a, const T &min_v, const T &max_v)
+{
+  T result = a;
+  for (int i = 0; i < T::type_length; i++) {
+    CLAMP(result[i], min_v[i], max_v[i]);
+  }
+  return result;
+}
+
+template<typename T> inline T clamp(const T &a, const bT &min_v, const bT &max_v)
+{
+  T result = a;
+  for (int i = 0; i < T::type_length; i++) {
+    CLAMP(result[i], min_v, max_v);
+  }
+  return result;
+}
+
+template<typename T, BLI_ENABLE_IF_FLT_VEC(T)> inline T mod(const T &a, const T &b)
+{
+  T result;
+  for (int i = 0; i < T::type_length; i++) {
+    BLI_assert(b[i] != 0);
+    result[i] = std::fmod(a[i], b[i]);
+  }
+  return result;
+}
+
+template<typename T, BLI_ENABLE_IF_FLT_VEC(T)> inline T mod(const T &a, bT b)
+{
+  BLI_assert(b != 0);
+  T result;
+  for (int i = 0; i < T::type_length; i++) {
+    result[i] = std::fmod(a[i], b);
+  }
+  return result;
+}
+
+template<typename T, BLI_ENABLE_IF_FLT_VEC(T)> inline T safe_mod(const T &a, const T &b)
+{
+  T result;
+  for (int i = 0; i < T::type_length; i++) {
+    result[i] = (b[i] != 0) ? std::fmod(a[i], b[i]) : 0;
+  }
+  return result;
+}
+
+template<typename T, BLI_ENABLE_IF_FLT_VEC(T)> inline T safe_mod(const T &a, bT b)
+{
+  if (b == 0) {
+    return T(0.0f);
+  }
+  T result;
+  for (int i = 0; i < T::type_length; i++) {
+    result[i] = std::fmod(a[i], b);
+  }
+  return result;
+}
+
+template<typename T> inline void min_max(const T &vector, T &min_vec, T &max_vec)
+{
+  min_vec = min(vector, min_vec);
+  max_vec = max(vector, max_vec);
+}
+
+template<typename T, BLI_ENABLE_IF_FLT_VEC(T)> inline T safe_divide(const T &a, const T &b)
+{
+  T result;
+  for (int i = 0; i < T::type_length; i++) {
+    result[i] = (b[i] == 0) ? 0 : a[i] / b[i];
+  }
+  return result;
+}
+
+template<typename T, BLI_ENABLE_IF_FLT_VEC(T)> inline T safe_divide(const T &a, const bT b)
+{
+  return (b != 0) ? a / b : T(0.0f);
+}
+
+template<typename T, BLI_ENABLE_IF_FLT_VEC(T)> inline T floor(const T &a)
+{
+  T result;
+  for (int i = 0; i < T::type_length; i++) {
+    result[i] = std::floor(a[i]);
+  }
+  return result;
+}
+
+template<typename T, BLI_ENABLE_IF_FLT_VEC(T)> inline T ceil(const T &a)
+{
+  T result;
+  for (int i = 0; i < T::type_length; i++) {
+    result[i] = std::ceil(a[i]);
+  }
+  return result;
+}
+
+template<typename T, BLI_ENABLE_IF_FLT_VEC(T)> inline T fract(const T &a)
+{
+  T result;
+  for (int i = 0; i < T::type_length; i++) {
+    result[i] = a[i] - std::floor(a[i]);
+  }
+  return result;
+}
+
+template<typename T, BLI_ENABLE_IF_FLT_VEC(T)> inline bT dot(const T &a, const T &b)
+{
+  bT result = a[0] * b[0];
+  for (int i = 1; i < T::type_length; i++) {
+    result += a[i] * b[i];
+  }
+  return result;
+}
+
+template<typename T> inline bT length_manhattan(const T &a)
+{
+  bT result = std::abs(a[0]);
+  for (int i = 1; i < T::type_length; i++) {
+    result += std::abs(a[i]);
+  }
+  return result;
+}
+
+template<typename T, BLI_ENABLE_IF_FLT_VEC(T)> inline bT length_squared(const T &a)
+{
+  return dot(a, a);
+}
+
+template<typename T, BLI_ENABLE_IF_FLT_VEC(T)> inline bT length(const T &a)
+{
+  return std::sqrt(length_squared(a));
+}
+
+template<typename T, BLI_ENABLE_IF_FLT_VEC(T)> inline bT distance_manhattan(const T &a, const T &b)
+{
+  return length_manhattan(a - b);
+}
+
+template<typename T, BLI_ENABLE_IF_FLT_VEC(T)> inline bT distance_squared(const T &a, const T &b)
+{
+  return length_squared(a - b);
+}
+
+template<typename T, BLI_ENABLE_IF_FLT_VEC(T)> inline bT distance(const T &a, const T &b)
+{
+  return length(a - b);
+}
+
+template<typename T> uint64_t vector_hash(const T &vec)
+{
+  BLI_STATIC_ASSERT(T::type_length <= 4, "Longer types need to implement vector_hash themself.");
+  const typename T::uint_type &uvec = *reinterpret_cast<const typename T::uint_type *>(&vec);
+  uint64_t result;
+  result = uvec[0] * uint64_t(435109);
+  if constexpr (T::type_length > 1) {
+    result ^= uvec[1] * uint64_t(380867);
+  }
+  if constexpr (T::type_length > 2) {
+    result ^= uvec[2] * uint64_t(1059217);
+  }
+  if constexpr (T::type_length > 3) {
+    result ^= uvec[3] * uint64_t(2002613);
+  }
+  return result;
+}
+
+template<typename T, BLI_ENABLE_IF_FLT_VEC(T)> inline T reflect(const T &incident, const T &normal)
+{
+  BLI_ASSERT_UNIT(normal);
+  return incident - 2.0 * dot(normal, incident) * normal;
+}
+
+template<typename T, BLI_ENABLE_IF_FLT_VEC(T)>
+inline T refract(const T &incident, const T &normal, const bT eta)
+{
+  float dot_ni = dot(normal, incident);
+  float k = 1.0f - eta * eta * (1.0f - dot_ni * dot_ni);
+  if (k < 0.0f) {
+    return T(0.0f);
+  }
+  return eta * incident - (eta * dot_ni + sqrt(k)) * normal;
+}
+
+template<typename T, BLI_ENABLE_IF_FLT_VEC(T)> inline T project(const T &p, const T &v_proj)
+{
+  if (UNLIKELY(is_zero(v_proj))) {
+    return T(0.0f);
+  }
+  return v_proj * (dot(p, v_proj) / dot(v_proj, v_proj));
+}
+
+template<typename T, BLI_ENABLE_IF_FLT_VEC(T)>
+inline T normalize_and_get_length(const T &v, bT &out_length)
+{
+  out_length = length_squared(v);
+  /* A larger value causes normalize errors in a scaled down models with camera extreme close. */
+  constexpr bT threshold = std::is_same_v<bT, double> ? 1.0e-70 : 1.0e-35f;
+  if (out_length > threshold) {
+    out_length = sqrt(out_length);
+    return v / out_length;
+  }
+  /* Either the vector is small or one of it's values contained `nan`. */
+  out_length = 0.0;
+  return T(0.0);
+}
+
+template<typename T, BLI_ENABLE_IF_FLT_VEC(T)> inline T normalize(const T &v)
+{
+  bT len;
+  return normalize_and_get_length(v, len);
+}
+
+template<typename T, BLI_ENABLE_IF_FLT_VEC(T), BLI_ENABLE_IF((T::type_length == 3))>
+inline T cross(const T &a, const T &b)
+{
+  return {a.y * b.z - a.z * b.y, a.z * b.x - a.x * b.z, a.x * b.y - a.y * b.x};
+}
+
+template<typename T,
+         BLI_ENABLE_IF((std::is_same_v<bT, float>)),
+         BLI_ENABLE_IF((T::type_length == 3))>
+inline T cross_high_precision(const T &a, const T &b)
+{
+  return {(float)((double)a.y * b.z - (double)a.z * b.y),
+          (float)((double)a.z * b.x - (double)a.x * b.z),
+          (float)((double)a.x * b.y - (double)a.y * b.x)};
+}
+
+template<typename T, BLI_ENABLE_IF_FLT_VEC(T), BLI_ENABLE_IF((T::type_length == 3))>
+inline T cross_poly(Span<T> poly)
+{
+  /* Newell's Method. */
+  int nv = static_cast<int>(poly.size());
+  if (nv < 3) {
+    return T(0, 0, 0);
+  }
+  const T *v_prev = &poly[nv - 1];
+  const T *v_curr = &poly[0];
+  T n(0, 0, 0);
+  for (int i = 0; i < nv;) {
+    n[0] = n[0] + ((*v_prev)[1] - (*v_curr)[1]) * ((*v_prev)[2] + (*v_curr)[2]);
+    n[1] = n[1] + ((*v_prev)[2] - (*v_curr)[2]) * ((*v_prev)[0] + (*v_curr)[0]);
+    n[2] = n[2] + ((*v_prev)[0] - (*v_curr)[0]) * ((*v_prev)[1] + (*v_curr)[1]);
+    v_prev = v_curr;
+    ++i;
+    if (i < nv) {
+      v_curr = &poly[i];
+    }
+  }
+  return n;
+}
+
+template<typename T, BLI_ENABLE_IF_FLT_VEC(T)> inline T interpolate(const T &a, const T &b, bT t)
+{
+  return a * (1 - t) + b * t;
+}
+
+template<typename T, BLI_ENABLE_IF_FLT_VEC(T)>
+inline T faceforward(const T &vector, const T &incident, const T &reference)
+{
+  return (dot(reference, incident) < 0) ? vector : -vector;
+}
+
+template<typename T> inline int dominant_axis(const T &a)
+{
+  T b = abs(a);
+  return ((b.x > b.y) ? ((b.x > b.z) ? 0 : 2) : ((b.y > b.z) ? 1 : 2));
+}
+
+/** Intersections. */
+
+template<typename T> struct isect_result {
+  enum {
+    LINE_LINE_COLINEAR = -1,
+    LINE_LINE_NONE = 0,
+    LINE_LINE_EXACT = 1,
+    LINE_LINE_CROSS = 2,
+  } kind;
+  bT lambda;
+};
+
+template<typename T, BLI_ENABLE_IF_FLT_VEC(T)>
+isect_result<T> isect_seg_seg(const T &v1, const T &v2, const T &v3, const T &v4);
+
+#undef BLI_ENABLE_IF_FLT_VEC
+#undef BLI_ENABLE_IF_INT_VEC
+#undef bT
+
+}  // namespace blender::math

source/blender/blenlib/BLI_memory_utils.hh

@@ -557,13 +557,4 @@ Container &move_assign_container(Container &dst, Container &&src) noexcept(
   return dst;
 }
 
-/**
- * Utility macro that wraps `std::enable_if` to make it a bit easier to use and less verbose for
- * SFINAE in common cases.
- *
- * \note Often one has to invoke this macro with double parenthesis. That's because the condition
- * often contains a comma and angle brackets are not recognized as parenthesis by the preprocessor.
- */
-#define BLI_ENABLE_IF(condition) typename std::enable_if_t<condition> * = nullptr
-
 }  // namespace blender

source/blender/blenlib/BLI_mesh_intersect.hh

@@ -28,12 +28,11 @@
 #  include <iostream>
 
 #  include "BLI_array.hh"
-#  include "BLI_double3.hh"
-#  include "BLI_float3.hh"
 #  include "BLI_index_range.hh"
 #  include "BLI_map.hh"
 #  include "BLI_math_mpq.hh"
-#  include "BLI_mpq3.hh"
+#  include "BLI_math_vec_mpq_types.hh"
+#  include "BLI_math_vec_types.hh"
 #  include "BLI_span.hh"
 #  include "BLI_utility_mixins.hh"
 #  include "BLI_vector.hh"

source/blender/blenlib/BLI_mpq2.hh

@@ -1,184 +0,0 @@
-/*
- * This program is free software; you can redistribute it and/or
- * modify it under the terms of the GNU General Public License
- * as published by the Free Software Foundation; either version 2
- * of the License, or (at your option) any later version.
- *
- * This program is distributed in the hope that it will be useful,
- * but WITHOUT ANY WARRANTY; without even the implied warranty of
- * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
- * GNU General Public License for more details.
- *
- * You should have received a copy of the GNU General Public License
- * along with this program; if not, write to the Free Software Foundation,
- * Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
- */
-
-#pragma once
-
-/** \file
- * \ingroup bli
- */
-
-#ifdef WITH_GMP
-
-#  include "BLI_math_mpq.hh"
-#  include "BLI_mpq3.hh"
-
-namespace blender {
-
-struct mpq2 {
-  mpq_class x, y;
-
-  mpq2() = default;
-
-  mpq2(const mpq_class *ptr) : x{ptr[0]}, y{ptr[1]}
-  {
-  }
-
-  mpq2(mpq_class x, mpq_class y) : x(x), y(y)
-  {
-  }
-
-  mpq2(const mpq2 &other) : x(other.x), y(other.y)
-  {
-  }
-
-  mpq2(mpq2 &&other) noexcept : x(std::move(other.x)), y(std::move(other.y))
-  {
-  }
-
-  ~mpq2() = default;
-
-  mpq2 &operator=(const mpq2 &other)
-  {
-    if (this != &other) {
-      x = other.x;
-      y = other.y;
-    }
-    return *this;
-  }
-
-  mpq2 &operator=(mpq2 &&other) noexcept
-  {
-    x = std::move(other.x);
-    y = std::move(other.y);
-    return *this;
-  }
-
-  mpq2(const mpq3 &other) : x(other.x), y(other.y)
-  {
-  }
-
-  operator mpq_class *()
-  {
-    return &x;
-  }
-
-  operator const mpq_class *() const
-  {
-    return &x;
-  }
-
-  /**
-   * Cannot do this exactly in rational arithmetic!
-   * Approximate by going in and out of doubles.
-   */
-  mpq_class length() const
-  {
-    mpq_class lsquared = dot(*this, *this);
-    return mpq_class(sqrt(lsquared.get_d()));
-  }
-
-  friend mpq2 operator+(const mpq2 &a, const mpq2 &b)
-  {
-    return {a.x + b.x, a.y + b.y};
-  }
-
-  friend mpq2 operator-(const mpq2 &a, const mpq2 &b)
-  {
-    return {a.x - b.x, a.y - b.y};
-  }
-
-  friend mpq2 operator*(const mpq2 &a, mpq_class b)
-  {
-    return {a.x * b, a.y * b};
-  }
-
-  friend mpq2 operator/(const mpq2 &a, mpq_class b)
-  {
-    BLI_assert(b != 0);
-    return {a.x / b, a.y / b};
-  }
-
-  friend mpq2 operator*(mpq_class a, const mpq2 &b)
-  {
-    return b * a;
-  }
-
-  friend bool operator==(const mpq2 &a, const mpq2 &b)
-  {
-    return a.x == b.x && a.y == b.y;
-  }
-
-  friend bool operator!=(const mpq2 &a, const mpq2 &b)
-  {
-    return a.x != b.x || a.y != b.y;
-  }
-
-  friend std::ostream &operator<<(std::ostream &stream, const mpq2 &v)
-  {
-    stream << "(" << v.x << ", " << v.y << ")";
-    return stream;
-  }
-
-  static mpq_class dot(const mpq2 &a, const mpq2 &b)
-  {
-    return a.x * b.x + a.y * b.y;
-  }
-
-  static mpq2 interpolate(const mpq2 &a, const mpq2 &b, mpq_class t)
-  {
-    return a * (1 - t) + b * t;
-  }
-
-  static mpq2 abs(const mpq2 &a)
-  {
-    mpq_class abs_x = (a.x >= 0) ? a.x : -a.x;
-    mpq_class abs_y = (a.y >= 0) ? a.y : -a.y;
-    return mpq2(abs_x, abs_y);
-  }
-
-  static mpq_class distance(const mpq2 &a, const mpq2 &b)
-  {
-    return (a - b).length();
-  }
-
-  static mpq_class distance_squared(const mpq2 &a, const mpq2 &b)
-  {
-    mpq2 diff = a - b;
-    return dot(diff, diff);
-  }
-
-  struct isect_result {
-    enum {
-      LINE_LINE_COLINEAR = -1,
-      LINE_LINE_NONE = 0,
-      LINE_LINE_EXACT = 1,
-      LINE_LINE_CROSS = 2,
-    } kind;
-    mpq_class lambda;
-  };
-
-  static isect_result isect_seg_seg(const mpq2 &v1,
-                                    const mpq2 &v2,
-                                    const mpq2 &v3,
-                                    const mpq2 &v4);
-
-  /** There is a sensible use for hashing on exact arithmetic types. */
-  uint64_t hash() const;
-};
-
-}  // namespace blender
-
-#endif /* WITH_GMP */

