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 @howardt opinion on the matter.
 - The `noexcept` on the copy constructor of `mpq(2|3)` is being removed.
 But according to @JacquesLucke it is not a real problem for now.

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

Reviewed By: brecht, sergey, JacquesLucke

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

1 files changed, 0 insertions, 143 deletions

diff --git a/source/blender/blenlib/BLI_double2.hh b/source/blender/blenlib/BLI_double2.hh
deleted file mode 100644
index 0abff01ab2f..00000000000
--- a/source/blender/blenlib/BLI_double2.hh
+++ /dev/null
@@ -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