rewrote entirely the triangle clipping algorithm

There is still a lot of work needed to refactor it properly.

- use the Sutherland–Hodgman algorithm, with some minor changes
- made clipping more general, allowing clipping of any coordinate,
  before and after division by w
- compute the z coordinate only at the fragment stage instead of each
  time clipping creates / moves a vertex, in addition to the fragment
  stage
- added VectorCoords to choose at compile-time different coordinates
  based on a template argument
- added transpose struct to allow shuffling of vectors coordinates
- added math::utils::lerp which interpolate linearly a float
- added Vector{2,3,4}::map() which maps a vector from one range to
  another
- added template parameter to DerivedVertex (and therefore
  TriangleDerived) to allow choosing which dimension to use

1 files changed, 16 insertions, 0 deletions

diff --git a/src/math/utils.hpp b/src/math/utils.hpp
index 5ec5959..5c8c62d 100644
--- a/src/math/utils.hpp
+++ b/src/math/utils.hpp
@@ -5,6 +5,14 @@
 #include <utility>
 #include "math/vector.hpp"
 
+namespace engine::math {
+
+struct Vector2;
+struct Vector3;
+struct Vector4;
+
+}
+
 namespace engine::math::utils {
 
 template<size_t size> struct Vector;
@@ -19,6 +27,14 @@ constexpr Vector<vector_size>::type array_to_vec(const std::array<float, vector_
     }(std::make_index_sequence<vector_size>());
 }
 
+constexpr float lerp(float a, float b, float t) {
+    return a + t * (b - a);
+}
+
+constexpr float map(float x, float from1, float from2, float to1, float to2) {
+    return to1 + (x - from1) * (to2 - to1) / (from2 - from1);
+}
+
 }
 
 #endif // MATH_UTILS_HPP