source/blender/blenlib/BLI_mpq3.hh

@@ -1,297 +0,0 @@
-/*
- * This program is free software; you can redistribute it and/or
- * modify it under the terms of the GNU General Public License
- * as published by the Free Software Foundation; either version 2
- * of the License, or (at your option) any later version.
- *
- * This program is distributed in the hope that it will be useful,
- * but WITHOUT ANY WARRANTY; without even the implied warranty of
- * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
- * GNU General Public License for more details.
- *
- * You should have received a copy of the GNU General Public License
- * along with this program; if not, write to the Free Software Foundation,
- * Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
- */
-
-#pragma once
-
-/** \file
- * \ingroup bli
- */
-
-#ifdef WITH_GMP
-
-#  include <iostream>
-
-#  include "BLI_math.h"
-#  include "BLI_math_mpq.hh"
-#  include "BLI_span.hh"
-
-namespace blender {
-
-struct mpq3 {
-  mpq_class x, y, z;
-
-  mpq3() = default;
-
-  mpq3(const mpq_class *ptr) : x{ptr[0]}, y{ptr[1]}, z{ptr[2]}
-  {
-  }
-
-  mpq3(const mpq_class (*ptr)[3]) : mpq3((const mpq_class *)ptr)
-  {
-  }
-
-  explicit mpq3(mpq_class value) : x(value), y(value), z(value)
-  {
-  }
-
-  explicit mpq3(int value) : x(value), y(value), z(value)
-  {
-  }
-
-  mpq3(mpq_class x, mpq_class y, mpq_class z) : x{x}, y{y}, z{z}
-  {
-  }
-
-  operator const mpq_class *() const
-  {
-    return &x;
-  }
-
-  operator mpq_class *()
-  {
-    return &x;
-  }
-
-  /* Cannot do this exactly in rational arithmetic!
-   * Approximate by going in and out of doubles.
-   */
-  mpq_class normalize_and_get_length()
-  {
-    double dv[3] = {x.get_d(), y.get_d(), z.get_d()};
-    double len = normalize_v3_db(dv);
-    this->x = mpq_class(dv[0]);
-    this->y = mpq_class(dv[1]);
-    this->z = mpq_class(dv[2]);
-    return len;
-  }
-
-  mpq3 normalized() const
-  {
-    double dv[3] = {x.get_d(), y.get_d(), z.get_d()};
-    double dr[3];
-    normalize_v3_v3_db(dr, dv);
-    return mpq3(mpq_class(dr[0]), mpq_class(dr[1]), mpq_class(dr[2]));
-  }
-
-  /* Cannot do this exactly in rational arithmetic!
-   * Approximate by going in and out of double.
-   */
-  mpq_class length() const
-  {
-    mpq_class lsquared = this->length_squared();
-    double dsquared = lsquared.get_d();
-    double d = sqrt(dsquared);
-    return mpq_class(d);
-  }
-
-  mpq_class length_squared() const
-  {
-    return x * x + y * y + z * z;
-  }
-
-  void reflect(const mpq3 &normal)
-  {
-    *this = this->reflected(normal);
-  }
-
-  mpq3 reflected(const mpq3 &normal) const
-  {
-    mpq3 result;
-    const mpq_class dot2 = 2 * dot(*this, normal);
-    result.x = this->x - (dot2 * normal.x);
-    result.y = this->y - (dot2 * normal.y);
-    result.z = this->z - (dot2 * normal.z);
-    return result;
-  }
-
-  static mpq3 safe_divide(const mpq3 &a, const mpq3 &b)
-  {
-    mpq3 result;
-    result.x = (b.x == 0) ? mpq_class(0) : a.x / b.x;
-    result.y = (b.y == 0) ? mpq_class(0) : a.y / b.y;
-    result.z = (b.z == 0) ? mpq_class(0) : a.z / b.z;
-    return result;
-  }
-
-  void invert()
-  {
-    x = -x;
-    y = -y;
-    z = -z;
-  }
-
-  friend mpq3 operator+(const mpq3 &a, const mpq3 &b)
-  {
-    return mpq3(a.x + b.x, a.y + b.y, a.z + b.z);
-  }
-
-  void operator+=(const mpq3 &b)
-  {
-    this->x += b.x;
-    this->y += b.y;
-    this->z += b.z;
-  }
-
-  friend mpq3 operator-(const mpq3 &a, const mpq3 &b)
-  {
-    return mpq3(a.x - b.x, a.y - b.y, a.z - b.z);
-  }
-
-  friend mpq3 operator-(const mpq3 &a)
-  {
-    return mpq3(-a.x, -a.y, -a.z);
-  }
-
-  void operator-=(const mpq3 &b)
-  {
-    this->x -= b.x;
-    this->y -= b.y;
-    this->z -= b.z;
-  }
-
-  void operator*=(mpq_class scalar)
-  {
-    this->x *= scalar;
-    this->y *= scalar;
-    this->z *= scalar;
-  }
-
-  void operator*=(const mpq3 &other)
-  {
-    this->x *= other.x;
-    this->y *= other.y;
-    this->z *= other.z;
-  }
-
-  friend mpq3 operator*(const mpq3 &a, const mpq3 &b)
-  {
-    return {a.x * b.x, a.y * b.y, a.z * b.z};
-  }
-
-  friend mpq3 operator*(const mpq3 &a, const mpq_class &b)
-  {
-    return mpq3(a.x * b, a.y * b, a.z * b);
-  }
-
-  friend mpq3 operator*(const mpq_class &a, const mpq3 &b)
-  {
-    return mpq3(a * b.x, a * b.y, a * b.z);
-  }
-
-  friend mpq3 operator/(const mpq3 &a, const mpq_class &b)
-  {
-    BLI_assert(b != 0);
-    return mpq3(a.x / b, a.y / b, a.z / b);
-  }
-
-  friend bool operator==(const mpq3 &a, const mpq3 &b)
-  {
-    return a.x == b.x && a.y == b.y && a.z == b.z;
-  }
-
-  friend bool operator!=(const mpq3 &a, const mpq3 &b)
-  {
-    return a.x != b.x || a.y != b.y || a.z != b.z;
-  }
-
-  friend std::ostream &operator<<(std::ostream &stream, const mpq3 &v)
-  {
-    stream << "(" << v.x << ", " << v.y << ", " << v.z << ")";
-    return stream;
-  }
-
-  static mpq_class dot(const mpq3 &a, const mpq3 &b)
-  {
-    return a.x * b.x + a.y * b.y + a.z * b.z;
-  }
-
-  static mpq_class dot_with_buffer(const mpq3 &a, const mpq3 &b, mpq3 &buffer)
-  {
-    buffer = a;
-    buffer *= b;
-    buffer.x += buffer.y;
-    buffer.x += buffer.z;
-    return buffer.x;
-  }
-
-  static mpq3 cross(const mpq3 &a, const mpq3 &b)
-  {
-    return mpq3(a[1] * b[2] - a[2] * b[1], a[2] * b[0] - a[0] * b[2], a[0] * b[1] - a[1] * b[0]);
-  }
-
-  static mpq3 cross_high_precision(const mpq3 &a, const mpq3 &b)
-  {
-    return cross(a, b);
-  }
-
-  static mpq3 project(const mpq3 &a, const mpq3 &b)
-  {
-    const mpq_class mul = mpq3::dot(a, b) / mpq3::dot(b, b);
-    return mpq3(mul * b[0], mul * b[1], mul * b[2]);
-  }
-
-  static mpq_class distance(const mpq3 &a, const mpq3 &b)
-  {
-    mpq3 diff(a.x - b.x, a.y - b.y, a.z - b.z);
-    return diff.length();
-  }
-
-  static mpq_class distance_squared(const mpq3 &a, const mpq3 &b)
-  {
-    mpq3 diff(a.x - b.x, a.y - b.y, a.z - b.z);
-    return mpq3::dot(diff, diff);
-  }
-
-  static mpq_class distance_squared_with_buffer(const mpq3 &a, const mpq3 &b, mpq3 &buffer)
-  {
-    buffer = a;
-    buffer -= b;
-    return mpq3::dot(buffer, buffer);
-  }
-
-  static mpq3 interpolate(const mpq3 &a, const mpq3 &b, mpq_class t)
-  {
-    mpq_class s = 1 - t;
-    return mpq3(a.x * s + b.x * t, a.y * s + b.y * t, a.z * s + b.z * t);
-  }
-
-  static mpq3 abs(const mpq3 &a)
-  {
-    mpq_class abs_x = (a.x >= 0) ? a.x : -a.x;
-    mpq_class abs_y = (a.y >= 0) ? a.y : -a.y;
-    mpq_class abs_z = (a.z >= 0) ? a.z : -a.z;
-    return mpq3(abs_x, abs_y, abs_z);
-  }
-
-  static int dominant_axis(const mpq3 &a)
-  {
-    mpq_class x = (a.x >= 0) ? a.x : -a.x;
-    mpq_class y = (a.y >= 0) ? a.y : -a.y;
-    mpq_class z = (a.z >= 0) ? a.z : -a.z;
-    return ((x > y) ? ((x > z) ? 0 : 2) : ((y > z) ? 1 : 2));
-  }
-
-  static mpq3 cross_poly(Span<mpq3> poly);
-
-  /** There is a sensible use for hashing on exact arithmetic types. */
-  uint64_t hash() const;
-};
-
-uint64_t hash_mpq_class(const mpq_class &value);
-
-}  // namespace blender
-
-#endif /* WITH_GMP */

source/blender/blenlib/BLI_noise.hh

@@ -16,9 +16,7 @@
 
 #pragma once
 
-#include "BLI_float2.hh"
-#include "BLI_float3.hh"
-#include "BLI_float4.hh"
+#include "BLI_math_vec_types.hh"
 
 namespace blender::noise {
 

source/blender/blenlib/BLI_rand.hh

@@ -20,9 +20,8 @@
 
 #pragma once
 
-#include "BLI_float2.hh"
-#include "BLI_float3.hh"
 #include "BLI_math.h"
+#include "BLI_math_vec_types.hh"
 #include "BLI_span.hh"
 #include "BLI_utildefines.h"
 

source/blender/blenlib/BLI_utildefines.h

@@ -840,6 +840,15 @@ extern bool BLI_memory_is_zero(const void *arr, const size_t arr_size);
 /** No-op for expressions we don't want to instantiate, but must remain valid. */
 #define EXPR_NOP(expr) (void)(0 ? ((void)(expr), 1) : 0)
 
+/**
+ * Utility macro that wraps `std::enable_if` to make it a bit easier to use and less verbose for
+ * SFINAE in common cases.
+ *
+ * \note Often one has to invoke this macro with double parenthesis. That's because the condition
+ * often contains a comma and angle brackets are not recognized as parenthesis by the preprocessor.
+ */
+#define BLI_ENABLE_IF(condition) typename std::enable_if_t<(condition)> * = nullptr
+
 /** \} */
 
 #ifdef __cplusplus

source/blender/blenlib/CMakeLists.txt

@@ -192,8 +192,6 @@ set(SRC
   BLI_dlrbTree.h
   BLI_dot_export.hh
   BLI_dot_export_attribute_enums.hh
-  BLI_double2.hh
-  BLI_double3.hh
   BLI_dynlib.h
   BLI_dynstr.h
   BLI_easing.h
@@ -207,9 +205,6 @@ set(SRC
   BLI_fileops.hh
   BLI_fileops_types.h
   BLI_filereader.h
-  BLI_float2.hh
-  BLI_float3.hh
-  BLI_float4.hh
   BLI_float4x4.hh
   BLI_fnmatch.h
   BLI_function_ref.hh
@@ -258,6 +253,8 @@ set(SRC
   BLI_math_statistics.h
   BLI_math_time.h
   BLI_math_vector.h
+  BLI_math_vec_types.hh
+  BLI_math_vec_mpq_types.hh
   BLI_memarena.h
   BLI_memblock.h
   BLI_memiter.h
@@ -267,8 +264,6 @@ set(SRC
   BLI_mesh_boolean.hh
   BLI_mesh_intersect.hh
   BLI_mmap.h
-  BLI_mpq2.hh
-  BLI_mpq3.hh
   BLI_multi_value_map.hh
   BLI_noise.h
   BLI_noise.hh
@@ -444,6 +439,7 @@ if(WITH_GTESTS)
     tests/BLI_math_rotation_test.cc
     tests/BLI_math_solvers_test.cc
     tests/BLI_math_time_test.cc
+    tests/BLI_math_vec_types_test.cc
     tests/BLI_math_vector_test.cc
     tests/BLI_memiter_test.cc
     tests/BLI_memory_utils_test.cc

source/blender/blenlib/intern/delaunay_2d.cc

@@ -25,11 +25,10 @@
 #include <sstream>
 
 #include "BLI_array.hh"
-#include "BLI_double2.hh"
 #include "BLI_linklist.h"
 #include "BLI_math_boolean.hh"
 #include "BLI_math_mpq.hh"
-#include "BLI_mpq2.hh"
+#include "BLI_math_vec_mpq_types.hh"
 #include "BLI_set.hh"
 #include "BLI_task.hh"
 #include "BLI_vector.hh"
@@ -38,6 +37,8 @@
 
 namespace blender::meshintersect {
 
+using namespace blender::math;
+
 /* Throughout this file, template argument T will be an
  * arithmetic-like type, like float, double, or mpq_class. */
 
@@ -788,11 +789,11 @@ bool in_line<mpq_class>(const FatCo<mpq_class> &a,
   }
   vec2<mpq_class> exact_ab = b.exact - a.exact;
   vec2<mpq_class> exact_ac = c.exact - a.exact;
-  if (vec2<mpq_class>::dot(exact_ab, exact_ac) < 0) {
+  if (dot(exact_ab, exact_ac) < 0) {
     return false;
   }
   vec2<mpq_class> exact_bc = c.exact - b.exact;
-  return vec2<mpq_class>::dot(exact_bc, exact_ac) >= 0;
+  return dot(exact_bc, exact_ac) >= 0;
 }
 #endif
 
@@ -801,11 +802,11 @@ bool in_line<double>(const FatCo<double> &a, const FatCo<double> &b, const FatCo
 {
   vec2<double> ab = b.approx - a.approx;
   vec2<double> ac = c.approx - a.approx;
-  if (vec2<double>::dot(ab, ac) < 0) {
+  if (dot(ab, ac) < 0) {
     return false;
   }
   vec2<double> bc = c.approx - b.approx;
-  return vec2<double>::dot(bc, ac) >= 0;
+  return dot(bc, ac) >= 0;
 }
 
 template<> CDTVert<double>::CDTVert(const vec2<double> &pt)
@@ -1081,7 +1082,7 @@ template<typename T> CDTEdge<T> *CDTArrangement<T>::split_edge(SymEdge<T> *se, T
   SymEdge<T> *sesymprev = prev(sesym);
   SymEdge<T> *sesymprevsym = sym(sesymprev);
   SymEdge<T> *senext = se->next;
-  CDTVert<T> *v = this->add_vert(vec2<T>::interpolate(*a, *b, lambda));
+  CDTVert<T> *v = this->add_vert(interpolate(*a, *b, lambda));
   CDTEdge<T> *e = this->add_edge(v, se->next->vert, se->face, sesym->face);
   sesym->vert = v;
   SymEdge<T> *newse = &e->symedges[0];
@@ -1704,16 +1705,16 @@ void fill_crossdata_for_intersect(const FatCo<T> &curco,
   BLI_assert(se_vcva->vert == vc && se_vcva->next->vert == va);
   BLI_assert(se_vcvb->vert == vc && se_vcvb->next->vert == vb);
   UNUSED_VARS_NDEBUG(vc);
-  auto isect = vec2<T>::isect_seg_seg(va->co.exact, vb->co.exact, curco.exact, v2->co.exact);
+  auto isect = isect_seg_seg<vec2<T>>(va->co.exact, vb->co.exact, curco.exact, v2->co.exact);
   T &lambda = isect.lambda;
   switch (isect.kind) {
-    case vec2<T>::isect_result::LINE_LINE_CROSS: {
+    case isect_result<vec2<T>>::LINE_LINE_CROSS: {
 #ifdef WITH_GMP
       if (!std::is_same<T, mpq_class>::value) {
 #else
       if (true) {
 #endif
-        double len_ab = vec2<double>::distance(va->co.approx, vb->co.approx);
+        double len_ab = distance(va->co.approx, vb->co.approx);
         if (lambda * len_ab <= epsilon) {
           fill_crossdata_for_through_vert(va, se_vcva, cd, cd_next);
         }
@@ -1735,7 +1736,7 @@ void fill_crossdata_for_intersect(const FatCo<T> &curco,
       }
       break;
     }
-    case vec2<T>::isect_result::LINE_LINE_EXACT: {
+    case isect_result<vec2<T>>::LINE_LINE_EXACT: {
       if (lambda == 0) {
         fill_crossdata_for_through_vert(va, se_vcva, cd, cd_next);
       }
@@ -1750,7 +1751,7 @@ void fill_crossdata_for_intersect(const FatCo<T> &curco,
       }
       break;
     }
-    case vec2<T>::isect_result::LINE_LINE_NONE: {
+    case isect_result<vec2<T>>::LINE_LINE_NONE: {
 #ifdef WITH_GMP
       if (std::is_same<T, mpq_class>::value) {
         BLI_assert(false);
@@ -1766,9 +1767,9 @@ void fill_crossdata_for_intersect(const FatCo<T> &curco,
       }
       break;
     }
-    case vec2<T>::isect_result::LINE_LINE_COLINEAR: {
-      if (vec2<double>::distance_squared(va->co.approx, v2->co.approx) <=
-          vec2<double>::distance_squared(vb->co.approx, v2->co.approx)) {
+    case isect_result<vec2<T>>::LINE_LINE_COLINEAR: {
+      if (distance_squared(va->co.approx, v2->co.approx) <=
+          distance_squared(vb->co.approx, v2->co.approx)) {
         fill_crossdata_for_through_vert(va, se_vcva, cd, cd_next);
       }
       else {
@@ -1845,7 +1846,7 @@ void get_next_crossing_from_edge(CrossData<T> *cd,
 {
   CDTVert<T> *va = cd->in->vert;
   CDTVert<T> *vb = cd->in->next->vert;
-  vec2<T> curco = vec2<T>::interpolate(va->co.exact, vb->co.exact, cd->lambda);
+  vec2<T> curco = interpolate(va->co.exact, vb->co.exact, cd->lambda);
   FatCo<T> fat_curco(curco);
   SymEdge<T> *se_ac = sym(cd->in)->next;
   CDTVert<T> *vc = se_ac->next->vert;
@@ -2386,7 +2387,7 @@ template<typename T> void remove_non_constraint_edges_leave_valid_bmesh(CDT_stat
       dissolvable_edges[i].e = e;
       const vec2<double> &co1 = e->symedges[0].vert->co.approx;
       const vec2<double> &co2 = e->symedges[1].vert->co.approx;
-      dissolvable_edges[i].len_squared = vec2<double>::distance_squared(co1, co2);
+      dissolvable_edges[i].len_squared = distance_squared(co1, co2);
       i++;
     }
   }
@@ -2569,18 +2570,18 @@ template<typename T> void detect_holes(CDT_state<T> *cdt_state)
           if (e->symedges[0].face->visit_index == e->symedges[1].face->visit_index) {
             continue; /* Don't count hits on edges between faces in same region. */
           }
-          auto isect = vec2<T>::isect_seg_seg(ray_end.exact,
+          auto isect = isect_seg_seg<vec2<T>>(ray_end.exact,
                                               mid.exact,
                                               e->symedges[0].vert->co.exact,
                                               e->symedges[1].vert->co.exact);
           switch (isect.kind) {
-            case vec2<T>::isect_result::LINE_LINE_CROSS: {
+            case isect_result<vec2<T>>::LINE_LINE_CROSS: {
               hits++;
               break;
             }
-            case vec2<T>::isect_result::LINE_LINE_EXACT:
-            case vec2<T>::isect_result::LINE_LINE_NONE:
-            case vec2<T>::isect_result::LINE_LINE_COLINEAR:
+            case isect_result<vec2<T>>::LINE_LINE_EXACT:
+            case isect_result<vec2<T>>::LINE_LINE_NONE:
+            case isect_result<vec2<T>>::LINE_LINE_COLINEAR:
               break;
           }
         }

source/blender/blenlib/intern/math_boolean.cc

@@ -18,15 +18,10 @@
  * \ingroup bli
  */
 
-#include "BLI_double2.hh"
-#include "BLI_double3.hh"
-#include "BLI_float2.hh"
-#include "BLI_float3.hh"
 #include "BLI_hash.hh"
 #include "BLI_math_boolean.hh"
 #include "BLI_math_mpq.hh"
-#include "BLI_mpq2.hh"
-#include "BLI_mpq3.hh"
+#include "BLI_math_vec_types.hh"
 #include "BLI_span.hh"
 #include "BLI_utildefines.h"
 

source/blender/blenlib/intern/math_vec.cc

@@ -18,89 +18,83 @@
  * \ingroup bli
  */
 
-#include "BLI_double2.hh"
-#include "BLI_double3.hh"
-#include "BLI_float2.hh"
-#include "BLI_float3.hh"
 #include "BLI_hash.hh"
-#include "BLI_math_mpq.hh"
-#include "BLI_mpq2.hh"
-#include "BLI_mpq3.hh"
+#include "BLI_math_vec_mpq_types.hh"
+#include "BLI_math_vector.hh"
 #include "BLI_span.hh"
 #include "BLI_utildefines.h"
 
-namespace blender {
+namespace blender::math {
 
-float2::isect_result float2::isect_seg_seg(const float2 &v1,
-                                           const float2 &v2,
-                                           const float2 &v3,
-                                           const float2 &v4)
+template<>
+isect_result<float2> isect_seg_seg(const float2 &v1,
+                                   const float2 &v2,
+                                   const float2 &v3,
+                                   const float2 &v4)
 {
-  float2::isect_result ans;
+  isect_result<float2> ans;
   float div = (v2[0] - v1[0]) * (v4[1] - v3[1]) - (v2[1] - v1[1]) * (v4[0] - v3[0]);
   if (div == 0.0f) {
     ans.lambda = 0.0f;
-    ans.mu = 0.0f;
-    ans.kind = float2::isect_result::LINE_LINE_COLINEAR;
+    ans.kind = isect_result<float2>::LINE_LINE_COLINEAR;
   }
   else {
     ans.lambda = ((v1[1] - v3[1]) * (v4[0] - v3[0]) - (v1[0] - v3[0]) * (v4[1] - v3[1])) / div;
-    ans.mu = ((v1[1] - v3[1]) * (v2[0] - v1[0]) - (v1[0] - v3[0]) * (v2[1] - v1[1])) / div;
-    if (ans.lambda >= 0.0f && ans.lambda <= 1.0f && ans.mu >= 0.0f && ans.mu <= 1.0f) {
-      if (ans.lambda == 0.0f || ans.lambda == 1.0f || ans.mu == 0.0f || ans.mu == 1.0f) {
-        ans.kind = float2::isect_result::LINE_LINE_EXACT;
+    float mu = ((v1[1] - v3[1]) * (v2[0] - v1[0]) - (v1[0] - v3[0]) * (v2[1] - v1[1])) / div;
+    if (ans.lambda >= 0.0f && ans.lambda <= 1.0f && mu >= 0.0f && mu <= 1.0f) {
+      if (ans.lambda == 0.0f || ans.lambda == 1.0f || mu == 0.0f || mu == 1.0f) {
+        ans.kind = isect_result<float2>::LINE_LINE_EXACT;
       }
       else {
-        ans.kind = float2::isect_result::LINE_LINE_CROSS;
+        ans.kind = isect_result<float2>::LINE_LINE_CROSS;
       }
     }
     else {
-      ans.kind = float2::isect_result::LINE_LINE_NONE;
+      ans.kind = isect_result<float2>::LINE_LINE_NONE;
     }
   }
   return ans;
 }
 
