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, 39 insertions, 1 deletions

diff --git a/source/blender/python/mathutils/mathutils_Quaternion.c b/source/blender/python/mathutils/mathutils_Quaternion.c
index 98ee2fbd7cc..786a9324adf 100644
--- a/source/blender/python/mathutils/mathutils_Quaternion.c
+++ b/source/blender/python/mathutils/mathutils_Quaternion.c
@@ -177,6 +177,28 @@ static PyObject *Quaternion_to_axis_angle(QuaternionObject *self)
 	return ret;
 }
 
+PyDoc_STRVAR(Quaternion_to_exponential_map_doc,
+".. method:: to_exponential_map()\n"
+"\n"
+"   Return the exponential map representation of the quaternion.\n"
+"\n"
+"   This representation consist of the rotation axis multiplied by the rotation angle."
+"   Such a representation is useful for interpolation between multiple orientations.\n"
+"\n"
+"   :return: exponential map.\n"
+"   :rtype: :class:`Vector` of size 3\n"
+);
+static PyObject *Quaternion_to_exponential_map(QuaternionObject *self)
+{
+	float expmap[3];
+
+	if (BaseMath_ReadCallback(self) == -1)
+		return NULL;
+
+	quat_to_expmap(expmap, self->quat);
+	return Vector_CreatePyObject(expmap, 3, NULL);
+}
+
 PyDoc_STRVAR(Quaternion_cross_doc,
 ".. method:: cross(other)\n"
 "\n"
@@ -1077,9 +1099,24 @@ static PyObject *Quaternion_new(PyTypeObject *type, PyObject *args, PyObject *kw
 		case 0:
 			break;
 		case 1:
-			if (mathutils_array_parse(quat, QUAT_SIZE, QUAT_SIZE, seq, "mathutils.Quaternion()") == -1)
+		{
+			int size;
+
+			if ((size = mathutils_array_parse(quat, 3, QUAT_SIZE, seq, "mathutils.Quaternion()")) == -1) {
 				return NULL;
+			}
+
+			if (size == 4) {
+				/* 4d: Quaternion (common case) */
+			}
+			else {
+				/* 3d: Interpret as exponential map */
+				BLI_assert(size == 3);
+				expmap_to_quat(quat, quat);
+			}
+
 			break;
+		}
 		case 2:
 		{
 			float axis[3];
@@ -1156,6 +1193,7 @@ static struct PyMethodDef Quaternion_methods[] = {
 	{"to_euler", (PyCFunction) Quaternion_to_euler, METH_VARARGS, Quaternion_to_euler_doc},
 	{"to_matrix", (PyCFunction) Quaternion_to_matrix, METH_NOARGS, Quaternion_to_matrix_doc},
 	{"to_axis_angle", (PyCFunction) Quaternion_to_axis_angle, METH_NOARGS, Quaternion_to_axis_angle_doc},
+	{"to_exponential_map", (PyCFunction) Quaternion_to_exponential_map, METH_NOARGS, Quaternion_to_exponential_map_doc},
 
 	/* operation between 2 or more types  */
 	{"cross", (PyCFunction) Quaternion_cross, METH_O, Quaternion_cross_doc},