[Bf-blender-cvs] [be72df4] master: BLI_math: add mat3_polar_decompose, interp_m3_m3m3 and interp_m4_m4m4.
Bastien Montagne
noreply at git.blender.org
Fri Oct 9 21:30:09 CEST 2015
Commit: be72df4f06ac86f76d6dc4b5503531dbbdddce86
Author: Bastien Montagne
Date: Fri Oct 9 20:57:37 2015 +0200
Branches: master
https://developer.blender.org/rBbe72df4f06ac86f76d6dc4b5503531dbbdddce86
BLI_math: add mat3_polar_decompose, interp_m3_m3m3 and interp_m4_m4m4.
mat3_polar_decompose gives the right polar decomposition of given matrix,
as a pair (U, P) of matrices.
interp_m3_m3m3 uses that polar decomposition to perform a correct matrix interpolation,
even with non-uniformly scaled ones (where blend_m3_m3m3 would fail).
interp_m4_m4m4 just adds translation interpolation to the _m3 variant.
===================================================================
M source/blender/blenlib/BLI_math_matrix.h
M source/blender/blenlib/intern/math_matrix.c
M tests/gtests/blenlib/CMakeLists.txt
===================================================================
diff --git a/source/blender/blenlib/BLI_math_matrix.h b/source/blender/blenlib/BLI_math_matrix.h
index d7a309e..80a399a 100644
--- a/source/blender/blenlib/BLI_math_matrix.h
+++ b/source/blender/blenlib/BLI_math_matrix.h
@@ -215,6 +215,8 @@ void mat4_to_loc_rot_size(float loc[3], float rot[3][3], float size[3], float wm
void mat4_to_loc_quat(float loc[3], float quat[4], float wmat[4][4]);
void mat4_decompose(float loc[3], float quat[4], float size[3], float wmat[4][4]);
+void mat3_polar_decompose(float mat3[3][3], float r_U[3][3], float r_P[3][3]);
+
void loc_eul_size_to_mat4(float R[4][4],
const float loc[3], const float eul[3], const float size[3]);
void loc_eulO_size_to_mat4(float R[4][4],
@@ -227,6 +229,9 @@ void loc_axisangle_size_to_mat4(float R[4][4],
void blend_m3_m3m3(float R[3][3], float A[3][3], float B[3][3], const float t);
void blend_m4_m4m4(float R[4][4], float A[4][4], float B[4][4], const float t);
+void interp_m3_m3m3(float R[3][3], float A[3][3], float B[3][3], const float t);
+void interp_m4_m4m4(float R[4][4], float A[4][4], float B[4][4], const float t);
+
bool is_negative_m3(float mat[3][3]);
bool is_negative_m4(float mat[4][4]);
diff --git a/source/blender/blenlib/intern/math_matrix.c b/source/blender/blenlib/intern/math_matrix.c
index 33d0fb8..8e41a86 100644
--- a/source/blender/blenlib/intern/math_matrix.c
+++ b/source/blender/blenlib/intern/math_matrix.c
@@ -1521,6 +1521,34 @@ void mat4_decompose(float loc[3], float quat[4], float size[3], float wmat[4][4]
mat3_to_quat(quat, rot);
}
+/**
+ * Right polar decomposition:
+ * M = UP
+ *
+ * U is the 'rotation'-like component, the closest orthogonal matrix to M.
+ * P is the 'scaling'-like component, defined in U space.
+ *
+ * See https://en.wikipedia.org/wiki/Polar_decomposition for more.
+ */
+void mat3_polar_decompose(float mat3[3][3], float r_U[3][3], float r_P[3][3])
+{
+ /* From svd decomposition (M = WSV*), we have:
+ * U = WV*
+ * P = VSV*
+ */
+ float W[3][3], S[3][3], V[3][3], Vt[3][3];
+ float sval[3];
+
+ BLI_svd_m3(mat3, W, sval, V);
+
+ size_to_mat3(S, sval);
+
+ transpose_m3_m3(Vt, V);
+ mul_m3_m3m3(r_U, W, Vt);
+ mul_m3_series(r_P, V, S, Vt);
+}
+
+
void scale_m3_fl(float m[3][3], float scale)
{
m[0][0] = m[1][1] = m[2][2] = scale;
@@ -1660,6 +1688,75 @@ void blend_m4_m4m4(float out[4][4], float dst[4][4], float src[4][4], const floa
loc_quat_size_to_mat4(out, floc, fquat, fsize);
}
+/**
+ * A polar-decomposition-based interpolation between matrix A and matrix B.