-double2::isect_result double2::isect_seg_seg(const double2 &v1,
-                                             const double2 &v2,
-                                             const double2 &v3,
-                                             const double2 &v4)
+template<>
+isect_result<double2> isect_seg_seg(const double2 &v1,
+                                    const double2 &v2,
+                                    const double2 &v3,
+                                    const double2 &v4)
 {
-  double2::isect_result ans;
+  isect_result<double2> ans;
   double div = (v2[0] - v1[0]) * (v4[1] - v3[1]) - (v2[1] - v1[1]) * (v4[0] - v3[0]);
   if (div == 0.0) {
     ans.lambda = 0.0;
-    ans.kind = double2::isect_result::LINE_LINE_COLINEAR;
+    ans.kind = isect_result<double2>::LINE_LINE_COLINEAR;
   }
   else {
     ans.lambda = ((v1[1] - v3[1]) * (v4[0] - v3[0]) - (v1[0] - v3[0]) * (v4[1] - v3[1])) / div;
     double mu = ((v1[1] - v3[1]) * (v2[0] - v1[0]) - (v1[0] - v3[0]) * (v2[1] - v1[1])) / div;
     if (ans.lambda >= 0.0 && ans.lambda <= 1.0 && mu >= 0.0 && mu <= 1.0) {
       if (ans.lambda == 0.0 || ans.lambda == 1.0 || mu == 0.0 || mu == 1.0) {
-        ans.kind = double2::isect_result::LINE_LINE_EXACT;
+        ans.kind = isect_result<double2>::LINE_LINE_EXACT;
       }
       else {
-        ans.kind = double2::isect_result::LINE_LINE_CROSS;
+        ans.kind = isect_result<double2>::LINE_LINE_CROSS;
       }
     }
     else {
-      ans.kind = double2::isect_result::LINE_LINE_NONE;
+      ans.kind = isect_result<double2>::LINE_LINE_NONE;
     }
   }
   return ans;
 }
 
 #ifdef WITH_GMP
-mpq2::isect_result mpq2::isect_seg_seg(const mpq2 &v1,
-                                       const mpq2 &v2,
-                                       const mpq2 &v3,
-                                       const mpq2 &v4)
+template<>
+isect_result<mpq2> isect_seg_seg(const mpq2 &v1, const mpq2 &v2, const mpq2 &v3, const mpq2 &v4)
 {
-  mpq2::isect_result ans;
+  isect_result<mpq2> ans;
   mpq_class div = (v2[0] - v1[0]) * (v4[1] - v3[1]) - (v2[1] - v1[1]) * (v4[0] - v3[0]);
   if (div == 0.0) {
     ans.lambda = 0.0;
-    ans.kind = mpq2::isect_result::LINE_LINE_COLINEAR;
+    ans.kind = isect_result<mpq2>::LINE_LINE_COLINEAR;
   }
   else {
     ans.lambda = ((v1[1] - v3[1]) * (v4[0] - v3[0]) - (v1[0] - v3[0]) * (v4[1] - v3[1])) / div;
@@ -109,66 +103,21 @@ mpq2::isect_result mpq2::isect_seg_seg(const mpq2 &v1,
     if (ans.lambda >= 0 && ans.lambda <= 1 &&
         ((div > 0 && mudiv >= 0 && mudiv <= div) || (div < 0 && mudiv <= 0 && mudiv >= div))) {
       if (ans.lambda == 0 || ans.lambda == 1 || mudiv == 0 || mudiv == div) {
-        ans.kind = mpq2::isect_result::LINE_LINE_EXACT;
+        ans.kind = isect_result<mpq2>::LINE_LINE_EXACT;
       }
       else {
-        ans.kind = mpq2::isect_result::LINE_LINE_CROSS;
+        ans.kind = isect_result<mpq2>::LINE_LINE_CROSS;
       }
     }
     else {
-      ans.kind = mpq2::isect_result::LINE_LINE_NONE;
+      ans.kind = isect_result<mpq2>::LINE_LINE_NONE;
     }
   }
   return ans;
 }
 #endif
 
-double3 double3::cross_poly(Span<double3> poly)
-{
-  /* Newell's Method. */
-  int nv = static_cast<int>(poly.size());
-  if (nv < 3) {
-    return double3(0, 0, 0);
-  }
-  const double3 *v_prev = &poly[nv - 1];
-  const double3 *v_curr = &poly[0];
-  double3 n(0, 0, 0);
-  for (int i = 0; i < nv;) {
-    n[0] = n[0] + ((*v_prev)[1] - (*v_curr)[1]) * ((*v_prev)[2] + (*v_curr)[2]);
-    n[1] = n[1] + ((*v_prev)[2] - (*v_curr)[2]) * ((*v_prev)[0] + (*v_curr)[0]);
-    n[2] = n[2] + ((*v_prev)[0] - (*v_curr)[0]) * ((*v_prev)[1] + (*v_curr)[1]);
-    v_prev = v_curr;
-    ++i;
-    if (i < nv) {
-      v_curr = &poly[i];
-    }
-  }
-  return n;
-}
-
 #ifdef WITH_GMP
-mpq3 mpq3::cross_poly(Span<mpq3> poly)
-{
-  /* Newell's Method. */
-  int nv = static_cast<int>(poly.size());
-  if (nv < 3) {
-    return mpq3(0);
-  }
-  const mpq3 *v_prev = &poly[nv - 1];
-  const mpq3 *v_curr = &poly[0];
-  mpq3 n(0);
-  for (int i = 0; i < nv;) {
-    n[0] = n[0] + ((*v_prev)[1] - (*v_curr)[1]) * ((*v_prev)[2] + (*v_curr)[2]);
-    n[1] = n[1] + ((*v_prev)[2] - (*v_curr)[2]) * ((*v_prev)[0] + (*v_curr)[0]);
-    n[2] = n[2] + ((*v_prev)[0] - (*v_curr)[0]) * ((*v_prev)[1] + (*v_curr)[1]);
-    v_prev = v_curr;
-    ++i;
-    if (i < nv) {
-      v_curr = &poly[i];
-    }
-  }
-  return n;
-}
 
 uint64_t hash_mpq_class(const mpq_class &value)
 {
@@ -176,20 +125,6 @@ uint64_t hash_mpq_class(const mpq_class &value)
   return get_default_hash(static_cast<float>(value.get_d()));
 }
 
-uint64_t mpq2::hash() const
-{
-  uint64_t hashx = hash_mpq_class(this->x);
-  uint64_t hashy = hash_mpq_class(this->y);
-  return hashx ^ (hashy * 33);
-}
-
-uint64_t mpq3::hash() const
-{
-  uint64_t hashx = hash_mpq_class(this->x);
-  uint64_t hashy = hash_mpq_class(this->y);
-  uint64_t hashz = hash_mpq_class(this->z);
-  return hashx ^ (hashy * 33) ^ (hashz * 33 * 37);
-}
 #endif
 
-}  // namespace blender
+}  // namespace blender::math

source/blender/blenlib/intern/mesh_boolean.cc

@@ -28,8 +28,6 @@
 #  include "BLI_array.hh"
 #  include "BLI_assert.h"
 #  include "BLI_delaunay_2d.h"
-#  include "BLI_double3.hh"
-#  include "BLI_float3.hh"
 #  include "BLI_hash.hh"
 #  include "BLI_kdopbvh.h"
 #  include "BLI_map.hh"
@@ -37,8 +35,9 @@
 #  include "BLI_math_boolean.hh"
 #  include "BLI_math_geom.h"
 #  include "BLI_math_mpq.hh"
+#  include "BLI_math_vec_mpq_types.hh"
+#  include "BLI_math_vec_types.hh"
 #  include "BLI_mesh_intersect.hh"
-#  include "BLI_mpq3.hh"
 #  include "BLI_set.hh"
 #  include "BLI_span.hh"
 #  include "BLI_stack.hh"
@@ -1633,13 +1632,13 @@ static Edge find_good_sorting_edge(const Vert *testp,
   ordinate[axis_next] = -abscissa[axis];
   ordinate[axis_next_next] = 0;
   /* By construction, dot(abscissa, ordinate) == 0, so they are perpendicular. */
-  mpq3 normal = mpq3::cross(abscissa, ordinate);
+  mpq3 normal = math::cross(abscissa, ordinate);
   if (dbg_level > 0) {
     std::cout << "abscissa = " << abscissa << "\n";
     std::cout << "ordinate = " << ordinate << "\n";
     std::cout << "normal = " << normal << "\n";
   }
-  mpq_class nlen2 = normal.length_squared();
+  mpq_class nlen2 = math::length_squared(normal);
   mpq_class max_abs_slope = -1;
   Edge esort;
   const Vector<Edge> &edges = tmtopo.vert_edges(closestp);
@@ -1648,12 +1647,12 @@ static Edge find_good_sorting_edge(const Vert *testp,
     const mpq3 &co_other = v_other->co_exact;
     mpq3 evec = co_other - co_closest;
     /* Get projection of evec onto plane of abscissa and ordinate. */
-    mpq3 proj_evec = evec - (mpq3::dot(evec, normal) / nlen2) * normal;
+    mpq3 proj_evec = evec - (math::dot(evec, normal) / nlen2) * normal;
     /* The projection calculations along the abscissa and ordinate should
      * be scaled by 1/abscissa and 1/ordinate respectively,
      * but we can skip: it won't affect which `evec` has the maximum slope. */
-    mpq_class evec_a = mpq3::dot(proj_evec, abscissa);
-    mpq_class evec_o = mpq3::dot(proj_evec, ordinate);
+    mpq_class evec_a = math::dot(proj_evec, abscissa);
+    mpq_class evec_o = math::dot(proj_evec, ordinate);
     if (dbg_level > 0) {
       std::cout << "e = " << e << "\n";
       std::cout << "v_other = " << v_other << "\n";
@@ -1791,8 +1790,8 @@ static mpq_class closest_on_tri_to_point(const mpq3 &p,
   ap = p;
   ap -= a;
 
-  mpq_class d1 = mpq3::dot_with_buffer(ab, ap, m);
-  mpq_class d2 = mpq3::dot_with_buffer(ac, ap, m);
+  mpq_class d1 = math::dot_with_buffer(ab, ap, m);
+  mpq_class d2 = math::dot_with_buffer(ac, ap, m);
   if (d1 <= 0 && d2 <= 0) {
     /* Barycentric coordinates (1,0,0). */
     *r_edge = -1;
@@ -1800,13 +1799,13 @@ static mpq_class closest_on_tri_to_point(const mpq3 &p,
     if (dbg_level > 0) {
       std::cout << "  answer = a\n";
     }
-    return mpq3::distance_squared_with_buffer(p, a, m);
+    return math::distance_squared_with_buffer(p, a, m);
   }
   /* Check if p in vertex region outside b. */
   bp = p;
   bp -= b;
-  mpq_class d3 = mpq3::dot_with_buffer(ab, bp, m);
-  mpq_class d4 = mpq3::dot_with_buffer(ac, bp, m);
+  mpq_class d3 = math::dot_with_buffer(ab, bp, m);
+  mpq_class d4 = math::dot_with_buffer(ac, bp, m);
   if (d3 >= 0 && d4 <= d3) {
     /* Barycentric coordinates (0,1,0). */
     *r_edge = -1;
@@ -1814,7 +1813,7 @@ static mpq_class closest_on_tri_to_point(const mpq3 &p,
     if (dbg_level > 0) {
       std::cout << "  answer = b\n";
     }
-    return mpq3::distance_squared_with_buffer(p, b, m);
+    return math::distance_squared_with_buffer(p, b, m);
   }
   /* Check if p in region of ab. */
   mpq_class vc = d1 * d4 - d3 * d2;
@@ -1829,13 +1828,13 @@ static mpq_class closest_on_tri_to_point(const mpq3 &p,
     if (dbg_level > 0) {
       std::cout << "  answer = on ab at " << r << "\n";
     }
-    return mpq3::distance_squared_with_buffer(p, r, m);
+    return math::distance_squared_with_buffer(p, r, m);
   }
   /* Check if p in vertex region outside c. */
   cp = p;
   cp -= c;
-  mpq_class d5 = mpq3::dot_with_buffer(ab, cp, m);
-  mpq_class d6 = mpq3::dot_with_buffer(ac, cp, m);
+  mpq_class d5 = math::dot_with_buffer(ab, cp, m);
+  mpq_class d6 = math::dot_with_buffer(ac, cp, m);
   if (d6 >= 0 && d5 <= d6) {
     /* Barycentric coordinates (0,0,1). */
     *r_edge = -1;
@@ -1843,7 +1842,7 @@ static mpq_class closest_on_tri_to_point(const mpq3 &p,
     if (dbg_level > 0) {
       std::cout << "  answer = c\n";
     }
-    return mpq3::distance_squared_with_buffer(p, c, m);
+    return math::distance_squared_with_buffer(p, c, m);
   }
   /* Check if p in edge region of ac. */
   mpq_class vb = d5 * d2 - d1 * d6;
@@ -1858,7 +1857,7 @@ static mpq_class closest_on_tri_to_point(const mpq3 &p,
     if (dbg_level > 0) {
       std::cout << "  answer = on ac at " << r << "\n";
     }
-    return mpq3::distance_squared_with_buffer(p, r, m);
+    return math::distance_squared_with_buffer(p, r, m);
   }
   /* Check if p in edge region of bc. */
   mpq_class va = d3 * d6 - d5 * d4;
@@ -1874,7 +1873,7 @@ static mpq_class closest_on_tri_to_point(const mpq3 &p,
     if (dbg_level > 0) {
       std::cout << "  answer = on bc at " << r << "\n";
     }
-    return mpq3::distance_squared_with_buffer(p, r, m);
+    return math::distance_squared_with_buffer(p, r, m);
   }
   /* p inside face region. Compute barycentric coordinates (u,v,w). */
   mpq_class denom = 1 / (va + vb + vc);
@@ -1890,7 +1889,7 @@ static mpq_class closest_on_tri_to_point(const mpq3 &p,
   if (dbg_level > 0) {
     std::cout << "  answer = inside at " << r << "\n";
   }
-  return mpq3::distance_squared_with_buffer(p, r, m);
+  return math::distance_squared_with_buffer(p, r, m);
 }
 
 static float closest_on_tri_to_point_float_dist_squared(const float3 &p,
@@ -2610,7 +2609,7 @@ static void test_tri_inside_shapes(const IMesh &tm,
   double3 test_point = calc_point_inside_tri_db(tri_test);
   /* Offset the test point a tiny bit in the tri_test normal direction. */
   tri_test.populate_plane(false);
-  double3 norm = tri_test.plane->norm.normalized();
+  double3 norm = math::normalize(tri_test.plane->norm);
   const double offset_amount = 1e-5;
   double3 offset_test_point = test_point + offset_amount * norm;
   if (dbg_level > 0) {
@@ -3002,7 +3001,7 @@ static void init_face_merge_state(FaceMergeState *fms,
       std::cout << "process tri = " << &tri << "\n";
     }
     BLI_assert(tri.plane_populated());
-    if (double3::dot(norm, tri.plane->norm) <= 0.0) {
+    if (math::dot(norm, tri.plane->norm) <= 0.0) {
       if (dbg_level > 0) {
         std::cout << "triangle has wrong orientation, skipping\n";
       }
@@ -3027,7 +3026,7 @@ static void init_face_merge_state(FaceMergeState *fms,
       }
       if (me_index == -1) {
         double3 vec = new_me.v2->co - new_me.v1->co;
-        new_me.len_squared = vec.length_squared();
+        new_me.len_squared = math::length_squared(vec);
         new_me.orig = tri.edge_orig[i];
         new_me.is_intersect = tri.is_intersect[i];
         new_me.dissolvable = (new_me.orig == NO_INDEX && !new_me.is_intersect);
@@ -3267,7 +3266,7 @@ static Vector<Face *> merge_tris_for_face(Vector<int> tris,
   bool done = false;
   double3 first_tri_normal = tm.face(tris[0])->plane->norm;
   double3 second_tri_normal = tm.face(tris[1])->plane->norm;
-  if (tris.size() == 2 && double3::dot(first_tri_normal, second_tri_normal) > 0.0) {
+  if (tris.size() == 2 && math::dot(first_tri_normal, second_tri_normal) > 0.0) {
     /* Is this a case where quad with one diagonal remained unchanged?
      * Worth special handling because this case will be very common. */
     Face &tri1 = *tm.face(tris[0]);
@@ -3332,7 +3331,7 @@ static bool approx_in_line(const double3 &a, const double3 &b, const double3 &c)
 {
   double3 vec1 = b - a;
   double3 vec2 = c - b;
-  double cos_ang = double3::dot(vec1.normalized(), vec2.normalized());
+  double cos_ang = math::dot(math::normalize(vec1), math::normalize(vec2));
   return fabs(cos_ang - 1.0) < 1e-4;
 }
 

source/blender/blenlib/intern/mesh_intersect.cc

@@ -30,15 +30,13 @@
 #  include "BLI_array.hh"
 #  include "BLI_assert.h"
 #  include "BLI_delaunay_2d.h"
-#  include "BLI_double3.hh"
-#  include "BLI_float3.hh"
 #  include "BLI_hash.hh"
 #  include "BLI_kdopbvh.h"
 #  include "BLI_map.hh"
 #  include "BLI_math_boolean.hh"
 #  include "BLI_math_mpq.hh"
-#  include "BLI_mpq2.hh"
-#  include "BLI_mpq3.hh"
+#  include "BLI_math_vec_mpq_types.hh"
+#  include "BLI_math_vec_types.hh"
 #  include "BLI_polyfill_2d.h"
 #  include "BLI_set.hh"
 #  include "BLI_span.hh"
@@ -198,14 +196,14 @@ void Face::populate_plane(bool need_exact)
       for (int i : index_range()) {
         co[i] = vert[i]->co_exact;
       }
-      normal_exact = mpq3::cross_poly(co);
+      normal_exact = math::cross_poly(co.as_span());
     }
     else {
       mpq3 tr02 = vert[0]->co_exact - vert[2]->co_exact;
       mpq3 tr12 = vert[1]->co_exact - vert[2]->co_exact;
-      normal_exact = mpq3::cross(tr02, tr12);
+      normal_exact = math::cross(tr02, tr12);
     }
-    mpq_class d_exact = -mpq3::dot(normal_exact, vert[0]->co_exact);
+    mpq_class d_exact = -math::dot(normal_exact, vert[0]->co_exact);
     plane = new Plane(normal_exact, d_exact);
   }
   else {
@@ -215,14 +213,14 @@ void Face::populate_plane(bool need_exact)
       for (int i : index_range()) {
         co[i] = vert[i]->co;
       }
-      normal = double3::cross_poly(co);
+      normal = math::cross_poly(co.as_span());
     }
     else {
       double3 tr02 = vert[0]->co - vert[2]->co;
       double3 tr12 = vert[1]->co - vert[2]->co;
-      normal = double3::cross_high_precision(tr02, tr12);
+      normal = math::cross(tr02, tr12);
     }
-    double d = -double3::dot(normal, vert[0]->co);
+    double d = -math::dot(normal, vert[0]->co);
     plane = new Plane(normal, d);
   }
 }
@@ -1098,15 +1096,15 @@ static mpq2 project_3d_to_2d(const mpq3 &p3d, int proj_axis)
  */
 static double supremum_dot_cross(const double3 &a, const double3 &b)
 {
-  double3 abs_a = double3::abs(a);
-  double3 abs_b = double3::abs(b);
+  double3 abs_a = math::abs(a);
+  double3 abs_b = math::abs(b);
   double3 c;
   /* This is dot(cross(a, b), cross(a,b)) but using absolute values for a and b
    * and always using + when operation is + or -. */
   c[0] = abs_a[1] * abs_b[2] + abs_a[2] * abs_b[1];
   c[1] = abs_a[2] * abs_b[0] + abs_a[0] * abs_b[2];
   c[2] = abs_a[0] * abs_b[1] + abs_a[1] * abs_b[0];
-  return double3::dot(c, c);
+  return math::dot(c, c);
 }
 
