Implement a new automatic handle algorithm to produce smooth F-Curves.

The legacy algorithm only considers two adjacent points when computing
the bezier handles, which cannot produce satisfactory results. Animators
are often forced to manually adjust all curves.

The new approach instead solves a system of equations to trace a cubic spline
with continuous second derivative through the whole segment of auto points,
delimited at ends by keyframes with handles set by other requirements.

This algorithm also adjusts Vector handles that face ordinary bezier keyframes
to achieve zero acceleration at the Vector keyframe, instead of simply pointing
it at the adjacent point.

Original idea and implementation by Benoit Bolsee <benoit.bolsee@online.be>;
code mostly rewritten to improve code clarity and extensibility.

Reviewers: aligorith

Differential Revision: https://developer.blender.org/D2884

1 files changed, 5 insertions, 0 deletions

diff --git a/source/blender/blenlib/BLI_math_solvers.h b/source/blender/blenlib/BLI_math_solvers.h
index 810c84cc830..b0193022837 100644
--- a/source/blender/blenlib/BLI_math_solvers.h
+++ b/source/blender/blenlib/BLI_math_solvers.h
@@ -48,6 +48,11 @@ bool BLI_eigen_solve_selfadjoint_m3(const float m3[3][3], float r_eigen_values[3
 
 void BLI_svd_m3(const float m3[3][3], float r_U[3][3], float r_S[], float r_V[3][3]);
 
+/***************************** Simple Solvers ************************************/
+
+bool BLI_tridiagonal_solve(const float *a, const float *b, const float *c, const float *d, float *r_x, const int count);
+bool BLI_tridiagonal_solve_cyclic(const float *a, const float *b, const float *c, const float *d, float *r_x, const int count);
+
 /**************************** Inline Definitions ******************************/
 #if 0  /* None so far. */
 #  if BLI_MATH_DO_INLINE