Currently vertices are mapped to B-Bone segments without taking the
rest pose curve into account. This is very simple and fast, but causes
poor deformations in some cases where the rest curvature is significant,
e.g. mouth corners in the new Rigify face rig.
This patch implements a new mapping mode that addresses this problem.
The general idea is to do an orthogonal projection on the curve. However,
since there is no analytical solution for bezier curves, it uses the
segment approximation:
* First, boundaries between segments are used for a binary space
partitioning search to narrow down the mapping to one segment.
* Then, a position on the segment is chosen via linear
interpolation between the BSP planes.
* Finally, to remove the sharp discontinuity at the evolute surface
a smoothing pass is applied to the chosen position by blending to
reduce the slope around the planes previously used in the BSP search.
In order to make per-vertex processing faster, a new array with the
necessary vectors converted to the pose space, as well as some
precomputed coefficients, is built.
The new mode is implemented as a per-bone option in order to ensure
backward compatibility, and also because the new mode may not be
optimal for all cases due to the difference in performance, and
complications like the smoothed but still present mapping
discontinuities around the evolute surface.
Wiki: https://wiki.blender.org/wiki/Source/Animation/B-Bone_Vertex_Mapping
Pull Request: #110758
Alexander Gavrilov