 /* The index of dot when inputs are plane_coords with index 1 is much higher.
@@ -1143,11 +1141,11 @@ static int filter_plane_side(const double3 &p,
                              const double3 &abs_plane_p,
                              const double3 &abs_plane_no)
 {
-  double d = double3::dot(p - plane_p, plane_no);
+  double d = math::dot(p - plane_p, plane_no);
   if (d == 0.0) {
     return 0;
   }
-  double supremum = double3::dot(abs_p + abs_plane_p, abs_plane_no);
+  double supremum = math::dot(abs_p + abs_plane_p, abs_plane_no);
   double err_bound = supremum * index_plane_side * DBL_EPSILON;
   if (fabs(d) > err_bound) {
     return d > 0 ? 1 : -1;
@@ -1178,9 +1176,9 @@ static inline mpq3 tti_interp(
   ab -= b;
   ac = a;
   ac -= c;
-  mpq_class den = mpq3::dot_with_buffer(ab, n, dotbuf);
+  mpq_class den = math::dot_with_buffer(ab, n, dotbuf);
   BLI_assert(den != 0);
-  mpq_class alpha = mpq3::dot_with_buffer(ac, n, dotbuf) / den;
+  mpq_class alpha = math::dot_with_buffer(ac, n, dotbuf) / den;
   return a - alpha * ab;
 }
 
@@ -1209,7 +1207,7 @@ static inline int tti_above(const mpq3 &a,
   n.y = ba.z * ca.x - ba.x * ca.z;
   n.z = ba.x * ca.y - ba.y * ca.x;
 
-  return sgn(mpq3::dot_with_buffer(ad, n, dotbuf));
+  return sgn(math::dot_with_buffer(ad, n, dotbuf));
 }
 
 /**
@@ -1428,11 +1426,11 @@ static ITT_value intersect_tri_tri(const IMesh &tm, int t1, int t2)
   const double3 &d_r2 = vr2->co;
   const double3 &d_n2 = tri2.plane->norm;
 
-  const double3 &abs_d_p1 = double3::abs(d_p1);
-  const double3 &abs_d_q1 = double3::abs(d_q1);
-  const double3 &abs_d_r1 = double3::abs(d_r1);
-  const double3 &abs_d_r2 = double3::abs(d_r2);
-  const double3 &abs_d_n2 = double3::abs(d_n2);
+  const double3 &abs_d_p1 = math::abs(d_p1);
+  const double3 &abs_d_q1 = math::abs(d_q1);
+  const double3 &abs_d_r1 = math::abs(d_r1);
+  const double3 &abs_d_r2 = math::abs(d_r2);
+  const double3 &abs_d_n2 = math::abs(d_n2);
 
   int sp1 = filter_plane_side(d_p1, d_r2, d_n2, abs_d_p1, abs_d_r2, abs_d_n2);
   int sq1 = filter_plane_side(d_q1, d_r2, d_n2, abs_d_q1, abs_d_r2, abs_d_n2);
@@ -1448,9 +1446,9 @@ static ITT_value intersect_tri_tri(const IMesh &tm, int t1, int t2)
   }
 
   const double3 &d_n1 = tri1.plane->norm;
-  const double3 &abs_d_p2 = double3::abs(d_p2);
-  const double3 &abs_d_q2 = double3::abs(d_q2);
-  const double3 &abs_d_n1 = double3::abs(d_n1);
+  const double3 &abs_d_p2 = math::abs(d_p2);
+  const double3 &abs_d_q2 = math::abs(d_q2);
+  const double3 &abs_d_n1 = math::abs(d_n1);
 
   int sp2 = filter_plane_side(d_p2, d_r1, d_n1, abs_d_p2, abs_d_r1, abs_d_n1);
   int sq2 = filter_plane_side(d_q2, d_r1, d_n1, abs_d_q2, abs_d_r1, abs_d_n1);
@@ -1477,17 +1475,17 @@ static ITT_value intersect_tri_tri(const IMesh &tm, int t1, int t2)
   if (sp1 == 0) {
     buf[0] = p1;
     buf[0] -= r2;
-    sp1 = sgn(mpq3::dot_with_buffer(buf[0], n2, buf[1]));
+    sp1 = sgn(math::dot_with_buffer(buf[0], n2, buf[1]));
   }
   if (sq1 == 0) {
     buf[0] = q1;
     buf[0] -= r2;
-    sq1 = sgn(mpq3::dot_with_buffer(buf[0], n2, buf[1]));
+    sq1 = sgn(math::dot_with_buffer(buf[0], n2, buf[1]));
   }
   if (sr1 == 0) {
     buf[0] = r1;
     buf[0] -= r2;
-    sr1 = sgn(mpq3::dot_with_buffer(buf[0], n2, buf[1]));
+    sr1 = sgn(math::dot_with_buffer(buf[0], n2, buf[1]));
   }
 
   if (dbg_level > 1) {
@@ -1509,17 +1507,17 @@ static ITT_value intersect_tri_tri(const IMesh &tm, int t1, int t2)
   if (sp2 == 0) {
     buf[0] = p2;
     buf[0] -= r1;
-    sp2 = sgn(mpq3::dot_with_buffer(buf[0], n1, buf[1]));
+    sp2 = sgn(math::dot_with_buffer(buf[0], n1, buf[1]));
   }
   if (sq2 == 0) {
     buf[0] = q2;
     buf[0] -= r1;
-    sq2 = sgn(mpq3::dot_with_buffer(buf[0], n1, buf[1]));
+    sq2 = sgn(math::dot_with_buffer(buf[0], n1, buf[1]));
   }
   if (sr2 == 0) {
     buf[0] = r2;
     buf[0] -= r1;
-    sr2 = sgn(mpq3::dot_with_buffer(buf[0], n1, buf[1]));
+    sr2 = sgn(math::dot_with_buffer(buf[0], n1, buf[1]));
   }
 
   if (dbg_level > 1) {
@@ -1721,7 +1719,7 @@ static CDT_data prepare_cdt_input(const IMesh &tm, int t, const Vector<ITT_value
   BLI_assert(tm.face(t)->plane_populated());
   ans.t_plane = tm.face(t)->plane;
   BLI_assert(ans.t_plane->exact_populated());
-  ans.proj_axis = mpq3::dominant_axis(ans.t_plane->norm_exact);
+  ans.proj_axis = math::dominant_axis(ans.t_plane->norm_exact);
   prepare_need_tri(ans, tm, t);
   for (const ITT_value &itt : itts) {
     switch (itt.kind) {
@@ -1757,7 +1755,7 @@ static CDT_data prepare_cdt_input_for_cluster(const IMesh &tm,
   BLI_assert(tm.face(t0)->plane_populated());
   ans.t_plane = tm.face(t0)->plane;
   BLI_assert(ans.t_plane->exact_populated());
-  ans.proj_axis = mpq3::dominant_axis(ans.t_plane->norm_exact);
+  ans.proj_axis = math::dominant_axis(ans.t_plane->norm_exact);
   for (const int t : cl) {
     prepare_need_tri(ans, tm, t);
   }
@@ -2004,9 +2002,9 @@ static bool is_quad_flip_first_third(const double3 &v1,
                                      const double3 &normal)
 {
   double3 dir_v3v1 = v3 - v1;
-  double3 tangent = double3::cross_high_precision(dir_v3v1, normal);
-  double dot = double3::dot(v1, tangent);
-  return (double3::dot(v4, tangent) >= dot) || (double3::dot(v2, tangent) <= dot);
+  double3 tangent = math::cross(dir_v3v1, normal);
+  double dot = math::dot(v1, tangent);
+  return (math::dot(v4, tangent) >= dot) || (math::dot(v2, tangent) <= dot);
 }
 
 /**
@@ -2124,7 +2122,7 @@ static Array<Face *> exact_triangulate_poly(Face *f, IMeshArena *arena)
     f->populate_plane(false);
   }
   const double3 &poly_normal = f->plane->norm;
-  int axis = double3::dominant_axis(poly_normal);
+  int axis = math::dominant_axis(poly_normal);
   /* If project down y axis as opposed to x or z, the orientation
    * of the polygon will be reversed.
    * Yet another reversal happens if the poly normal in the dominant
@@ -2203,15 +2201,15 @@ static bool face_is_degenerate(const Face *f)
   }
   double3 da = v2->co - v0->co;
   double3 db = v2->co - v1->co;
-  double3 dab = double3::cross_high_precision(da, db);
-  double dab_length_squared = dab.length_squared();
+  double3 dab = math::cross(da, db);
+  double dab_length_squared = math::length_squared(dab);
   double err_bound = supremum_dot_cross(dab, dab) * index_dot_cross * DBL_EPSILON;
   if (dab_length_squared > err_bound) {
     return false;
   }
   mpq3 a = v2->co_exact - v0->co_exact;
   mpq3 b = v2->co_exact - v1->co_exact;
-  mpq3 ab = mpq3::cross(a, b);
+  mpq3 ab = math::cross(a, b);
   if (ab.x == 0 && ab.y == 0 && ab.z == 0) {
     return true;
   }
@@ -2231,8 +2229,8 @@ static bool any_degenerate_tris_fast(const Array<Face *> triangulation)
     }
     double3 da = v2->co - v0->co;
     double3 db = v2->co - v1->co;
-    double da_length_squared = da.length_squared();
-    double db_length_squared = db.length_squared();
+    double da_length_squared = math::length_squared(da);
+    double db_length_squared = math::length_squared(db);
     if (da_length_squared == 0.0 || db_length_squared == 0.0) {
       return true;
     }
@@ -2240,8 +2238,8 @@ static bool any_degenerate_tris_fast(const Array<Face *> triangulation)
      * The triangle is almost degenerate if sin t is almost 0.
      * sin^2 t = |da x db|^2 / (|da|^2 |db|^2)
      */
-    double3 dab = double3::cross_high_precision(da, db);
-    double dab_length_squared = dab.length_squared();
+    double3 dab = math::cross(da, db);
+    double dab_length_squared = math::length_squared(dab);
     double sin_squared_t = dab_length_squared / (da_length_squared * db_length_squared);
     if (sin_squared_t < 1e-8) {
       return true;

source/blender/blenlib/intern/noise.cc

@@ -50,9 +50,7 @@
 #include <cmath>
 #include <cstdint>
 
-#include "BLI_float2.hh"
-#include "BLI_float3.hh"
-#include "BLI_float4.hh"
+#include "BLI_math_vec_types.hh"
 #include "BLI_math_base_safe.h"
 #include "BLI_noise.hh"
 #include "BLI_utildefines.h"
@@ -1469,7 +1467,7 @@ void voronoi_smooth_f1(const float w,
       correctionFactor /= 1.0f + 3.0f * smoothness;
       if (r_color != nullptr) {
         const float3 cellColor = hash_float_to_float3(cellPosition + cellOffset);
-        smoothColor = float3::interpolate(smoothColor, cellColor, h) - correctionFactor;
+        smoothColor = math::interpolate(smoothColor, cellColor, h) - correctionFactor;
       }
       if (r_w != nullptr) {
         smoothPosition = mix(smoothPosition, pointPosition, h) - correctionFactor;
@@ -1592,7 +1590,7 @@ static float voronoi_distance(const float2 a,
 {
   switch (metric) {
     case NOISE_SHD_VORONOI_EUCLIDEAN:
-      return float2::distance(a, b);
+      return math::distance(a, b);
     case NOISE_SHD_VORONOI_MANHATTAN:
       return fabsf(a.x - b.x) + fabsf(a.y - b.y);
     case NOISE_SHD_VORONOI_CHEBYCHEV:
@@ -1615,7 +1613,7 @@ void voronoi_f1(const float2 coord,
                 float3 *r_color,
                 float2 *r_position)
 {
-  const float2 cellPosition = float2::floor(coord);
+  const float2 cellPosition = math::floor(coord);
   const float2 localPosition = coord - cellPosition;
 
   float minDistance = 8.0f;
@@ -1654,7 +1652,7 @@ void voronoi_smooth_f1(const float2 coord,
                        float3 *r_color,
                        float2 *r_position)
 {
-  const float2 cellPosition = float2::floor(coord);
+  const float2 cellPosition = math::floor(coord);
   const float2 localPosition = coord - cellPosition;
   const float smoothness_clamped = max_ff(smoothness, FLT_MIN);
 
@@ -1676,11 +1674,10 @@ void voronoi_smooth_f1(const float2 coord,
         correctionFactor /= 1.0f + 3.0f * smoothness;
         if (r_color != nullptr) {
           const float3 cellColor = hash_float_to_float3(cellPosition + cellOffset);
-          smoothColor = float3::interpolate(smoothColor, cellColor, h) - correctionFactor;
+          smoothColor = math::interpolate(smoothColor, cellColor, h) - correctionFactor;
         }
         if (r_position != nullptr) {
-          smoothPosition = float2::interpolate(smoothPosition, pointPosition, h) -
-                           correctionFactor;
+          smoothPosition = math::interpolate(smoothPosition, pointPosition, h) - correctionFactor;
         }
       }
     }
@@ -1704,7 +1701,7 @@ void voronoi_f2(const float2 coord,
                 float3 *r_color,
                 float2 *r_position)
 {
-  const float2 cellPosition = float2::floor(coord);
+  const float2 cellPosition = math::floor(coord);
   const float2 localPosition = coord - cellPosition;
 
   float distanceF1 = 8.0f;
@@ -1748,7 +1745,7 @@ void voronoi_f2(const float2 coord,
 
 void voronoi_distance_to_edge(const float2 coord, const float randomness, float *r_distance)
 {
-  const float2 cellPosition = float2::floor(coord);
+  const float2 cellPosition = math::floor(coord);
   const float2 localPosition = coord - cellPosition;
 
   float2 vectorToClosest = float2(0.0f, 0.0f);
@@ -1777,7 +1774,7 @@ void voronoi_distance_to_edge(const float2 coord, const float randomness, float
       const float2 perpendicularToEdge = vectorToPoint - vectorToClosest;
       if (dot_v2v2(perpendicularToEdge, perpendicularToEdge) > 0.0001f) {
         const float distanceToEdge = dot_v2v2((vectorToClosest + vectorToPoint) / 2.0f,
-                                              perpendicularToEdge.normalized());
+                                              math::normalize(perpendicularToEdge));
         minDistance = std::min(minDistance, distanceToEdge);
       }
     }
@@ -1787,7 +1784,7 @@ void voronoi_distance_to_edge(const float2 coord, const float randomness, float
 
 void voronoi_n_sphere_radius(const float2 coord, const float randomness, float *r_radius)
 {
-  const float2 cellPosition = float2::floor(coord);
+  const float2 cellPosition = math::floor(coord);
   const float2 localPosition = coord - cellPosition;
 
   float2 closestPoint = float2(0.0f, 0.0f);
@@ -1798,7 +1795,7 @@ void voronoi_n_sphere_radius(const float2 coord, const float randomness, float *
       const float2 cellOffset = float2(i, j);
       const float2 pointPosition = cellOffset +
                                    hash_float_to_float2(cellPosition + cellOffset) * randomness;
-      const float distanceToPoint = float2::distance(pointPosition, localPosition);
+      const float distanceToPoint = math::distance(pointPosition, localPosition);
       if (distanceToPoint < minDistance) {
         minDistance = distanceToPoint;
         closestPoint = pointPosition;
@@ -1817,14 +1814,14 @@ void voronoi_n_sphere_radius(const float2 coord, const float randomness, float *
       const float2 cellOffset = float2(i, j) + closestPointOffset;
       const float2 pointPosition = cellOffset +
                                    hash_float_to_float2(cellPosition + cellOffset) * randomness;
-      const float distanceToPoint = float2::distance(closestPoint, pointPosition);
+      const float distanceToPoint = math::distance(closestPoint, pointPosition);
       if (distanceToPoint < minDistance) {
         minDistance = distanceToPoint;
         closestPointToClosestPoint = pointPosition;
       }
     }
   }
-  *r_radius = float2::distance(closestPointToClosestPoint, closestPoint) / 2.0f;
+  *r_radius = math::distance(closestPointToClosestPoint, closestPoint) / 2.0f;
 }
 
 /* **** 3D Voronoi **** */
@@ -1836,7 +1833,7 @@ static float voronoi_distance(const float3 a,
 {
   switch (metric) {
     case NOISE_SHD_VORONOI_EUCLIDEAN:
-      return float3::distance(a, b);
+      return math::distance(a, b);
     case NOISE_SHD_VORONOI_MANHATTAN:
       return fabsf(a.x - b.x) + fabsf(a.y - b.y) + fabsf(a.z - b.z);
     case NOISE_SHD_VORONOI_CHEBYCHEV:
@@ -1860,7 +1857,7 @@ void voronoi_f1(const float3 coord,
                 float3 *r_color,
                 float3 *r_position)
 {
-  const float3 cellPosition = float3::floor(coord);
+  const float3 cellPosition = math::floor(coord);
   const float3 localPosition = coord - cellPosition;
 
   float minDistance = 8.0f;
@@ -1902,7 +1899,7 @@ void voronoi_smooth_f1(const float3 coord,
                        float3 *r_color,
                        float3 *r_position)
 {
-  const float3 cellPosition = float3::floor(coord);
+  const float3 cellPosition = math::floor(coord);
   const float3 localPosition = coord - cellPosition;
   const float smoothness_clamped = max_ff(smoothness, FLT_MIN);
 
@@ -1925,10 +1922,10 @@ void voronoi_smooth_f1(const float3 coord,
           correctionFactor /= 1.0f + 3.0f * smoothness;
           if (r_color != nullptr) {
             const float3 cellColor = hash_float_to_float3(cellPosition + cellOffset);
-            smoothColor = float3::interpolate(smoothColor, cellColor, h) - correctionFactor;
+            smoothColor = math::interpolate(smoothColor, cellColor, h) - correctionFactor;
           }
           if (r_position != nullptr) {
-            smoothPosition = float3::interpolate(smoothPosition, pointPosition, h) -
+            smoothPosition = math::interpolate(smoothPosition, pointPosition, h) -
                              correctionFactor;
           }
         }
@@ -1954,7 +1951,7 @@ void voronoi_f2(const float3 coord,
                 float3 *r_color,
                 float3 *r_position)
 {
-  const float3 cellPosition = float3::floor(coord);
+  const float3 cellPosition = math::floor(coord);
   const float3 localPosition = coord - cellPosition;
 
   float distanceF1 = 8.0f;
@@ -2000,7 +1997,7 @@ void voronoi_f2(const float3 coord,
 
 void voronoi_distance_to_edge(const float3 coord, const float randomness, float *r_distance)
 {
-  const float3 cellPosition = float3::floor(coord);
+  const float3 cellPosition = math::floor(coord);
   const float3 localPosition = coord - cellPosition;
 
   float3 vectorToClosest = float3(0.0f, 0.0f, 0.0f);
@@ -2032,7 +2029,7 @@ void voronoi_distance_to_edge(const float3 coord, const float randomness, float
         const float3 perpendicularToEdge = vectorToPoint - vectorToClosest;
         if (dot_v3v3(perpendicularToEdge, perpendicularToEdge) > 0.0001f) {
           const float distanceToEdge = dot_v3v3((vectorToClosest + vectorToPoint) / 2.0f,
-                                                perpendicularToEdge.normalized());
+                                                math::normalize(perpendicularToEdge));
           minDistance = std::min(minDistance, distanceToEdge);
         }
       }
@@ -2043,7 +2040,7 @@ void voronoi_distance_to_edge(const float3 coord, const float randomness, float
 
 void voronoi_n_sphere_radius(const float3 coord, const float randomness, float *r_radius)
 {
-  const float3 cellPosition = float3::floor(coord);
+  const float3 cellPosition = math::floor(coord);
   const float3 localPosition = coord - cellPosition;
 
   float3 closestPoint = float3(0.0f, 0.0f, 0.0f);
@@ -2055,7 +2052,7 @@ void voronoi_n_sphere_radius(const float3 coord, const float randomness, float *
         const float3 cellOffset = float3(i, j, k);
         const float3 pointPosition = cellOffset +
                                      hash_float_to_float3(cellPosition + cellOffset) * randomness;
-        const float distanceToPoint = float3::distance(pointPosition, localPosition);
+        const float distanceToPoint = math::distance(pointPosition, localPosition);
         if (distanceToPoint < minDistance) {
           minDistance = distanceToPoint;
           closestPoint = pointPosition;
@@ -2076,7 +2073,7 @@ void voronoi_n_sphere_radius(const float3 coord, const float randomness, float *
         const float3 cellOffset = float3(i, j, k) + closestPointOffset;
         const float3 pointPosition = cellOffset +
                                      hash_float_to_float3(cellPosition + cellOffset) * randomness;
-        const float distanceToPoint = float3::distance(closestPoint, pointPosition);
+        const float distanceToPoint = math::distance(closestPoint, pointPosition);
         if (distanceToPoint < minDistance) {
           minDistance = distanceToPoint;
           closestPointToClosestPoint = pointPosition;
@@ -2084,7 +2081,7 @@ void voronoi_n_sphere_radius(const float3 coord, const float randomness, float *
       }
     }
   }
-  *r_radius = float3::distance(closestPointToClosestPoint, closestPoint) / 2.0f;
+  *r_radius = math::distance(closestPointToClosestPoint, closestPoint) / 2.0f;
 }
 
