Curves: Correct and improve Catmull Rom interpolation

Correct interpolation of integer POD types for Catmull Rom
interpolation as implemented in eaf416693dcb.

**Problem description**
`attribute_math::DefaultMixer<T>::mix_in()` assumes/asserts positive
weights but the basis function for Catmull-Rom splines generates
negative weights (see image in revision). Passing negative weights will
yield correct result as sum(weights) = 1 (after multiplication by 0.5)
but the assert is still triggered in debug builds. This patch adjusts
the behavior by extending the mix functions with mix4(). The benefit
of using mix#() over a DefaultMixer is that the result no longer needs
to be divided by the weight sum, instead utilizing that the basis weight
sum is constant (see plot).

**Changes**
 * Added mix4() and updated catmull_rom::interpolate() to use it.
 * Removed TODOs from catmull_rom functions.
 * Moved mix definitions to be ordered as 2, 3, 4 in the header.

**Implementation specifics**
`catmull_rom::interpolate()` uses a constexpr to differentiate between
POD types which multiplies the result with 0.5 after weighting the
values, this reduces the number of multiplications for 1D, 2D, 3D
vectors (https://godbolt.org/z/8M1z9Pxx6). While this could be
considered unnecessary, I didn't want to change the original behavior
as it could influence performance (did not measure performance here
as this should ensure the logic is ~identical for FP types).

Differential Revision: https://developer.blender.org/D15997

1 files changed, 3 insertions, 11 deletions

diff --git a/source/blender/blenkernel/intern/curve_catmull_rom.cc b/source/blender/blenkernel/intern/curve_catmull_rom.cc
index dac88948036..b5f1a7cc450 100644
--- a/source/blender/blenkernel/intern/curve_catmull_rom.cc
+++ b/source/blender/blenkernel/intern/curve_catmull_rom.cc
@@ -17,7 +17,7 @@ int calculate_evaluated_num(const int points_num, const bool cyclic, const int r
 }
 
 /* Adapted from Cycles #catmull_rom_basis_eval function. */
-void calculate_basis(const float parameter, float r_weights[4])
+void calculate_basis(const float parameter, float4 &r_weights)
 {
   const float t = parameter;
   const float s = 1.0f - parameter;
@@ -139,11 +139,7 @@ void interpolate_to_evaluated(const GSpan src,
 {
   attribute_math::convert_to_static_type(src.type(), [&](auto dummy) {
     using T = decltype(dummy);
-    /* TODO: Use DefaultMixer or other generic mixing in the basis evaluation function to simplify
-     * supporting more types. */
-    if constexpr (is_same_any_v<T, float, float2, float3, float4, int8_t, int, int64_t>) {
-      interpolate_to_evaluated(src.typed<T>(), cyclic, resolution, dst.typed<T>());
-    }
+    interpolate_to_evaluated(src.typed<T>(), cyclic, resolution, dst.typed<T>());
   });
 }
 
@@ -154,11 +150,7 @@ void interpolate_to_evaluated(const GSpan src,
 {
   attribute_math::convert_to_static_type(src.type(), [&](auto dummy) {
     using T = decltype(dummy);
-    /* TODO: Use DefaultMixer or other generic mixing in the basis evaluation function to simplify
-     * supporting more types. */
-    if constexpr (is_same_any_v<T, float, float2, float3, float4, int8_t, int, int64_t>) {
-      interpolate_to_evaluated(src.typed<T>(), cyclic, evaluated_offsets, dst.typed<T>());
-    }
+    interpolate_to_evaluated(src.typed<T>(), cyclic, evaluated_offsets, dst.typed<T>());
   });
 }