BLI: Refactor vector types & functions to use templates

This patch implements the vector types (i.e:float2) by making heavy
usage of templating. All vector functions are now outside of the vector
classes (inside the blender::math namespace) and are not vector size
dependent for the most part.

In the ongoing effort to make shaders less GL centric, we are aiming
to share more code between GLSL and C++ to avoid code duplication.

Motivations:
- We are aiming to share UBO and SSBO structures between GLSL and C++.
  This means we will use many of the existing vector types and others we
  currently don't have (uintX, intX). All these variations were asking
  for many more code duplication.
- Deduplicate existing code which is duplicated for each vector size.
- We also want to share small functions. Which means that vector functions
  should be static and not in the class namespace.
- Reduce friction to use these types in new projects due to their
  incompleteness.
- The current state of the BLI_(float|double|mpq)(2|3|4).hh is a bit of a
  let down. Most clases are incomplete, out of sync with each others with
  different codestyles, and some functions that should be static are not
  (i.e: float3::reflect()).

Upsides:
- Still support .x, .y, .z, .w for readability.
- Compact, readable and easilly extendable.
- All of the vector functions are available for all the vectors types and
  can be restricted to certain types. Also template specialization let us
  define exception for special class (like mpq).
- With optimization ON, the compiler unroll the loops and performance is
  the same.

Downsides:
- Might impact debugability. Though I would arge that the bugs are rarelly
  caused by the vector class itself (since the operations are quite trivial)
  but by the type conversions.
- Might impact compile time. I did not saw a significant impact since the
  usage is not really widespread.
- Functions needs to be rewritten to support arbitrary vector length. For
  instance, one can't call len_squared_v3v3 in math::length_squared() and
  call it a day.
- Type cast does not work with the template version of the math:: vector
  functions. Meaning you need to manually cast float * and (float *)[3] to
  float3 for the function calls.
  i.e: math::distance_squared(float3(nearest.co), positions[i]);
- Some parts might loose in readability:
  float3::dot(v1.normalized(), v2.normalized())
  becoming
  math::dot(math::normalize(v1), math::normalize(v2))
  But I propose, when appropriate, to use
  using namespace blender::math; on function local or file scope to
  increase readability. dot(normalize(v1), normalize(v2))

Consideration:
- Include back .length() method. It is quite handy and is more C++
  oriented.
- I considered the GLM library as a candidate for replacement.
  It felt like too much for what we need and would be difficult to
  extend / modify to our needs.
- I used Macros to reduce code in operators declaration and potential
  copy paste bugs. This could reduce debugability and could be reverted.
- This touches delaunay_2d.cc and the intersection code. I would like to
  know @Howard Trickey (howardt) opinion on the matter.
- The noexcept on the copy constructor of mpq(2|3) is being removed.
  But according to @Jacques Lucke (JacquesLucke) it is not a real problem
  for now.

I would like to give a huge thanks to @Jacques Lucke (JacquesLucke) who
helped during this and pushed me to reduce the duplication further.

Reviewed By: brecht, sergey, JacquesLucke

Differential Revision: http://developer.blender.org/D13791

1 files changed, 25 insertions, 26 deletions

diff --git a/source/blender/blenlib/intern/mesh_boolean.cc b/source/blender/blenlib/intern/mesh_boolean.cc
index ce4db0c6b9d..a3eae1896d3 100644
--- a/source/blender/blenlib/intern/mesh_boolean.cc
+++ b/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;
 }