 /* **** 4D Voronoi **** */
@@ -2096,7 +2093,7 @@ static float voronoi_distance(const float4 a,
 {
   switch (metric) {
     case NOISE_SHD_VORONOI_EUCLIDEAN:
-      return float4::distance(a, b);
+      return math::distance(a, b);
     case NOISE_SHD_VORONOI_MANHATTAN:
       return fabsf(a.x - b.x) + fabsf(a.y - b.y) + fabsf(a.z - b.z) + fabsf(a.w - b.w);
     case NOISE_SHD_VORONOI_CHEBYCHEV:
@@ -2121,7 +2118,7 @@ void voronoi_f1(const float4 coord,
                 float3 *r_color,
                 float4 *r_position)
 {
-  const float4 cellPosition = float4::floor(coord);
+  const float4 cellPosition = math::floor(coord);
   const float4 localPosition = coord - cellPosition;
 
   float minDistance = 8.0f;
@@ -2166,7 +2163,7 @@ void voronoi_smooth_f1(const float4 coord,
                        float3 *r_color,
                        float4 *r_position)
 {
-  const float4 cellPosition = float4::floor(coord);
+  const float4 cellPosition = math::floor(coord);
   const float4 localPosition = coord - cellPosition;
   const float smoothness_clamped = max_ff(smoothness, FLT_MIN);
 
@@ -2191,10 +2188,10 @@ void voronoi_smooth_f1(const float4 coord,
             correctionFactor /= 1.0f + 3.0f * smoothness;
             if (r_color != nullptr) {
               const float3 cellColor = hash_float_to_float3(cellPosition + cellOffset);
-              smoothColor = float3::interpolate(smoothColor, cellColor, h) - correctionFactor;
+              smoothColor = math::interpolate(smoothColor, cellColor, h) - correctionFactor;
             }
             if (r_position != nullptr) {
-              smoothPosition = float4::interpolate(smoothPosition, pointPosition, h) -
+              smoothPosition = math::interpolate(smoothPosition, pointPosition, h) -
                                correctionFactor;
             }
           }
@@ -2221,7 +2218,7 @@ void voronoi_f2(const float4 coord,
                 float3 *r_color,
                 float4 *r_position)
 {
-  const float4 cellPosition = float4::floor(coord);
+  const float4 cellPosition = math::floor(coord);
   const float4 localPosition = coord - cellPosition;
 
   float distanceF1 = 8.0f;
@@ -2270,7 +2267,7 @@ void voronoi_f2(const float4 coord,
 
 void voronoi_distance_to_edge(const float4 coord, const float randomness, float *r_distance)
 {
-  const float4 cellPosition = float4::floor(coord);
+  const float4 cellPosition = math::floor(coord);
   const float4 localPosition = coord - cellPosition;
 
   float4 vectorToClosest = float4(0.0f, 0.0f, 0.0f, 0.0f);
@@ -2307,7 +2304,7 @@ void voronoi_distance_to_edge(const float4 coord, const float randomness, float
           const float4 perpendicularToEdge = vectorToPoint - vectorToClosest;
           if (dot_v4v4(perpendicularToEdge, perpendicularToEdge) > 0.0001f) {
             const float distanceToEdge = dot_v4v4((vectorToClosest + vectorToPoint) / 2.0f,
-                                                  float4::normalize(perpendicularToEdge));
+                                                  math::normalize(perpendicularToEdge));
             minDistance = std::min(minDistance, distanceToEdge);
           }
         }
@@ -2319,7 +2316,7 @@ void voronoi_distance_to_edge(const float4 coord, const float randomness, float
 
 void voronoi_n_sphere_radius(const float4 coord, const float randomness, float *r_radius)
 {
-  const float4 cellPosition = float4::floor(coord);
+  const float4 cellPosition = math::floor(coord);
   const float4 localPosition = coord - cellPosition;
 
   float4 closestPoint = float4(0.0f, 0.0f, 0.0f, 0.0f);
@@ -2333,7 +2330,7 @@ void voronoi_n_sphere_radius(const float4 coord, const float randomness, float *
           const float4 pointPosition = cellOffset +
                                        hash_float_to_float4(cellPosition + cellOffset) *
                                            randomness;
-          const float distanceToPoint = float4::distance(pointPosition, localPosition);
+          const float distanceToPoint = math::distance(pointPosition, localPosition);
           if (distanceToPoint < minDistance) {
             minDistance = distanceToPoint;
             closestPoint = pointPosition;
@@ -2357,7 +2354,7 @@ void voronoi_n_sphere_radius(const float4 coord, const float randomness, float *
           const float4 pointPosition = cellOffset +
                                        hash_float_to_float4(cellPosition + cellOffset) *
                                            randomness;
-          const float distanceToPoint = float4::distance(closestPoint, pointPosition);
+          const float distanceToPoint = math::distance(closestPoint, pointPosition);
           if (distanceToPoint < minDistance) {
             minDistance = distanceToPoint;
             closestPointToClosestPoint = pointPosition;
@@ -2366,7 +2363,7 @@ void voronoi_n_sphere_radius(const float4 coord, const float randomness, float *
       }
     }
   }
-  *r_radius = float4::distance(closestPointToClosestPoint, closestPoint) / 2.0f;
+  *r_radius = math::distance(closestPointToClosestPoint, closestPoint) / 2.0f;
 }
 
 /** \} */

source/blender/blenlib/tests/BLI_delaunay_2d_test.cc

@@ -21,10 +21,9 @@ extern "C" {
 #define DO_RANDOM_TESTS 0
 
 #include "BLI_array.hh"
-#include "BLI_double2.hh"
 #include "BLI_math_boolean.hh"
 #include "BLI_math_mpq.hh"
-#include "BLI_mpq2.hh"
+#include "BLI_math_vec_mpq_types.hh"
 #include "BLI_vector.hh"
 
 #include "BLI_delaunay_2d.h"

source/blender/blenlib/tests/BLI_math_vec_types_test.cc

@@ -0,0 +1,149 @@
+/* Apache License, Version 2.0 */
+
+#include "testing/testing.h"
+
+#include "BLI_math_vec_types.hh"
+
+namespace blender::tests {
+
+using namespace blender::math;
+
+TEST(math_vec_types, ScalarConstructorUnsigned)
+{
+  float2 u(5u);
+  EXPECT_EQ(u[0], 5.0f);
+  EXPECT_EQ(u[1], 5.0f);
+}
+
+TEST(math_vec_types, ScalarConstructorInt)
+{
+  float2 i(-5);
+  EXPECT_EQ(i[0], -5.0f);
+  EXPECT_EQ(i[1], -5.0f);
+}
+
+TEST(math_vec_types, ScalarConstructorFloat)
+{
+  float2 f(5.2f);
+  EXPECT_FLOAT_EQ(f[0], 5.2f);
+  EXPECT_FLOAT_EQ(f[1], 5.2f);
+}
+
+TEST(math_vec_types, ScalarConstructorDouble)
+{
+  float2 d(5.2);
+  EXPECT_FLOAT_EQ(d[0], 5.2f);
+  EXPECT_FLOAT_EQ(d[1], 5.2f);
+}
+
+TEST(math_vec_types, MultiScalarConstructorVec2)
+{
+  int2 i(5.5f, -1.8);
+  EXPECT_EQ(i[0], 5);
+  EXPECT_EQ(i[1], -1);
+}
+
+TEST(math_vec_types, MultiScalarConstructorVec3)
+{
+  int3 i(5.5f, -1.8, 6u);
+  EXPECT_EQ(i[0], 5);
+  EXPECT_EQ(i[1], -1);
+  EXPECT_EQ(i[2], 6);
+}
+
+TEST(math_vec_types, MultiScalarConstructorVec4)
+{
+  int4 i(5.5f, -1.8, 6u, 0.888f);
+  EXPECT_EQ(i[0], 5);
+  EXPECT_EQ(i[1], -1);
+  EXPECT_EQ(i[2], 6);
+  EXPECT_EQ(i[3], 0);
+}
+
+TEST(math_vec_types, MixedScalarVectorConstructorVec3)
+{
+  float3 fl_v2(float2(5.5f), 1.8f);
+  EXPECT_FLOAT_EQ(fl_v2[0], 5.5f);
+  EXPECT_FLOAT_EQ(fl_v2[1], 5.5f);
+  EXPECT_FLOAT_EQ(fl_v2[2], 1.8f);
+
+  float3 v2_fl(1.8f, float2(5.5f));
+  EXPECT_FLOAT_EQ(v2_fl[0], 1.8f);
+  EXPECT_FLOAT_EQ(v2_fl[1], 5.5f);
+  EXPECT_FLOAT_EQ(v2_fl[2], 5.5f);
+}
+
+TEST(math_vec_types, MixedScalarVectorConstructorVec4)
+{
+  int4 v2_fl_fl(float2(1), 2, 3);
+  EXPECT_EQ(v2_fl_fl[0], 1);
+  EXPECT_EQ(v2_fl_fl[1], 1);
+  EXPECT_EQ(v2_fl_fl[2], 2);
+  EXPECT_EQ(v2_fl_fl[3], 3);
+
+  float4 fl_v2_fl(1, int2(2), 3);
+  EXPECT_EQ(fl_v2_fl[0], 1);
+  EXPECT_EQ(fl_v2_fl[1], 2);
+  EXPECT_EQ(fl_v2_fl[2], 2);
+  EXPECT_EQ(fl_v2_fl[3], 3);
+
+  double4 fl_fl_v2(1, 2, double2(3));
+  EXPECT_EQ(fl_fl_v2[0], 1);
+  EXPECT_EQ(fl_fl_v2[1], 2);
+  EXPECT_EQ(fl_fl_v2[2], 3);
+  EXPECT_EQ(fl_fl_v2[3], 3);
+
+  int4 v2_v2(float2(1), uint2(2));
+  EXPECT_EQ(v2_v2[0], 1);
+  EXPECT_EQ(v2_v2[1], 1);
+  EXPECT_EQ(v2_v2[2], 2);
+  EXPECT_EQ(v2_v2[3], 2);
+
+  float4 v3_fl(uint3(1), 2);
+  EXPECT_EQ(v3_fl[0], 1);
+  EXPECT_EQ(v3_fl[1], 1);
+  EXPECT_EQ(v3_fl[2], 1);
+  EXPECT_EQ(v3_fl[3], 2);
+
+  uint4 fl_v3(1, float3(2));
+  EXPECT_EQ(fl_v3[0], 1);
+  EXPECT_EQ(fl_v3[1], 2);
+  EXPECT_EQ(fl_v3[2], 2);
+  EXPECT_EQ(fl_v3[3], 2);
+}
+
+TEST(math_vec_types, ComponentMasking)
+{
+  int4 i(0, 1, 2, 3);
+  float2 f2 = float2(i);
+  EXPECT_EQ(f2[0], 0.0f);
+  EXPECT_EQ(f2[1], 1.0f);
+}
+
+TEST(math_vec_types, PointerConversion)
+{
+  float array[3] = {1.0f, 2.0f, 3.0f};
+  float3 farray(array);
+  EXPECT_EQ(farray[0], 1.0f);
+  EXPECT_EQ(farray[1], 2.0f);
+  EXPECT_EQ(farray[2], 3.0f);
+}
+
+TEST(math_vec_types, PointerArrayConversion)
+{
+  float array[1][3] = {{1.0f, 2.0f, 3.0f}};
+  float(*ptr)[3] = array;
+  float3 fptr(ptr);
+  EXPECT_EQ(fptr[0], 1.0f);
+  EXPECT_EQ(fptr[1], 2.0f);
+  EXPECT_EQ(fptr[2], 3.0f);
+}
+
+TEST(math_vec_types, VectorTypeConversion)
+{
+  double2 d(int2(float2(5.75f, -1.57f)));
+  EXPECT_EQ(d[0], 5.0);
+  EXPECT_EQ(d[1], -1.0);
+}
+
+}  // namespace blender::tests

source/blender/blenlib/tests/BLI_memory_utils_test.cc

@@ -1,6 +1,6 @@
 /* Apache License, Version 2.0 */
 
-#include "BLI_float3.hh"
+#include "BLI_math_vec_types.hh"
 #include "BLI_memory_utils.hh"
 #include "BLI_strict_flags.h"
 #include "testing/testing.h"

source/blender/blenlib/tests/BLI_mesh_boolean_test.cc

@@ -11,8 +11,8 @@
 #include "BLI_array.hh"
 #include "BLI_map.hh"
 #include "BLI_math_mpq.hh"
+#include "BLI_math_vec_mpq_types.hh"
 #include "BLI_mesh_boolean.hh"
-#include "BLI_mpq3.hh"
 #include "BLI_vector.hh"
 
 #ifdef WITH_GMP

source/blender/blenlib/tests/BLI_mesh_intersect_test.cc

@@ -10,8 +10,8 @@
 
 #include "BLI_array.hh"
 #include "BLI_math_mpq.hh"
+#include "BLI_math_vec_mpq_types.hh"
 #include "BLI_mesh_intersect.hh"
-#include "BLI_mpq3.hh"
 #include "BLI_task.h"
 #include "BLI_vector.hh"
 

source/blender/compositor/COM_defines.h

@@ -18,7 +18,7 @@
 
 #pragma once
 
-#include "BLI_float2.hh"
+#include "BLI_math_vec_types.hh"
 
 #include "DNA_vec_types.h"
 

source/blender/draw/CMakeLists.txt

@@ -197,6 +197,7 @@ set(SRC
 
   DRW_engine.h
   DRW_select_buffer.h
+  intern/DRW_gpu_wrapper.hh
   intern/DRW_render.h
   intern/draw_cache.h
   intern/draw_cache_extract.h

