Fix T37500: implement Bendy bone segment deformation interpolation.

Previously B-Bone deformation mapped every vertex to just one
B-Bone segment. This results in abrupt transformation differences
between the sides of each threshold plane, reducing the quality
of B-Bone deformation and making the use of shape keys impractical.

This commit replaces this approach with a linear blend between
the two closest segment transformations, effectively representing
the B-Bone as two weight-blended plain bones for each vertex.

In order to distribute the interpolation more evenly along the
bone, segment matrices for deformation are now computed at points
between the segments and at the ends of the B-Bone. The computation
also uses the true tangents of the Bezier curve for the orientation.
The nodes at the end of the bone require some special handling to
deal with zero-length Bezier handles caused by a zero ease value.

The Copy Transforms constraint now also smoothly interpolates
rotation and scaling along the bone shape when enabled.

The initial version of the patch was submitted by @Sam200.

Differential Revision: https://developer.blender.org/D4635

1 files changed, 3 insertions, 0 deletions

diff --git a/source/blender/blenlib/BLI_math_matrix.h b/source/blender/blenlib/BLI_math_matrix.h
index 8e35b197e14..49e05f5401e 100644
--- a/source/blender/blenlib/BLI_math_matrix.h
+++ b/source/blender/blenlib/BLI_math_matrix.h
@@ -59,6 +59,9 @@ void swap_m4m4(float A[4][4], float B[4][4]);
 void add_m3_m3m3(float R[3][3], const float A[3][3], const float B[3][3]);
 void add_m4_m4m4(float R[4][4], const float A[4][4], const float B[4][4]);
 
+void madd_m3_m3m3fl(float R[3][3], const float A[3][3], const float B[3][3], const float f);
+void madd_m4_m4m4fl(float R[4][4], const float A[4][4], const float B[4][4], const float f);
+
 void sub_m3_m3m3(float R[3][3], const float A[3][3], const float B[3][3]);
 void sub_m4_m4m4(float R[4][4], const float A[4][4], const float B[4][4]);