Cleanup: use determinant_m3(m) < 0 to implement is_negative_m3/m4

Use a more direct method of checking if a matrix is negative instead of
using cross & dot product.

Also replace some determinant_m3() < 0 checks with is_negative_m3.

source/blender/blenlib/BLI_math_matrix.h

@@ -528,7 +528,18 @@ void interp_m3_m3m3(float R[3][3], const float A[3][3], const float B[3][3], flo
  */
 void interp_m4_m4m4(float R[4][4], const float A[4][4], const float B[4][4], float t);
 
+/**
+ * Return true when the matrices determinant is less than zero.
+ *
+ * \note This is often used to check if a matrix flips content in 3D space,
+ * where transforming geometry (for example) would flip the direction of polygon normals
+ * from pointing outside a closed volume, to pointing inside (or the reverse).
+ *
+ * When the matrix is constructed from location, rotation & scale
+ * as matrix will be negative when it has an odd number of negative scales.
+ */
 bool is_negative_m3(const float mat[3][3]);
+/** A version of #is_negative_m3 that takes a 4x4 matrix. */
 bool is_negative_m4(const float mat[4][4]);
 
 bool is_zero_m3(const float mat[3][3]);

source/blender/blenlib/intern/math_matrix.c

@@ -2456,11 +2456,11 @@ void interp_m3_m3m3(float R[3][3], const float A[3][3], const float B[3][3], con
    * Note that a flip of two axes is just a rotation of 180 degrees around the third axis, and
    * three flipped axes are just an 180 degree rotation + a single axis flip. It is thus sufficient
    * to solve this problem for single axis flips. */
-  if (determinant_m3_array(U_A) < 0) {
+  if (is_negative_m3(U_A)) {
     mul_m3_fl(U_A, -1.0f);
     mul_m3_fl(P_A, -1.0f);
   }
-  if (determinant_m3_array(U_B) < 0) {
+  if (is_negative_m3(U_B)) {
     mul_m3_fl(U_B, -1.0f);
     mul_m3_fl(P_B, -1.0f);
   }
@@ -2501,16 +2501,14 @@ void interp_m4_m4m4(float R[4][4], const float A[4][4], const float B[4][4], con
 
 bool is_negative_m3(const float mat[3][3])
 {
-  float vec[3];
-  cross_v3_v3v3(vec, mat[0], mat[1]);
-  return (dot_v3v3(vec, mat[2]) < 0.0f);
+  return determinant_m3_array(mat) < 0.0f;
 }
 
 bool is_negative_m4(const float mat[4][4])
 {
-  float vec[3];
-  cross_v3_v3v3(vec, mat[0], mat[1]);
-  return (dot_v3v3(vec, mat[2]) < 0.0f);
+  /* Don't use #determinant_m4 as only the 3x3 components are needed
+   * when the matrix is used as a transformation to represent location/scale/rotation. */
+  return determinant_m4_mat3_array(mat) < 0.0f;
 }
 
 bool is_zero_m3(const float mat[3][3])

source/blender/io/wavefront_obj/exporter/obj_export_mesh.cc

@@ -133,7 +133,7 @@ void OBJMesh::set_world_axes_transform(const eIOAxis forward, const eIOAxis up)
   copy_m3_m4(normal_matrix, world_and_axes_transform_);
   invert_m3_m3(world_and_axes_normal_transform_, normal_matrix);
   transpose_m3(world_and_axes_normal_transform_);
-  mirrored_transform_ = determinant_m3_array(world_and_axes_normal_transform_) < 0;
+  mirrored_transform_ = is_negative_m3(world_and_axes_normal_transform_);
 }
 
 int OBJMesh::tot_vertices() const