source/blender/draw/intern/DRW_gpu_wrapper.hh

@@ -0,0 +1,812 @@
+/*
+ * This program is free software; you can redistribute it and/or
+ * modify it under the terms of the GNU General Public License
+ * as published by the Free Software Foundation; either version 2
+ * of the License, or (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software Foundation,
+ * Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ *
+ * Copyright 2022, Blender Foundation.
+ */
+
+#pragma once
+
+/** \file
+ * \ingroup draw
+ *
+ * Wrapper classes that make it easier to use GPU objects in C++.
+ *
+ * All Buffers need to be sent to GPU memory before being used. This is done by using the
+ * `push_update()`.
+ *
+ * A Storage[Array]Buffer can hold much more data than a Uniform[Array]Buffer
+ * which can only holds 16KB of data.
+ *
+ * All types are not copyable and Buffers are not Movable.
+ *
+ * drw::UniformArrayBuffer<T, len>
+ *   Uniform buffer object containing an array of T with len elements.
+ *   Data can be accessed using the [] operator.
+ *
+ * drw::UniformBuffer<T>
+ *   A uniform buffer object class inheriting from T.
+ *   Data can be accessed just like a normal T object.
+ *
+ * drw::StorageArrayBuffer<T, len>
+ *   Storage buffer object containing an array of T with len elements.
+ *   The item count can be changed after creation using `resize()`.
+ *   However, this requires the invalidation of the whole buffer and
+ *   discarding all data inside it.
+ *   Data can be accessed using the [] operator.
+ *
+ * drw::StorageBuffer<T>
+ *   A storage buffer object class inheriting from T.
+ *   Data can be accessed just like a normal T object.
+ *
+ * drw::Texture
+ *   A simple wrapper to GPUTexture. A drw::Texture can be created without allocation.
+ *   The `ensure_[1d|2d|3d|cube][_array]()` method is here to make sure the underlying texture
+ *   will meet the requirements and create (or recreate) the GPUTexture if needed.
+ *
+ * drw::TextureFromPool
+ *   A GPUTexture from the viewport texture pool. This texture can be shared with other engines
+ *   and its content is undefined when aquiring it.
+ *   A drw::TextureFromPool is acquired for rendering using `acquire()` and released once the
+ *   rendering is done using `release()`. The same texture can be acquired & released multiple
+ *   time in one draw loop.
+ *   The `sync()` method *MUST* be called once during the cache populate (aka: Sync) phase.
+ *
+ * drw::Framebuffer
+ *   Simple wrapper to GPUFramebuffer that can be moved.
+ *
+ */
+
+#include "MEM_guardedalloc.h"
+
+#include "draw_texture_pool.h"
+
+#include "BLI_float4.hh"
+#include "BLI_int2.hh"
+#include "BLI_int3.hh"
+#include "BLI_int4.hh"
+#include "BLI_span.hh"
+#include "BLI_utildefines.h"
+#include "BLI_utility_mixins.hh"
+
+#include "GPU_framebuffer.h"
+#include "GPU_texture.h"
+#include "GPU_uniform_buffer.h"
+#include "GPU_vertex_buffer.h"
+
+namespace blender::draw {
+
+/* -------------------------------------------------------------------- */
+/** \name Implementation Details
+ * \{ */
+
+namespace detail {
+
+template<
+    /** Type of the values stored in this uniform buffer. */
+    typename T,
+    /** The number of values that can be stored in this uniform buffer. */
+    int64_t len,
+    /** True if the buffer only resides on GPU memory and cannot be accessed. */
+    bool device_only>
+class DataBuffer {
+ protected:
+  T *data_ = nullptr;
+  int64_t len_ = len;
+
+  BLI_STATIC_ASSERT((sizeof(T) % 16) == 0, "Type need to be aligned to size of float4.");
+
+ public:
+  /**
+   * Get the value at the given index. This invokes undefined behavior when the
+   * index is out of bounds.
+   */
+  const T &operator[](int64_t index) const
+  {
+    BLI_STATIC_ASSERT(!device_only, "");
+    BLI_assert(index >= 0);
+    BLI_assert(index < len);
+    return data_[index];
+  }
+
+  T &operator[](int64_t index)
+  {
+    BLI_STATIC_ASSERT(!device_only, "");
+    BLI_assert(index >= 0);
+    BLI_assert(index < len);
+    return data_[index];
+  }
+
+  /**
+   * Get a pointer to the beginning of the array.
+   */
+  const T *data() const
+  {
+    BLI_STATIC_ASSERT(!device_only, "");
+    return data_;
+  }
+  T *data()
+  {
+    BLI_STATIC_ASSERT(!device_only, "");
+    return data_;
+  }
+
+  /**
+   * Iterator
+   */
+  const T *begin() const
+  {
+    BLI_STATIC_ASSERT(!device_only, "");
+    return data_;
+  }
+  const T *end() const
+  {
+    BLI_STATIC_ASSERT(!device_only, "");
+    return data_ + len;
+  }
+
+  T *begin()
+  {
+    BLI_STATIC_ASSERT(!device_only, "");
+    return data_;
+  }
+  T *end()
+  {
+    BLI_STATIC_ASSERT(!device_only, "");
+    return data_ + len;
+  }
+
+  operator Span<T>() const
+  {
+    BLI_STATIC_ASSERT(!device_only, "");
+    return Span<T>(data_, len);
+  }
+};
+
+template<typename T, int64_t len, bool device_only>
+class UniformCommon : public DataBuffer<T, len, false>, NonMovable, NonCopyable {
+ protected:
+  GPUUniformBuf *ubo_;
+
+#ifdef DEBUG
+  const char *name_ = typeid(T).name();
+#else
+  constexpr static const char *name_ = "UniformBuffer";
+#endif
+
+ public:
+  UniformCommon()
+  {
+    ubo_ = GPU_uniformbuf_create_ex(sizeof(T) * len, nullptr, name_);
+  }
+
+  ~UniformCommon()
+  {
+    GPU_uniformbuf_free(ubo_);
+  }
+
+  void push_update(void)
+  {
+    GPU_uniformbuf_update(ubo_, this->data_);
+  }
+
+  /* To be able to use it with DRW_shgroup_*_ref(). */
+  operator GPUUniformBuf *() const
+  {
+    return ubo_;
+  }
+
+  /* To be able to use it with DRW_shgroup_*_ref(). */
+  GPUUniformBuf **operator&()
+  {
+    return &ubo_;
+  }
+};
+
+template<typename T, int64_t len, bool device_only>
+class StorageCommon : public DataBuffer<T, len, false>, NonMovable, NonCopyable {
+ protected:
+  /* Use vertex buffer for now. Until there is a complete GPUStorageBuf implementation. */
+  GPUVertBuf *ssbo_;
+
+#ifdef DEBUG
+  const char *name_ = typeid(T).name();
+#else
+  constexpr static const char *name_ = "StorageBuffer";
+#endif
+
+ public:
+  StorageCommon()
+  {
+    init(len);
+  }
+
+  ~StorageCommon()
+  {
+    GPU_vertbuf_discard(ssbo_);
+  }
+
+  void resize(int64_t new_size)
+  {
+    BLI_assert(new_size > 0);
+    if (new_size != this->len_) {
+      GPU_vertbuf_discard(ssbo_);
+      this->init(new_size);
+    }
+  }
+
+  operator GPUVertBuf *() const
+  {
+    return ssbo_;
+  }
+  /* To be able to use it with DRW_shgroup_*_ref(). */
+  GPUVertBuf **operator&()
+  {
+    return &ssbo_;
+  }
+
+ private:
+  void init(int64_t new_size)
+  {
+    this->len_ = new_size;
+
+    GPUVertFormat format = {0};
+    GPU_vertformat_attr_add(&format, "dummy", GPU_COMP_F32, 1, GPU_FETCH_FLOAT);
+
+    GPUUsageType usage = device_only ? GPU_USAGE_DEVICE_ONLY : GPU_USAGE_DYNAMIC;
+    ssbo_ = GPU_vertbuf_create_with_format_ex(&format, usage);
+    GPU_vertbuf_data_alloc(ssbo_, divide_ceil_u(sizeof(T) * this->len_, 4));
+    if (!device_only) {
+      this->data_ = (T *)GPU_vertbuf_get_data(ssbo_);
+      GPU_vertbuf_use(ssbo_);
+    }
+  }
+};
+
+}  // namespace detail
+
+/** \} */
+
+/* -------------------------------------------------------------------- */
+/** \name Uniform Buffers
+ * \{ */
+
+template<
+    /** Type of the values stored in this uniform buffer. */
+    typename T,
+    /** The number of values that can be stored in this uniform buffer. */
+    int64_t len
+    /** True if the buffer only resides on GPU memory and cannot be accessed. */
+    /* TODO(fclem): Currently unsupported. */
+    /* bool device_only = false */>
+class UniformArrayBuffer : public detail::UniformCommon<T, len, false> {
+ public:
+  UniformArrayBuffer()
+  {
+    /* TODO(fclem) We should map memory instead. */
+    this->data_ = MEM_mallocN_aligned(this->name_);
+  }
+};
+
+template<
+    /** Type of the values stored in this uniform buffer. */
+    typename T
+    /** True if the buffer only resides on GPU memory and cannot be accessed. */
+    /* TODO(fclem): Currently unsupported. */
+    /* bool device_only = false */>
+class UniformBuffer : public T, public detail::UniformCommon<T, 1, false> {
+ public:
+  UniformBuffer()
+  {
+    /* TODO(fclem) How could we map this? */
+    this->data_ = static_cast<T *>(this);
+  }
+
+  UniformBuffer<T> &operator=(const T &other)
+  {
+    *static_cast<T *>(this) = other;
+    return *this;
+  }
+};
+
+/** \} */
+
+/* -------------------------------------------------------------------- */
+/** \name Storage Buffer
+ * \{ */
+
+template<
+    /** Type of the values stored in this uniform buffer. */
+    typename T,
+    /** The number of values that can be stored in this uniform buffer. */
+    int64_t len,
+    /** True if created on device and no memory host memory is allocated. */
+    bool device_only = false>
+class StorageArrayBuffer : public detail::StorageCommon<T, len, device_only> {
+ public:
+  void push_update(void)
+  {
+    BLI_assert(!device_only);
+    /* Get the data again to tag for update. The actual pointer should not
+     * change. */
+    this->data_ = (T *)GPU_vertbuf_get_data(this->ssbo_);
+    GPU_vertbuf_use(this->ssbo_);
+  }
+};
+
+template<
+    /** Type of the values stored in this uniform buffer. */
+    typename T,
+    /** True if created on device and no memory host memory is allocated. */
+    bool device_only = false>
+class StorageBuffer : public T, public detail::StorageCommon<T, 1, device_only> {
+ public:
+  void push_update(void)
+  {
+    BLI_assert(!device_only);
+    /* TODO(fclem): Avoid a full copy. */
+    T &vert_data = *(T *)GPU_vertbuf_get_data(this->ssbo_);
+    vert_data = *this;
+
+    GPU_vertbuf_use(this->ssbo_);
+  }
+
+  StorageBuffer<T> &operator=(const T &other)
+  {
+    *static_cast<T *>(this) = other;
+    return *this;
+  }
+};
+
+/** \} */
+
+/* -------------------------------------------------------------------- */
+/** \name Texture
+ * \{ */
+
+class Texture : NonCopyable {
+ protected:
+  GPUTexture *tx_ = nullptr;
+  const char *name_;
+
+ public:
+  Texture(const char *name = "gpu::Texture") : name_(name)
+  {
+  }
+
+  Texture(const char *name,
+          eGPUTextureFormat format,
+          int extent,
+          float *data = nullptr,
+          bool cubemap = false,
+          int mips = 1)
+      : name_(name)
+  {
+    tx_ = create(extent, 0, 0, mips, format, data, false, cubemap);
+  }
+
+  Texture(const char *name,
+          eGPUTextureFormat format,
+          int extent,
+          int layers,
+          float *data = nullptr,
+          bool cubemap = false,
+          int mips = 1)
+      : name_(name)
+  {
+    tx_ = create(extent, layers, 0, mips, format, data, true, cubemap);
+  }
+
+  Texture(
+      const char *name, eGPUTextureFormat format, int2 extent, float *data = nullptr, int mips = 1)
+      : name_(name)
+  {
+    tx_ = create(UNPACK2(extent), 0, mips, format, data, false, false);
+  }
+
+  Texture(const char *name,
+          eGPUTextureFormat format,
+          int2 extent,
+          int layers,
+          float *data = nullptr,
+          int mips = 1)
+      : name_(name)
+  {
+    tx_ = create(UNPACK2(extent), layers, mips, format, data, true, false);
+  }
+
+  Texture(
+      const char *name, eGPUTextureFormat format, int3 extent, float *data = nullptr, int mips = 1)
+      : name_(name)
+  {
+    tx_ = create(UNPACK3(extent), mips, format, data, false, false);
+  }
+
+  ~Texture()
+  {
+    free();
+  }
+
+  /* To be able to use it with DRW_shgroup_uniform_texture(). */
+  operator GPUTexture *() const
+  {
+    BLI_assert(tx_ != nullptr);
+    return tx_;
+  }
+
+  /* To be able to use it with DRW_shgroup_uniform_texture_ref(). */
+  GPUTexture **operator&()
+  {
+    return &tx_;
+  }
+
+  Texture &operator=(Texture &&a)
+  {
+    if (*this != a) {
+      this->tx_ = a.tx_;
+      this->name_ = a.name_;
+      a.tx_ = nullptr;
+    }
+    return *this;
+  }
+
+  /**
+   * Ensure the texture has the correct properties. Recreating it if needed.
+   * Return true if a texture has been created.
+   */
+  bool ensure_1d(eGPUTextureFormat format, int extent, float *data = nullptr, int mips = 1)
+  {
+    return ensure_impl(extent, 0, 0, mips, format, data, false, false);
+  }
+
+  /**
+   * Ensure the texture has the correct properties. Recreating it if needed.
+   * Return true if a texture has been created.
+   */
+  bool ensure_1d_array(
+      eGPUTextureFormat format, int extent, int layers, float *data = nullptr, int mips = 1)
+  {
+    return ensure_impl(extent, layers, 0, mips, format, data, true, false);
+  }
+
+  /**
+   * Ensure the texture has the correct properties. Recreating it if needed.
+   * Return true if a texture has been created.
+   */
+  bool ensure_2d(eGPUTextureFormat format, const int2 &extent, float *data = nullptr, int mips = 1)
+  {
+    return ensure_impl(UNPACK2(extent), 0, mips, format, data, false, false);
+  }
+
+  /**
+   * Ensure the texture has the correct properties. Recreating it if needed.
+   * Return true if a texture has been created.
+   */
+  bool ensure_2d_array(eGPUTextureFormat format,
+                       const int2 &extent,
+                       int layers,
+                       float *data = nullptr,
+                       int mips = 1)
+  {
+    return ensure_impl(UNPACK2(extent), layers, mips, format, data, true, false);
+  }
+
+  /**
+   * Ensure the texture has the correct properties. Recreating it if needed.
+   * Return true if a texture has been created.
+   */
+  bool ensure_3d(eGPUTextureFormat format, const int3 &extent, float *data = nullptr, int mips = 1)
+  {
+    return ensure_impl(UNPACK3(extent), mips, format, data, false, false);
+  }
+
+  /**
+   * Ensure the texture has the correct properties. Recreating it if needed.
+   * Return true if a texture has been created.
+   */
+  bool ensure_cube(eGPUTextureFormat format, int extent, float *data = nullptr, int mips = 1)
+  {
+    return ensure_impl(extent, extent, 0, mips, format, data, false, true);
+  }
+
+  /**
+   * Ensure the texture has the correct properties. Recreating it if needed.
+   * Return true if a texture has been created.
+   */
+  bool ensure_cube_array(
+      eGPUTextureFormat format, int extent, int layers, float *data = nullptr, int mips = 1)
+  {
+    return ensure_impl(extent, extent, layers, mips, format, data, false, true);
+  }
+
+  /**
+   * Returns true if the texture has been allocated or acquired from the pool.
+   */
+  bool is_valid(void) const
+  {
+    return tx_ != nullptr;
+  }
+
+  int width(void) const
+  {
+    return GPU_texture_width(tx_);
+  }
+
+  int height(void) const
+  {
+    return GPU_texture_height(tx_);
+  }
+
+  bool depth(void) const
+  {
+    return GPU_texture_depth(tx_);
+  }
+
+  bool is_stencil(void) const
+  {
+    return GPU_texture_stencil(tx_);
+  }
+
+  bool is_integer(void) const
+  {
+    return GPU_texture_integer(tx_);
+  }
+
+  bool is_cube(void) const
+  {
+    return GPU_texture_cube(tx_);
+  }
+
+  bool is_array(void) const
+  {
+    return GPU_texture_array(tx_);
+  }
+
+  int3 size(int miplvl = 0) const
+  {
+    int3 size(0);
+    GPU_texture_get_mipmap_size(tx_, miplvl, size);
+    return size;
+  }
+
+  /**
+   * Clear the entirety of the texture using one pixel worth of data.
+   */
+  void clear(float4 values)
+  {
+    GPU_texture_clear(tx_, GPU_DATA_FLOAT, &values[0]);
+  }
+
+  /**
+   * Clear the entirety of the texture using one pixel worth of data.
+   */
+  void clear(uint4 values)
+  {
+    GPU_texture_clear(tx_, GPU_DATA_UINT, &values[0]);
+  }
+
+  /**
+   * Clear the entirety of the texture using one pixel worth of data.
+   */
+  void clear(uchar4 values)
+  {
+    GPU_texture_clear(tx_, GPU_DATA_UBYTE, &values[0]);
+  }
+
+  /**
+   * Clear the entirety of the texture using one pixel worth of data.
+   */
+  void clear(int4 values)
+  {
+    GPU_texture_clear(tx_, GPU_DATA_INT, &values[0]);
+  }
+
+  /**
+   * Returns a buffer containing the texture data for the specified miplvl.
+   * The memory block needs to be manually freed by MEM_freeN().
+   */
+  template<typename T> T *read(eGPUDataFormat format, int miplvl = 0)
+  {
+    return reinterpret_cast<T *>(GPU_texture_read(tx_, format, miplvl));
+  }
+
+  void filter_mode(bool do_filter)
+  {
+    GPU_texture_filter_mode(tx_, do_filter);
+  }
+
+  /**
+   * Free the internal texture but not the drw::Texture itself.
+   */
+  void free()
+  {
+    GPU_TEXTURE_FREE_SAFE(tx_);
+  }
+
+ private:
+  bool ensure_impl(int w,
+                   int h = 0,
+                   int d = 0,
+                   int mips = 1,
+                   eGPUTextureFormat format = GPU_RGBA8,
+                   float *data = nullptr,
+                   bool layered = false,
+                   bool cubemap = false)
+
+  {
+    /* TODO(fclem) In the future, we need to check if mip_count did not change.
+     * For now it's ok as we always define all mip level.*/
+    if (tx_) {
+      int3 size = this->size();
+      if (size != int3(w, h, d) || GPU_texture_format(tx_) != format ||
+          GPU_texture_cube(tx_) != cubemap || GPU_texture_array(tx_) != layered) {
+        GPU_TEXTURE_FREE_SAFE(tx_);
+      }
+    }
+    if (tx_ == nullptr) {
+      tx_ = create(w, h, d, mips, format, data, layered, cubemap);
+      if (mips > 1) {
+        /* TODO(fclem) Remove once we have immutable storage or when mips are
+         * generated on creation. */
+        GPU_texture_generate_mipmap(tx_);
+      }
+      return true;
+    }
+    return false;
+  }
+
+  GPUTexture *create(int w,
+                     int h,
+                     int d,
+                     int mips,
+                     eGPUTextureFormat format,
+                     float *data,
+                     bool layered,
+                     bool cubemap)
+  {
+    if (h == 0) {
+      return GPU_texture_create_1d(name_, w, mips, format, data);
+    }
+    else if (d == 0) {
+      if (layered) {
+        return GPU_texture_create_1d_array(name_, w, h, mips, format, data);
+      }
+      else {
+        return GPU_texture_create_2d(name_, w, h, mips, format, data);
+      }
+    }
+    else if (cubemap) {
+      if (layered) {
+        return GPU_texture_create_cube_array(name_, w, d, mips, format, data);
+      }
+      else {
+        return GPU_texture_create_cube(name_, w, mips, format, data);
+      }
+    }
+    else {
+      if (layered) {
+        return GPU_texture_create_2d_array(name_, w, h, d, mips, format, data);
+      }
+      else {
+        return GPU_texture_create_3d(name_, w, h, d, mips, format, GPU_DATA_FLOAT, data);
+      }
+    }
+  }
+};
+
+class TextureFromPool : public Texture, NonMovable {
+ private:
+  GPUTexture *tx_tmp_saved_ = nullptr;
+
+ public:
+  TextureFromPool(const char *name = "gpu::Texture") : Texture(name){};
+
+  /* Always use `release()` after rendering. */
+  void acquire(int w, int h, eGPUTextureFormat format, void *owner_)
+  {
+    if (this->tx_ == nullptr) {
+      if (tx_tmp_saved_ != nullptr) {
+        this->tx_ = tx_tmp_saved_;
+        return;
+      }
+      DrawEngineType *owner = (DrawEngineType *)owner_;
+      this->tx_ = DRW_texture_pool_query_2d(w, h, format, owner);
+    }
+  }
+
+  void release(void)
+  {
+    tx_tmp_saved_ = this->tx_;
+    this->tx_ = nullptr;
+  }
+
+  /**
+   * Clears any reference. Workaround for pool texture not being able to release on demand.
+   * Needs to be called at during the sync phase.
+   */
+  void sync(void)
+  {
+    tx_tmp_saved_ = nullptr;
+  }
+
+  /** Remove methods that are forbidden with this type of textures. */
+  bool ensure_1d(int, int, eGPUTextureFormat, float *) = delete;
+  bool ensure_1d_array(int, int, int, eGPUTextureFormat, float *) = delete;
+  bool ensure_2d(int, int, int, eGPUTextureFormat, float *) = delete;
+  bool ensure_2d_array(int, int, int, int, eGPUTextureFormat, float *) = delete;
+  bool ensure_3d(int, int, int, int, eGPUTextureFormat, float *) = delete;
+  bool ensure_cube(int, int, eGPUTextureFormat, float *) = delete;
+  bool ensure_cube_array(int, int, int, eGPUTextureFormat, float *) = delete;
+  void filter_mode(bool) = delete;
+  void free() = delete;
+  /**
+   * Forbid the use of DRW_shgroup_uniform_texture.
+   * Use DRW_shgroup_uniform_texture_ref instead.
+   */
+  operator GPUTexture *() const = delete;
+};
+
+/** \} */
+
+/* -------------------------------------------------------------------- */
+/** \name Framebuffer
+ * \{ */
+
+class Framebuffer : NonCopyable {
+ private:
+  GPUFrameBuffer *fb_ = nullptr;
+  const char *name_;
+
+ public:
+  Framebuffer() : name_(""){};
+  Framebuffer(const char *name) : name_(name){};
+
+  ~Framebuffer()
+  {
+    GPU_FRAMEBUFFER_FREE_SAFE(fb_);
+  }
+
+  void ensure(GPUAttachment depth = GPU_ATTACHMENT_NONE,
+              GPUAttachment color1 = GPU_ATTACHMENT_NONE,
+              GPUAttachment color2 = GPU_ATTACHMENT_NONE,
+              GPUAttachment color3 = GPU_ATTACHMENT_NONE,
+              GPUAttachment color4 = GPU_ATTACHMENT_NONE,
+              GPUAttachment color5 = GPU_ATTACHMENT_NONE,
+              GPUAttachment color6 = GPU_ATTACHMENT_NONE,
+              GPUAttachment color7 = GPU_ATTACHMENT_NONE,
+              GPUAttachment color8 = GPU_ATTACHMENT_NONE)
+  {
+    GPU_framebuffer_ensure_config(
+        &fb_, {depth, color1, color2, color3, color4, color5, color6, color7, color8});
+  }
+
+  Framebuffer &operator=(Framebuffer &&a)
+  {
+    if (*this != a) {
+      this->fb_ = a.fb_;
+      this->name_ = a.name_;
+      a.fb_ = nullptr;
+    }
+    return *this;
+  }
+
+  operator GPUFrameBuffer *() const
+  {
+    return fb_;
+  }
+};
+
+/** \} */
+
+}  // namespace blender::draw

source/blender/draw/intern/draw_cache_impl_curve.cc

@@ -26,8 +26,8 @@
 #include "MEM_guardedalloc.h"
 
 #include "BLI_array.hh"
-#include "BLI_float3.hh"
 #include "BLI_listbase.h"
+#include "BLI_math_vec_types.hh"
 #include "BLI_math_vector.h"
 #include "BLI_span.hh"
 #include "BLI_utildefines.h"

source/blender/draw/intern/mesh_extractors/extract_mesh_vbo_attributes.cc

@@ -25,9 +25,7 @@
 
 #include <functional>
 
-#include "BLI_float2.hh"
-#include "BLI_float3.hh"
-#include "BLI_float4.hh"
+#include "BLI_math_vec_types.hh"
 #include "BLI_string.h"
 
 #include "BKE_attribute.h"

source/blender/editors/space_node/node_group.cc

@@ -28,9 +28,9 @@
 #include "DNA_anim_types.h"
 #include "DNA_node_types.h"
 
-#include "BLI_float2.hh"
 #include "BLI_linklist.h"
 #include "BLI_listbase.h"
+#include "BLI_math_vec_types.hh"
 #include "BLI_string.h"
 #include "BLI_vector.hh"
 

source/blender/editors/space_node/node_intern.hh

@@ -23,7 +23,7 @@
 
 #pragma once
 
-#include "BLI_float2.hh"
+#include "BLI_math_vec_types.hh"
 #include "BLI_vector.hh"
 
 #include "BKE_node.h"
@@ -43,9 +43,6 @@ struct bNodeLink;
 struct bNodeSocket;
 struct wmGizmoGroupType;
 struct wmKeyConfig;
-namespace blender {
-struct float2;
-}
 struct wmWindow;
 
 /** Temporary data used in node link drag modal operator. */

source/blender/editors/space_node/node_select.cc

@@ -111,11 +111,13 @@ static bNode *node_under_mouse_select(bNodeTree &ntree, int mx, int my)
 
 static bNode *node_under_mouse_tweak(bNodeTree &ntree, const float2 &mouse)
 {
+  using namespace blender::math;
+
   LISTBASE_FOREACH_BACKWARD (bNode *, node, &ntree.nodes) {
     if (node->type == NODE_REROUTE) {
       bNodeSocket *socket = (bNodeSocket *)node->inputs.first;
       const float2 location{socket->locx, socket->locy};
-      if (float2::distance(mouse, location) < 24.0f) {
+      if (distance(mouse, location) < 24.0f) {
         return node;
       }
     }

source/blender/editors/space_spreadsheet/spreadsheet_column.cc

@@ -19,9 +19,8 @@
 #include "MEM_guardedalloc.h"
 
