Drivers: add an Average Scale option to the Transform Channel driver vars.

Unlike location and rotation, there is a meaningful definition of
overall/average scaling via the total change in the volume. This
adds an option to retrieve that via a single driver variable,
instead of having to use three and an expression.

Using the determinant to compute the volume scaling also allows
detecting flipping due to negative scale - this is impossible
to do via the three variable approach.

The volume_scale functions are added purely for code readability:
'volume scale factor' is easier to understand than determinant.

Differential Revision: https://developer.blender.org/D4803

2 files changed, 24 insertions, 0 deletions

diff --git a/source/blender/blenlib/BLI_math_matrix.h b/source/blender/blenlib/BLI_math_matrix.h
index 652f096f32d..cc3159556bf 100644
--- a/source/blender/blenlib/BLI_math_matrix.h
+++ b/source/blender/blenlib/BLI_math_matrix.h
@@ -260,6 +260,7 @@ float determinant_m2(float a, float b, float c, float d);
 float determinant_m3(
     float a, float b, float c, float d, float e, float f, float g, float h, float i);
 float determinant_m3_array(const float m[3][3]);
+float determinant_m4_mat3_array(const float m[4][4]);
 float determinant_m4(const float A[4][4]);
 
 #define PSEUDOINVERSE_EPSILON 1e-8f
@@ -277,6 +278,9 @@ void invert_m4_m4_safe(float Ainv[4][4], const float A[4][4]);
 void scale_m3_fl(float R[3][3], float scale);
 void scale_m4_fl(float R[4][4], float scale);
 
+float mat3_to_volume_scale(const float M[3][3]);
+float mat4_to_volume_scale(const float M[4][4]);
+
 float mat3_to_scale(const float M[3][3]);
 float mat4_to_scale(const float M[4][4]);
 float mat4_to_xy_scale(const float M[4][4]);
diff --git a/source/blender/blenlib/intern/math_matrix.c b/source/blender/blenlib/intern/math_matrix.c
index e09fae7d140..0fd947b6b1a 100644
--- a/source/blender/blenlib/intern/math_matrix.c
+++ b/source/blender/blenlib/intern/math_matrix.c
@@ -931,6 +931,13 @@ float determinant_m3_array(const float m[3][3])
           m[2][0] * (m[0][1] * m[1][2] - m[0][2] * m[1][1]));
 }
 
+float determinant_m4_mat3_array(const float m[4][4])
+{
+  return (m[0][0] * (m[1][1] * m[2][2] - m[1][2] * m[2][1]) -
+          m[1][0] * (m[0][1] * m[2][2] - m[0][2] * m[2][1]) +
+          m[2][0] * (m[0][1] * m[1][2] - m[0][2] * m[1][1]));
+}
+
 bool invert_m3_ex(float m[3][3], const float epsilon)
 {
   float tmp[3][3];
@@ -1641,6 +1648,19 @@ void mat4_to_size(float size[3], const float mat[4][4])
   size[2] = len_v3(mat[2]);
 }
 
+/* This computes the overall volume scale factor of a transformation matrix.
+ * For an orthogonal matrix, it is the product of all three scale values.
+ * Returns a negative value if the transform is flipped by negative scale. */
+float mat3_to_volume_scale(const float mat[3][3])
+{
+  return determinant_m3_array(mat);
+}
+
+float mat4_to_volume_scale(const float mat[4][4])
+{
+  return determinant_m4_mat3_array(mat);
+}
+
 /* this gets the average scale of a matrix, only use when your scaling
  * data that has no idea of scale axis, examples are bone-envelope-radius
  * and curve radius */