+ *
+ * \note This code is about five times slower as the 'naive' interpolation done by \a blend_m3_m3m3
+ * (it typically remains below 2 usec on an average i74700, while \a blend_m3_m3m3 remains below 0.4 usec).
+ * However, it gives expected results even with non-uniformaly scaled matrices, see T46418 for an example.
+ *
+ * Based on "Matrix Animation and Polar Decomposition", by Ken Shoemake & Tom Duff
+ *
+ * @return R the interpolated matrix.
+ * @param A the intput matrix which is totally effective with \a t = 0.0.
+ * @param B the intput matrix which is totally effective with \a t = 1.0.
+ * @param t the interpolation factor.
+ */
+void interp_m3_m3m3(float R[3][3], float A[3][3], float B[3][3], const float t)
+{
+ /* 'Rotation' component ('U' part of polar decomposition, the closest orthogonal matrix to M3 rot/scale
+ * transformation matrix), spherically interpolated. */
+ float U_A[3][3], U_B[3][3], U[3][3];
+ float quat_A[4], quat_B[4], quat[4];
+ /* 'Scaling' component ('P' part of polar decomposition, i.e. scaling in U-defined space), linearly interpolated. */
+ float P_A[3][3], P_B[3][3], P[3][3];
+
+ int i;
+
+ mat3_polar_decompose(A, U_A, P_A);
+ mat3_polar_decompose(B, U_B, P_B);
+
+ mat3_to_quat(quat_A, U_A);
+ mat3_to_quat(quat_B, U_B);
+ interp_qt_qtqt(quat, quat_A, quat_B, t);
+ quat_to_mat3(U, quat);
+
+ for (i = 0; i < 3; i++) {
+ interp_v3_v3v3(P[i], P_A[i], P_B[i], t);
+ }
+
+ /* And we reconstruct rot/scale matrix from interpolated polar components */
+ mul_m3_m3m3(R, U, P);
+}
+
+/**
+ * Complete transform matrix interpolation, based on polar-decomposition-based interpolation from interp_m3_m3m3.
+ *
+ * @return R the interpolated matrix.
+ * @param A the intput matrix which is totally effective with \a t = 0.0.
+ * @param B the intput matrix which is totally effective with \a t = 1.0.
+ * @param t the interpolation factor.
+ */
+void interp_m4_m4m4(float R[4][4], float A[4][4], float B[4][4], const float t)
+{
+ float A3[3][3], B3[3][3], R3[3][3];
+
+ /* Location component, linearly interpolated. */
+ float loc_A[3], loc_B[3], loc[3];
+
+ copy_v3_v3(loc_A, A[3]);
+ copy_v3_v3(loc_B, B[3]);
+ interp_v3_v3v3(loc, loc_A, loc_B, t);
+
+ copy_m3_m4(A3, A);
+ copy_m3_m4(B3, B);
+
+ interp_m3_m3m3(R3, A3, B3, t);
+
+ copy_m4_m3(R, R3);
+ copy_v3_v3(R[3], loc);
+}
+
bool is_negative_m3(float mat[3][3])
{
float vec[3];
diff --git a/tests/gtests/blenlib/CMakeLists.txt b/tests/gtests/blenlib/CMakeLists.txt
index acd9f94..e10d6b1 100644
--- a/tests/gtests/blenlib/CMakeLists.txt
+++ b/tests/gtests/blenlib/CMakeLists.txt
@@ -37,11 +37,11 @@ set(CMAKE_EXE_LINKER_FLAGS_DEBUG "${CMAKE_EXE_LINKER_FLAGS_DEBUG} ${PLATFORM_LIN
BLENDER_TEST(BLI_stack "bf_blenlib")
BLENDER_TEST(BLI_math_color "bf_blenlib")
-BLENDER_TEST(BLI_math_geom "bf_blenlib")
+BLENDER_TEST(BLI_math_geom "bf_blenlib;extern_eigen3")
BLENDER_TEST(BLI_math_base "bf_blenlib")
BLENDER_TEST(BLI_string "bf_blenlib")
BLENDER_TEST(BLI_path_util "bf_blenlib;extern_wcwidth;${ZLIB_LIBRARIES}")
-BLENDER_TEST(BLI_polyfill2d "bf_blenlib")
+BLENDER_TEST(BLI_polyfill2d "bf_blenlib;extern_eigen3")
BLENDER_TEST(BLI_listbase "bf_blenlib")
BLENDER_TEST(BLI_hash_mm2a "bf_blenlib")
BLENDER_TEST(BLI_ghash "bf_blenlib")
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