 #include "BLI_color.hh"
-#include "BLI_float2.hh"
-#include "BLI_float3.hh"
 #include "BLI_hash.hh"
+#include "BLI_math_vec_types.hh"
 #include "BLI_string.h"
 #include "BLI_string_ref.hh"
 

source/blender/editors/space_spreadsheet/spreadsheet_layout.cc

@@ -17,8 +17,7 @@
 #include <iomanip>
 #include <sstream>
 
-#include "BLI_float2.hh"
-#include "BLI_float3.hh"
+#include "BLI_math_vec_types.hh"
 
 #include "BKE_geometry_set.hh"
 

source/blender/editors/space_spreadsheet/spreadsheet_row_filter.cc

@@ -123,9 +123,7 @@ static void apply_row_filter(const SpreadsheetRowFilter &row_filter,
         const float threshold_sq = row_filter.threshold;
         apply_filter_operation(
             column_data.typed<float2>(),
-            [&](const float2 cell) {
-              return float2::distance_squared(cell, value) > threshold_sq;
-            },
+            [&](const float2 cell) { return math::distance_squared(cell, value) > threshold_sq; },
             prev_mask,
             new_indices);
         break;
@@ -155,9 +153,7 @@ static void apply_row_filter(const SpreadsheetRowFilter &row_filter,
         const float threshold_sq = row_filter.threshold;
         apply_filter_operation(
             column_data.typed<float3>(),
-            [&](const float3 cell) {
-              return float3::distance_squared(cell, value) > threshold_sq;
-            },
+            [&](const float3 cell) { return math::distance_squared(cell, value) > threshold_sq; },
             prev_mask,
             new_indices);
         break;

source/blender/functions/intern/cpp_types.cc

@@ -18,9 +18,8 @@
 #include "FN_field_cpp_type.hh"
 
 #include "BLI_color.hh"
-#include "BLI_float2.hh"
-#include "BLI_float3.hh"
 #include "BLI_float4x4.hh"
+#include "BLI_math_vec_types.hh"
 
 namespace blender::fn {
 

source/blender/io/gpencil/intern/gpencil_io_base.cc

@@ -23,9 +23,8 @@
  * \ingroup bgpencil
  */
 
-#include "BLI_float2.hh"
-#include "BLI_float3.hh"
 #include "BLI_float4x4.hh"
+#include "BLI_math_vec_types.hh"
 #include "BLI_path_util.h"
 #include "BLI_span.hh"
 
@@ -283,7 +282,7 @@ float GpencilIO::stroke_point_radius_get(bGPDlayer *gpl, bGPDstroke *gps)
   const float2 screen_ex = gpencil_3D_point_to_2D(&pt->x);
 
   const float2 v1 = screen_co - screen_ex;
-  float radius = v1.length();
+  float radius = math::length(v1);
   BKE_gpencil_free_stroke(gps_perimeter);
 
   return MAX2(radius, 1.0f);

source/blender/io/gpencil/intern/gpencil_io_base.hh

@@ -22,9 +22,8 @@
  * \ingroup bgpencil
  */
 
-#include "BLI_float2.hh"
-#include "BLI_float3.hh"
 #include "BLI_float4x4.hh"
+#include "BLI_math_vec_types.hh"
 #include "BLI_vector.hh"
 
 #include "DNA_space_types.h" /* for FILE_MAX */

source/blender/io/gpencil/intern/gpencil_io_import_svg.cc

@@ -21,8 +21,8 @@
  * \ingroup bgpencil
  */
 
-#include "BLI_float3.hh"
 #include "BLI_math.h"
+#include "BLI_math_vec_types.hh"
 #include "BLI_span.hh"
 
 #include "DNA_gpencil_types.h"

source/blender/io/wavefront_obj/exporter/obj_export_mesh.hh

@@ -22,7 +22,7 @@
 
 #include <optional>
 
-#include "BLI_float3.hh"
+#include "BLI_math_vec_types.hh"
 #include "BLI_utility_mixins.hh"
 #include "BLI_vector.hh"
 

source/blender/io/wavefront_obj/exporter/obj_export_mtl.cc

@@ -21,8 +21,8 @@
 #include "BKE_image.h"
 #include "BKE_node.h"
 
-#include "BLI_float3.hh"
 #include "BLI_map.hh"
+#include "BLI_math_vec_types.hh"
 #include "BLI_path_util.h"
 
 #include "DNA_material_types.h"

source/blender/io/wavefront_obj/exporter/obj_export_mtl.hh

@@ -20,8 +20,8 @@
 
 #pragma once
 
-#include "BLI_float3.hh"
 #include "BLI_map.hh"
+#include "BLI_math_vec_types.hh"
 #include "BLI_string_ref.hh"
 #include "BLI_vector.hh"
 

source/blender/io/wavefront_obj/exporter/obj_export_nurbs.cc

@@ -18,9 +18,9 @@
  * \ingroup obj
  */
 
-#include "BLI_float3.hh"
 #include "BLI_listbase.h"
 #include "BLI_math.h"
+#include "BLI_math_vec_types.hh"
 
 #include "DEG_depsgraph.h"
 #include "DEG_depsgraph_query.h"

source/blender/modifiers/intern/MOD_mesh_to_volume.cc

@@ -197,8 +197,8 @@ static float compute_voxel_size(const ModifierEvalContext *ctx,
   /* Compute the voxel size based on the desired number of voxels and the approximated bounding box
    * of the volume. */
   const BoundBox *bb = BKE_object_boundbox_get(mvmd->object);
-  const float diagonal = float3::distance(transform * float3(bb->vec[6]),
-                                          transform * float3(bb->vec[0]));
+  const float diagonal = math::distance(transform * float3(bb->vec[6]),
+                                        transform * float3(bb->vec[0]));
   const float approximate_volume_side_length = diagonal + mvmd->exterior_band_width * 2.0f;
   const float voxel_size = approximate_volume_side_length / mvmd->voxel_amount / volume_simplify;
   return voxel_size;

source/blender/modifiers/intern/MOD_nodes.cc

@@ -28,8 +28,8 @@
 #include "MEM_guardedalloc.h"
 
 #include "BLI_array.hh"
-#include "BLI_float3.hh"
 #include "BLI_listbase.h"
+#include "BLI_math_vec_types.hh"
 #include "BLI_multi_value_map.hh"
 #include "BLI_set.hh"
 #include "BLI_string.h"

source/blender/nodes/NOD_math_functions.hh

@@ -18,9 +18,9 @@
 
 #include "DNA_node_types.h"
 
-#include "BLI_float3.hh"
 #include "BLI_math_base_safe.h"
 #include "BLI_math_rotation.h"
+#include "BLI_math_vec_types.hh"
 #include "BLI_string_ref.hh"
 
 namespace blender::nodes {
@@ -240,6 +240,8 @@ template<typename Callback>
 inline bool try_dispatch_float_math_fl3_fl3_to_fl3(const NodeVectorMathOperation operation,
                                                    Callback &&callback)
 {
+  using namespace blender::math;
+
   const FloatMathOperationInfo *info = get_float3_math_operation_info(operation);
   if (info == nullptr) {
     return false;
@@ -259,40 +261,21 @@ inline bool try_dispatch_float_math_fl3_fl3_to_fl3(const NodeVectorMathOperation
     case NODE_VECTOR_MATH_MULTIPLY:
       return dispatch([](float3 a, float3 b) { return a * b; });
     case NODE_VECTOR_MATH_DIVIDE:
-      return dispatch([](float3 a, float3 b) {
-        return float3(safe_divide(a.x, b.x), safe_divide(a.y, b.y), safe_divide(a.z, b.z));
-      });
+      return dispatch([](float3 a, float3 b) { return safe_divide(a, b); });
     case NODE_VECTOR_MATH_CROSS_PRODUCT:
-      return dispatch([](float3 a, float3 b) { return float3::cross_high_precision(a, b); });
+      return dispatch([](float3 a, float3 b) { return cross_high_precision(a, b); });
     case NODE_VECTOR_MATH_PROJECT:
-      return dispatch([](float3 a, float3 b) {
-        float length_squared = b.length_squared();
-        return (length_squared != 0.0) ? (float3::dot(a, b) / length_squared) * b : float3(0.0f);
-      });
+      return dispatch([](float3 a, float3 b) { return project(a, b); });
     case NODE_VECTOR_MATH_REFLECT:
-      return dispatch([](float3 a, float3 b) {
-        b.normalize();
-        return a.reflected(b);
-      });
+      return dispatch([](float3 a, float3 b) { return reflect(a, normalize(b)); });
     case NODE_VECTOR_MATH_SNAP:
-      return dispatch([](float3 a, float3 b) {
-        return float3(floor(safe_divide(a.x, b.x)),
-                      floor(safe_divide(a.y, b.y)),
-                      floor(safe_divide(a.z, b.z))) *
-               b;
-      });
+      return dispatch([](float3 a, float3 b) { return floor(safe_divide(a, b)) * b; });
     case NODE_VECTOR_MATH_MODULO:
-      return dispatch([](float3 a, float3 b) {
-        return float3(safe_modf(a.x, b.x), safe_modf(a.y, b.y), safe_modf(a.z, b.z));
-      });
+      return dispatch([](float3 a, float3 b) { return mod(a, b); });
     case NODE_VECTOR_MATH_MINIMUM:
-      return dispatch([](float3 a, float3 b) {
-        return float3(min_ff(a.x, b.x), min_ff(a.y, b.y), min_ff(a.z, b.z));
-      });
+      return dispatch([](float3 a, float3 b) { return min(a, b); });
     case NODE_VECTOR_MATH_MAXIMUM:
-      return dispatch([](float3 a, float3 b) {
-        return float3(max_ff(a.x, b.x), max_ff(a.y, b.y), max_ff(a.z, b.z));
-      });
+      return dispatch([](float3 a, float3 b) { return max(a, b); });
     default:
       return false;
   }
@@ -306,6 +289,8 @@ template<typename Callback>
 inline bool try_dispatch_float_math_fl3_fl3_to_fl(const NodeVectorMathOperation operation,
                                                   Callback &&callback)
 {
+  using namespace blender::math;
+
   const FloatMathOperationInfo *info = get_float3_math_operation_info(operation);
   if (info == nullptr) {
     return false;
@@ -319,9 +304,9 @@ inline bool try_dispatch_float_math_fl3_fl3_to_fl(const NodeVectorMathOperation
 
   switch (operation) {
     case NODE_VECTOR_MATH_DOT_PRODUCT:
-      return dispatch([](float3 a, float3 b) { return float3::dot(a, b); });
+      return dispatch([](float3 a, float3 b) { return dot(a, b); });
     case NODE_VECTOR_MATH_DISTANCE:
-      return dispatch([](float3 a, float3 b) { return float3::distance(a, b); });
+      return dispatch([](float3 a, float3 b) { return distance(a, b); });
     default:
       return false;
   }
@@ -335,6 +320,8 @@ template<typename Callback>
 inline bool try_dispatch_float_math_fl3_fl3_fl3_to_fl3(const NodeVectorMathOperation operation,
                                                        Callback &&callback)
 {
+  using namespace blender::math;
+
   const FloatMathOperationInfo *info = get_float3_math_operation_info(operation);
   if (info == nullptr) {
     return false;
@@ -354,7 +341,7 @@ inline bool try_dispatch_float_math_fl3_fl3_fl3_to_fl3(const NodeVectorMathOpera
         return float3(wrapf(a.x, b.x, c.x), wrapf(a.y, b.y, c.y), wrapf(a.z, b.z, c.z));
       });
     case NODE_VECTOR_MATH_FACEFORWARD:
-      return dispatch([](float3 a, float3 b, float3 c) { return float3::faceforward(a, b, c); });
+      return dispatch([](float3 a, float3 b, float3 c) { return faceforward(a, b, c); });
     default:
       return false;
   }
@@ -368,6 +355,8 @@ template<typename Callback>
 inline bool try_dispatch_float_math_fl3_fl3_fl_to_fl3(const NodeVectorMathOperation operation,
                                                       Callback &&callback)
 {
+  using namespace blender::math;
+
   const FloatMathOperationInfo *info = get_float3_math_operation_info(operation);
   if (info == nullptr) {
     return false;
@@ -381,8 +370,7 @@ inline bool try_dispatch_float_math_fl3_fl3_fl_to_fl3(const NodeVectorMathOperat
 
   switch (operation) {
     case NODE_VECTOR_MATH_REFRACT:
-      return dispatch(
-          [](float3 a, float3 b, float c) { return float3::refract(a, b.normalized(), c); });
+      return dispatch([](float3 a, float3 b, float c) { return refract(a, normalize(b), c); });
     default:
       return false;
   }
@@ -396,6 +384,8 @@ template<typename Callback>
 inline bool try_dispatch_float_math_fl3_to_fl(const NodeVectorMathOperation operation,
                                               Callback &&callback)
 {
+  using namespace blender::math;
+
   const FloatMathOperationInfo *info = get_float3_math_operation_info(operation);
   if (info == nullptr) {
     return false;
@@ -409,7 +399,7 @@ inline bool try_dispatch_float_math_fl3_to_fl(const NodeVectorMathOperation oper
 
   switch (operation) {
     case NODE_VECTOR_MATH_LENGTH:
-      return dispatch([](float3 in) { return in.length(); });
+      return dispatch([](float3 in) { return length(in); });
     default:
       return false;
   }
@@ -450,6 +440,8 @@ template<typename Callback>
 inline bool try_dispatch_float_math_fl3_to_fl3(const NodeVectorMathOperation operation,
                                                Callback &&callback)
 {
+  using namespace blender::math;
+
   const FloatMathOperationInfo *info = get_float3_math_operation_info(operation);
   if (info == nullptr) {
     return false;
@@ -463,20 +455,15 @@ inline bool try_dispatch_float_math_fl3_to_fl3(const NodeVectorMathOperation ope
 
   switch (operation) {
     case NODE_VECTOR_MATH_NORMALIZE:
-      return dispatch([](float3 in) {
-        float3 out = in;
-        out.normalize();
-        return out;
-      }); /* Should be safe. */
+      return dispatch([](float3 in) { return normalize(in); }); /* Should be safe. */
     case NODE_VECTOR_MATH_FLOOR:
-      return dispatch([](float3 in) { return float3(floor(in.x), floor(in.y), floor(in.z)); });
+      return dispatch([](float3 in) { return floor(in); });
     case NODE_VECTOR_MATH_CEIL:
-      return dispatch([](float3 in) { return float3(ceil(in.x), ceil(in.y), ceil(in.z)); });
+      return dispatch([](float3 in) { return ceil(in); });
     case NODE_VECTOR_MATH_FRACTION:
-      return dispatch(
-          [](float3 in) { return in - float3(floor(in.x), floor(in.y), floor(in.z)); });
+      return dispatch([](float3 in) { return fract(in); });
     case NODE_VECTOR_MATH_ABSOLUTE:
-      return dispatch([](float3 in) { return float3::abs(in); });
+      return dispatch([](float3 in) { return abs(in); });
     case NODE_VECTOR_MATH_SINE:
       return dispatch([](float3 in) { return float3(sinf(in.x), sinf(in.y), sinf(in.z)); });
     case NODE_VECTOR_MATH_COSINE:

source/blender/nodes/NOD_socket_declarations.hh

@@ -21,7 +21,7 @@
 #include "RNA_types.h"
 
 #include "BLI_color.hh"
-#include "BLI_float3.hh"
+#include "BLI_math_vec_types.hh"
 
 namespace blender::nodes::decl {
 

source/blender/nodes/function/node_function_util.hh

@@ -18,7 +18,7 @@
 
 #include <string.h>
 
-#include "BLI_float3.hh"
+#include "BLI_math_vec_types.hh"
 #include "BLI_utildefines.h"
 
 #include "MEM_guardedalloc.h"

source/blender/nodes/function/nodes/node_fn_align_euler_to_vector.cc

@@ -69,14 +69,14 @@ static void align_rotations_auto_pivot(IndexMask mask,
       float3 old_axis;
       mul_v3_m3v3(old_axis, old_rotation, local_main_axis);
 
-      const float3 new_axis = vector.normalized();
-      float3 rotation_axis = float3::cross_high_precision(old_axis, new_axis);
+      const float3 new_axis = math::normalize(vector);
+      float3 rotation_axis = math::cross_high_precision(old_axis, new_axis);
       if (is_zero_v3(rotation_axis)) {
         /* The vectors are linearly dependent, so we fall back to another axis. */
-        rotation_axis = float3::cross_high_precision(old_axis, float3(1, 0, 0));
+        rotation_axis = math::cross_high_precision(old_axis, float3(1, 0, 0));
         if (is_zero_v3(rotation_axis)) {
           /* This is now guaranteed to not be zero. */
-          rotation_axis = float3::cross_high_precision(old_axis, float3(0, 1, 0));
+          rotation_axis = math::cross_high_precision(old_axis, float3(0, 1, 0));
         }
       }
 

source/blender/nodes/function/nodes/node_fn_compare.cc

@@ -265,7 +265,7 @@ static const fn::MultiFunction *get_multi_function(bNode &node)
             case NODE_COMPARE_MODE_DOT_PRODUCT: {
               static fn::CustomMF_SI_SI_SI_SO<float3, float3, float, bool> fn{
                   "Less Than - Dot Product",
-                  [](float3 a, float3 b, float comp) { return float3::dot(a, b) < comp; }};
+                  [](float3 a, float3 b, float comp) { return math::dot(a, b) < comp; }};
               return &fn;
             }
             case NODE_COMPARE_MODE_DIRECTION: {
@@ -283,7 +283,7 @@ static const fn::MultiFunction *get_multi_function(bNode &node)
             case NODE_COMPARE_MODE_LENGTH: {
               static fn::CustomMF_SI_SI_SO<float3, float3, bool> fn{
                   "Less Than - Length",
-                  [](float3 a, float3 b) { return a.length() < b.length(); }};
+                  [](float3 a, float3 b) { return math::length(a) < math::length(b); }};
               return &fn;
             }
           }
@@ -299,7 +299,7 @@ static const fn::MultiFunction *get_multi_function(bNode &node)
             case NODE_COMPARE_MODE_DOT_PRODUCT: {
               static fn::CustomMF_SI_SI_SI_SO<float3, float3, float, bool> fn{
                   "Less Equal - Dot Product",
-                  [](float3 a, float3 b, float comp) { return float3::dot(a, b) <= comp; }};
+                  [](float3 a, float3 b, float comp) { return math::dot(a, b) <= comp; }};
               return &fn;
             }
             case NODE_COMPARE_MODE_DIRECTION: {
@@ -317,7 +317,7 @@ static const fn::MultiFunction *get_multi_function(bNode &node)
             case NODE_COMPARE_MODE_LENGTH: {
               static fn::CustomMF_SI_SI_SO<float3, float3, bool> fn{
                   "Less Equal - Length",
-                  [](float3 a, float3 b) { return a.length() <= b.length(); }};
+                  [](float3 a, float3 b) { return math::length(a) <= math::length(b); }};
               return &fn;
             }
           }
@@ -333,7 +333,7 @@ static const fn::MultiFunction *get_multi_function(bNode &node)
             case NODE_COMPARE_MODE_DOT_PRODUCT: {
               static fn::CustomMF_SI_SI_SI_SO<float3, float3, float, bool> fn{
                   "Greater Than - Dot Product",
-                  [](float3 a, float3 b, float comp) { return float3::dot(a, b) > comp; }};
+                  [](float3 a, float3 b, float comp) { return math::dot(a, b) > comp; }};
               return &fn;
             }
             case NODE_COMPARE_MODE_DIRECTION: {
@@ -351,7 +351,7 @@ static const fn::MultiFunction *get_multi_function(bNode &node)
             case NODE_COMPARE_MODE_LENGTH: {
               static fn::CustomMF_SI_SI_SO<float3, float3, bool> fn{
                   "Greater Than - Length",
-                  [](float3 a, float3 b) { return a.length() > b.length(); }};
+                  [](float3 a, float3 b) { return math::length(a) > math::length(b); }};
               return &fn;
             }
           }
@@ -367,7 +367,7 @@ static const fn::MultiFunction *get_multi_function(bNode &node)
             case NODE_COMPARE_MODE_DOT_PRODUCT: {
               static fn::CustomMF_SI_SI_SI_SO<float3, float3, float, bool> fn{
                   "Greater Equal - Dot Product",
-                  [](float3 a, float3 b, float comp) { return float3::dot(a, b) >= comp; }};
+                  [](float3 a, float3 b, float comp) { return math::dot(a, b) >= comp; }};
               return &fn;
             }
             case NODE_COMPARE_MODE_DIRECTION: {
@@ -385,7 +385,7 @@ static const fn::MultiFunction *get_multi_function(bNode &node)
             case NODE_COMPARE_MODE_LENGTH: {
               static fn::CustomMF_SI_SI_SO<float3, float3, bool> fn{
                   "Greater Equal - Length",
-                  [](float3 a, float3 b) { return a.length() >= b.length(); }};
+                  [](float3 a, float3 b) { return math::length(a) >= math::length(b); }};
               return &fn;
             }
           }
@@ -402,7 +402,7 @@ static const fn::MultiFunction *get_multi_function(bNode &node)
             case NODE_COMPARE_MODE_DOT_PRODUCT: {
               static fn::CustomMF_SI_SI_SI_SI_SO<float3, float3, float, float, bool> fn{
                   "Equal - Dot Product", [](float3 a, float3 b, float comp, float epsilon) {
-                    return abs(float3::dot(a, b) - comp) <= epsilon;
+                    return abs(math::dot(a, b) - comp) <= epsilon;
                   }};
               return &fn;
             }
@@ -424,7 +424,7 @@ static const fn::MultiFunction *get_multi_function(bNode &node)
             case NODE_COMPARE_MODE_LENGTH: {
               static fn::CustomMF_SI_SI_SI_SO<float3, float3, float, bool> fn{
                   "Equal - Length", [](float3 a, float3 b, float epsilon) {
-                    return abs(a.length() - b.length()) <= epsilon;
+                    return abs(math::length(a) - math::length(b)) <= epsilon;
                   }};
               return &fn;
             }
@@ -442,7 +442,7 @@ static const fn::MultiFunction *get_multi_function(bNode &node)
             case NODE_COMPARE_MODE_DOT_PRODUCT: {
               static fn::CustomMF_SI_SI_SI_SI_SO<float3, float3, float, float, bool> fn{
                   "Not Equal - Dot Product", [](float3 a, float3 b, float comp, float epsilon) {
-                    return abs(float3::dot(a, b) - comp) >= epsilon;
+                    return abs(math::dot(a, b) - comp) >= epsilon;
                   }};
               return &fn;
             }
@@ -464,7 +464,7 @@ static const fn::MultiFunction *get_multi_function(bNode &node)
             case NODE_COMPARE_MODE_LENGTH: {
               static fn::CustomMF_SI_SI_SI_SO<float3, float3, float, bool> fn{
                   "Not Equal - Length", [](float3 a, float3 b, float epsilon) {
-                    return abs(a.length() - b.length()) > epsilon;
+                    return abs(math::length(a) - math::length(b)) > epsilon;
                   }};
               return &fn;
             }

