mathutils: added exponential map to Quaternion

Added conversion to and from exponential map representation. This
representation is useful for interpolation of > 2 quaternions, or in
PD controllers.

Implementation in C functions quat_to_expmap,
quat_normalized_to_expmap, and expmap_to_quat with Python API, unit
tests and documentation.

Added Quaternion.to_exponential_map() and Quaternion(3-vector) to
Python API.

Reviewers: campbellbarton

Projects: #bf_blender

Differential Revision: https://developer.blender.org/D1049

1 files changed, 5 insertions, 0 deletions

diff --git a/source/blender/blenlib/BLI_math_rotation.h b/source/blender/blenlib/BLI_math_rotation.h
index 905889a33d7..fbd026f7617 100644
--- a/source/blender/blenlib/BLI_math_rotation.h
+++ b/source/blender/blenlib/BLI_math_rotation.h
@@ -119,6 +119,11 @@ void mat4_to_axis_angle(float axis[3], float *angle, float M[4][4]);
 void axis_angle_to_mat3_single(float R[3][3], const char axis, const float angle);
 void      angle_to_mat2(float R[2][2], const float angle);
 
+/****************************** Exponential Map ******************************/
+void quat_to_expmap(float expmap[3], const float q[4]);
+void quat_normalized_to_expmap(float expmap[3], const float q[4]);
+void expmap_to_quat(float r[4], const float expmap[3]);
+
 /******************************** XYZ Eulers *********************************/
 
 void eul_to_quat(float quat[4], const float eul[3]);