source/blender/nodes/geometry/node_geometry_util.hh

@@ -18,7 +18,7 @@
 
 #include <string.h>
 
-#include "BLI_float3.hh"
+#include "BLI_math_vec_types.hh"
 #include "BLI_utildefines.h"
 
 #include "MEM_guardedalloc.h"

source/blender/nodes/geometry/nodes/legacy/node_geo_legacy_align_rotation_to_vector.cc

@@ -90,14 +90,14 @@ static void align_rotations_auto_pivot(const VArray<float3> &vectors,
       float3 old_axis;
       mul_v3_m3v3(old_axis, old_rotation, local_main_axis);
 
-      const float3 new_axis = vector.normalized();
-      float3 rotation_axis = float3::cross_high_precision(old_axis, new_axis);
+      const float3 new_axis = math::normalize(vector);
+      float3 rotation_axis = math::cross_high_precision(old_axis, new_axis);
       if (is_zero_v3(rotation_axis)) {
         /* The vectors are linearly dependent, so we fall back to another axis. */
-        rotation_axis = float3::cross_high_precision(old_axis, float3(1, 0, 0));
+        rotation_axis = math::cross_high_precision(old_axis, float3(1, 0, 0));
         if (is_zero_v3(rotation_axis)) {
           /* This is now guaranteed to not be zero. */
-          rotation_axis = float3::cross_high_precision(old_axis, float3(0, 1, 0));
+          rotation_axis = math::cross_high_precision(old_axis, float3(0, 1, 0));
         }
       }
 

source/blender/nodes/geometry/nodes/legacy/node_geo_legacy_attribute_proximity.cc

@@ -81,7 +81,7 @@ static void calculate_mesh_proximity(const VArray<float3> &positions,
 
     for (int i : range) {
       /* Use the distance to the last found point as upper bound to speedup the bvh lookup. */
-      nearest.dist_sq = float3::distance_squared(nearest.co, positions[i]);
+      nearest.dist_sq = math::distance_squared(float3(nearest.co), positions[i]);
 
       BLI_bvhtree_find_nearest(
           bvh_data.tree, positions[i], &nearest, bvh_data.nearest_callback, &bvh_data);

source/blender/nodes/geometry/nodes/legacy/node_geo_legacy_attribute_transfer.cc

@@ -229,7 +229,7 @@ static void get_closest_mesh_corners(const Mesh &mesh,
       const MLoop &loop = mesh.mloop[loop_index];
       const int vertex_index = loop.v;
       const MVert &mvert = mesh.mvert[vertex_index];
-      const float distance_sq = float3::distance_squared(position, mvert.co);
+      const float distance_sq = math::distance_squared(position, float3(mvert.co));
       if (distance_sq < min_distance_sq) {
         min_distance_sq = distance_sq;
         closest_loop_index = loop_index;

source/blender/nodes/geometry/nodes/legacy/node_geo_legacy_curve_to_points.cc

@@ -241,13 +241,13 @@ static void copy_uniform_sample_point_attributes(Span<SplinePtr> splines,
       spline.sample_with_index_factors<float3>(
           spline.evaluated_tangents(), uniform_samples, data.tangents.slice(offset, size));
       for (float3 &tangent : data.tangents) {
-        tangent.normalize();
+        tangent = math::normalize(tangent);
       }
 
       spline.sample_with_index_factors<float3>(
           spline.evaluated_normals(), uniform_samples, data.normals.slice(offset, size));
       for (float3 &normals : data.normals) {
-        normals.normalize();
+        normals = math::normalize(normals);
       }
     }
   });

source/blender/nodes/geometry/nodes/legacy/node_geo_legacy_points_to_volume.cc

@@ -161,7 +161,7 @@ static float compute_voxel_size(const GeoNodeExecParams &params,
   }
 
   /* The voxel size adapts to the final size of the volume. */
-  const float diagonal = float3::distance(min, max);
+  const float diagonal = math::distance(min, max);
   const float extended_diagonal = diagonal + 2.0f * radius;
   const float voxel_size = extended_diagonal / voxel_amount;
   return voxel_size;

source/blender/nodes/geometry/nodes/legacy/node_geo_legacy_raycast.cc

@@ -107,7 +107,7 @@ static void raycast_to_mesh(const Mesh &mesh,
   for (const int i : ray_origins.index_range()) {
     const float ray_length = ray_lengths[i];
     const float3 ray_origin = ray_origins[i];
-    const float3 ray_direction = ray_directions[i].normalized();
+    const float3 ray_direction = math::normalize(ray_directions[i]);
 
     BVHTreeRayHit hit;
     hit.index = -1;

source/blender/nodes/geometry/nodes/node_geo_curve_fill.cc

@@ -16,7 +16,7 @@
 
 #include "BLI_array.hh"
 #include "BLI_delaunay_2d.h"
-#include "BLI_double2.hh"
+#include "BLI_math_vec_types.hh"
 
 #include "DNA_mesh_types.h"
 #include "DNA_meshdata_types.h"

source/blender/nodes/geometry/nodes/node_geo_curve_fillet.cc

@@ -122,9 +122,9 @@ static Array<float3> calculate_directions(const Span<float3> positions)
   Array<float3> directions(size);
 
   for (const int i : IndexRange(size - 1)) {
-    directions[i] = (positions[i + 1] - positions[i]).normalized();
+    directions[i] = math::normalize(positions[i + 1] - positions[i]);
   }
-  directions[size - 1] = (positions[0] - positions[size - 1]).normalized();
+  directions[size - 1] = math::normalize(positions[0] - positions[size - 1]);
 
   return directions;
 }
@@ -135,9 +135,9 @@ static Array<float3> calculate_axes(const Span<float3> directions)
   const int size = directions.size();
   Array<float3> axes(size);
 
-  axes[0] = float3::cross(-directions[size - 1], directions[0]).normalized();
+  axes[0] = math::normalize(math::cross(-directions[size - 1], directions[0]));
   for (const int i : IndexRange(1, size - 1)) {
-    axes[i] = float3::cross(-directions[i - 1], directions[i]).normalized();
+    axes[i] = math::normalize(math::cross(-directions[i - 1], directions[i]));
   }
 
   return axes;
@@ -248,8 +248,8 @@ static void limit_radii(FilletData &fd, const bool cyclic)
 
   if (cyclic) {
     /* Calculate lengths between adjacent control points. */
-    const float len_prev = float3::distance(positions[0], positions[size - 1]);
-    const float len_next = float3::distance(positions[0], positions[1]);
+    const float len_prev = math::distance(positions[0], positions[size - 1]);
+    const float len_next = math::distance(positions[0], positions[1]);
 
     /* Calculate tangent lengths of fillets in control points. */
     const float tan_len = radii[0] * tan(angles[0] / 2.0f);
@@ -271,16 +271,16 @@ static void limit_radii(FilletData &fd, const bool cyclic)
   }
 
   /* Initialize max_radii to largest possible radii. */
-  float prev_dist = float3::distance(positions[1], positions[0]);
+  float prev_dist = math::distance(positions[1], positions[0]);
   for (const int i : IndexRange(1, size - 2)) {
-    const float temp_dist = float3::distance(positions[i], positions[i + 1]);
+    const float temp_dist = math::distance(positions[i], positions[i + 1]);
     max_radii[i] = std::min(prev_dist, temp_dist) / tan(angles[i] / 2.0f);
     prev_dist = temp_dist;
   }
 
   /* Max radii calculations for each index. */
   for (const int i : IndexRange(start, fillet_count - 1)) {
-    const float len_next = float3::distance(positions[i], positions[i + 1]);
+    const float len_next = math::distance(positions[i], positions[i + 1]);
     const float tan_len = radii[i] * tan(angles[i] / 2.0f);
     const float tan_len_next = radii[i + 1] * tan(angles[i + 1] / 2.0f);
 
@@ -415,7 +415,8 @@ static void update_bezier_positions(const FilletData &fd,
     const float3 center = get_center(dst_spline.positions()[i_dst] - positions[i_src], fd, i_src);
     /* Calculate the vector of the radius formed by the first vertex. */
     float3 radius_vec = dst_spline.positions()[i_dst] - center;
-    const float radius = radius_vec.normalize_and_get_length();
+    float radius;
+    radius_vec = math::normalize_and_get_length(radius_vec, radius);
 
     dst_spline.handle_types_right().slice(1, count - 2).fill(BezierSpline::HandleType::Align);
     dst_spline.handle_types_left().slice(1, count - 2).fill(BezierSpline::HandleType::Align);

source/blender/nodes/geometry/nodes/node_geo_curve_primitive_circle.cc

@@ -101,8 +101,8 @@ static void node_update(bNodeTree *ntree, bNode *node)
 
 static bool colinear_f3_f3_f3(const float3 p1, const float3 p2, const float3 p3)
 {
-  const float3 a = (p2 - p1).normalized();
-  const float3 b = (p3 - p1).normalized();
+  const float3 a = math::normalize(p2 - p1);
+  const float3 b = math::normalize(p3 - p1);
   return (ELEM(a, b, b * -1.0f));
 }
 
@@ -122,18 +122,18 @@ static std::unique_ptr<CurveEval> create_point_circle_curve(
 
   float3 center;
   /* Midpoints of `P1->P2` and `P2->P3`. */
-  const float3 q1 = float3::interpolate(p1, p2, 0.5f);
-  const float3 q2 = float3::interpolate(p2, p3, 0.5f);
+  const float3 q1 = math::interpolate(p1, p2, 0.5f);
+  const float3 q2 = math::interpolate(p2, p3, 0.5f);
 
   /* Normal Vectors of `P1->P2` and `P2->P3` */
-  const float3 v1 = (p2 - p1).normalized();
-  const float3 v2 = (p3 - p2).normalized();
+  const float3 v1 = math::normalize(p2 - p1);
+  const float3 v2 = math::normalize(p3 - p2);
 
   /* Normal of plane of main 2 segments P1->P2 and `P2->P3`. */
-  const float3 v3 = float3::cross(v1, v2).normalized();
+  const float3 v3 = math::normalize(math::cross(v1, v2));
 
   /* Normal of plane of first perpendicular bisector and `P1->P2`. */
-  const float3 v4 = float3::cross(v3, v1).normalized();
+  const float3 v4 = math::normalize(math::cross(v3, v1));
 
   /* Determine Center-point from the intersection of 3 planes. */
   float plane_1[4], plane_2[4], plane_3[4];
@@ -148,7 +148,7 @@ static std::unique_ptr<CurveEval> create_point_circle_curve(
   }
 
   /* Get the radius from the center-point to p1. */
-  const float r = float3::distance(p1, center);
+  const float r = math::distance(p1, center);
   const float theta_step = ((2 * M_PI) / (float)resolution);
   for (const int i : IndexRange(resolution)) {
 

source/blender/nodes/geometry/nodes/node_geo_curve_primitive_line.cc

@@ -100,7 +100,7 @@ static std::unique_ptr<CurveEval> create_direction_line_curve(const float3 start
   spline->resize(2);
   MutableSpan<float3> positions = spline->positions();
   positions[0] = start;
-  positions[1] = direction.normalized() * length + start;
+  positions[1] = math::normalize(direction) * length + start;
 
   spline->radii().fill(1.0f);
   spline->tilts().fill(0.0f);

source/blender/nodes/geometry/nodes/node_geo_curve_primitive_quadratic_bezier.cc

@@ -58,9 +58,9 @@ static std::unique_ptr<CurveEval> create_quadratic_bezier_curve(const float3 p1,
   const float step = 1.0f / resolution;
   for (const int i : IndexRange(resolution + 1)) {
     const float factor = step * i;
-    const float3 q1 = float3::interpolate(p1, p2, factor);
-    const float3 q2 = float3::interpolate(p2, p3, factor);
-    positions[i] = float3::interpolate(q1, q2, factor);
+    const float3 q1 = math::interpolate(p1, p2, factor);
+    const float3 q2 = math::interpolate(p2, p3, factor);
+    positions[i] = math::interpolate(q1, q2, factor);
   }
 
   curve->add_spline(std::move(spline));

source/blender/nodes/geometry/nodes/node_geo_curve_sample.cc

@@ -185,7 +185,7 @@ class SampleCurveFunction : public fn::MultiFunction {
       for (const int i : mask) {
         const Spline::LookupResult &lookup = lookups[i];
         const Span<float3> evaluated_tangents = splines[spline_indices[i]]->evaluated_tangents();
-        sampled_tangents[i] = sample_with_lookup(lookup, evaluated_tangents).normalized();
+        sampled_tangents[i] = math::normalize(sample_with_lookup(lookup, evaluated_tangents));
       }
     }
 
@@ -193,7 +193,7 @@ class SampleCurveFunction : public fn::MultiFunction {
       for (const int i : mask) {
         const Spline::LookupResult &lookup = lookups[i];
         const Span<float3> evaluated_normals = splines[spline_indices[i]]->evaluated_normals();
-        sampled_normals[i] = sample_with_lookup(lookup, evaluated_normals).normalized();
+        sampled_normals[i] = math::normalize(sample_with_lookup(lookup, evaluated_normals));
       }
     }
   }

source/blender/nodes/geometry/nodes/node_geo_curve_spline_parameter.cc

@@ -96,7 +96,7 @@ static void calculate_nurbs_lengths(const NURBSpline &spline, MutableSpan<float>
   float length = 0.0f;
   for (const int i : IndexRange(positions.size() - 1)) {
     lengths[i] = length;
-    length += float3::distance(positions[i], positions[i + 1]);
+    length += math::distance(positions[i], positions[i + 1]);
   }
   lengths.last() = length;
 }

source/blender/nodes/geometry/nodes/node_geo_curve_to_points.cc

@@ -285,7 +285,7 @@ static void copy_uniform_sample_point_attributes(const Span<SplinePtr> splines,
         spline.sample_with_index_factors<float3>(
             spline.evaluated_tangents(), uniform_samples, data.tangents.slice(offset, size));
         for (float3 &tangent : data.tangents) {
-          tangent.normalize();
+          tangent = math::normalize(tangent);
         }
       }
 
@@ -293,7 +293,7 @@ static void copy_uniform_sample_point_attributes(const Span<SplinePtr> splines,
         spline.sample_with_index_factors<float3>(
             spline.evaluated_normals(), uniform_samples, data.normals.slice(offset, size));
         for (float3 &normals : data.normals) {
-          normals.normalize();
+          normals = math::normalize(normals);
         }
       }
     }

source/blender/nodes/geometry/nodes/node_geo_image_texture.cc

@@ -21,7 +21,7 @@
 
 #include "BKE_image.h"
 
-#include "BLI_float4.hh"
+#include "BLI_math_vec_types.hh"
 #include "BLI_threads.h"
 #include "BLI_timeit.hh"
 

source/blender/nodes/geometry/nodes/node_geo_mesh_primitive_line.cc

@@ -155,8 +155,8 @@ static void node_geo_exec(GeoNodeExecParams params)
     if (count_mode == GEO_NODE_MESH_LINE_COUNT_RESOLUTION) {
       /* Don't allow asymptotic count increase for low resolution values. */
       const float resolution = std::max(params.extract_input<float>("Resolution"), 0.0001f);
-      const int count = total_delta.length() / resolution + 1;
-      const float3 delta = total_delta.normalized() * resolution;
+      const int count = math::length(total_delta) / resolution + 1;
+      const float3 delta = math::normalize(total_delta) * resolution;
       mesh = create_line_mesh(start, delta, count);
     }
     else if (count_mode == GEO_NODE_MESH_LINE_COUNT_TOTAL) {
@@ -204,7 +204,7 @@ Mesh *create_line_mesh(const float3 start, const float3 delta, const int count)
   MutableSpan<MEdge> edges{mesh->medge, mesh->totedge};
 
   short normal[3];
-  normal_float_to_short_v3(normal, delta.normalized());
+  normal_float_to_short_v3(normal, math::normalize(delta));
 
   for (const int i : verts.index_range()) {
     copy_v3_v3(verts[i].co, start + delta * i);

source/blender/nodes/geometry/nodes/node_geo_points_to_volume.cc

@@ -166,7 +166,7 @@ static float compute_voxel_size(const GeoNodeExecParams &params,
   }
 
   /* The voxel size adapts to the final size of the volume. */
-  const float diagonal = float3::distance(min, max);
+  const float diagonal = math::distance(min, max);
   const float extended_diagonal = diagonal + 2.0f * radius;
   const float voxel_size = extended_diagonal / voxel_amount;
   return voxel_size;

source/blender/nodes/geometry/nodes/node_geo_proximity.cc

@@ -85,7 +85,7 @@ static bool calculate_mesh_proximity(const VArray<float3> &positions,
     for (int i : range) {
       const int index = mask[i];
       /* Use the distance to the last found point as upper bound to speedup the bvh lookup. */
-      nearest.dist_sq = float3::distance_squared(nearest.co, positions[index]);
+      nearest.dist_sq = math::distance_squared(float3(nearest.co), positions[index]);
 
       BLI_bvhtree_find_nearest(
           bvh_data.tree, positions[index], &nearest, bvh_data.nearest_callback, &bvh_data);

source/blender/nodes/geometry/nodes/node_geo_raycast.cc

@@ -163,7 +163,7 @@ static void raycast_to_mesh(IndexMask mask,
   for (const int i : mask) {
     const float ray_length = ray_lengths[i];
     const float3 ray_origin = ray_origins[i];
-    const float3 ray_direction = ray_directions[i].normalized();
+    const float3 ray_direction = math::normalize(ray_directions[i]);
 
     BVHTreeRayHit hit;
     hit.index = -1;