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.
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@ -215,6 +215,8 @@ void mat4_to_loc_rot_size(float loc[3], float rot[3][3], float size[3], float wm
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void mat4_to_loc_quat(float loc[3], float quat[4], float wmat[4][4]);
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void mat4_decompose(float loc[3], float quat[4], float size[3], float wmat[4][4]);
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void mat3_polar_decompose(float mat3[3][3], float r_U[3][3], float r_P[3][3]);
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void loc_eul_size_to_mat4(float R[4][4],
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const float loc[3], const float eul[3], const float size[3]);
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void loc_eulO_size_to_mat4(float R[4][4],
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@ -227,6 +229,9 @@ void loc_axisangle_size_to_mat4(float R[4][4],
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void blend_m3_m3m3(float R[3][3], float A[3][3], float B[3][3], const float t);
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void blend_m4_m4m4(float R[4][4], float A[4][4], float B[4][4], const float t);
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void interp_m3_m3m3(float R[3][3], float A[3][3], float B[3][3], const float t);
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void interp_m4_m4m4(float R[4][4], float A[4][4], float B[4][4], const float t);
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bool is_negative_m3(float mat[3][3]);
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bool is_negative_m4(float mat[4][4]);
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@ -1521,6 +1521,34 @@ void mat4_decompose(float loc[3], float quat[4], float size[3], float wmat[4][4]
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mat3_to_quat(quat, rot);
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}
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/**
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* Right polar decomposition:
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* M = UP
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*
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* U is the 'rotation'-like component, the closest orthogonal matrix to M.
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* P is the 'scaling'-like component, defined in U space.
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*
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* See https://en.wikipedia.org/wiki/Polar_decomposition for more.
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*/
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void mat3_polar_decompose(float mat3[3][3], float r_U[3][3], float r_P[3][3])
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{
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/* From svd decomposition (M = WSV*), we have:
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* U = WV*
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* P = VSV*
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*/
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float W[3][3], S[3][3], V[3][3], Vt[3][3];
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float sval[3];
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BLI_svd_m3(mat3, W, sval, V);
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size_to_mat3(S, sval);
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transpose_m3_m3(Vt, V);
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mul_m3_m3m3(r_U, W, Vt);
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mul_m3_series(r_P, V, S, Vt);
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}
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void scale_m3_fl(float m[3][3], float scale)
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{
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m[0][0] = m[1][1] = m[2][2] = scale;
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@ -1660,6 +1688,75 @@ void blend_m4_m4m4(float out[4][4], float dst[4][4], float src[4][4], const floa
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loc_quat_size_to_mat4(out, floc, fquat, fsize);
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}
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/**
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* A polar-decomposition-based interpolation between matrix A and matrix B.
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*
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* \note This code is about five times slower as the 'naive' interpolation done by \a blend_m3_m3m3
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* (it typically remains below 2 usec on an average i74700, while \a blend_m3_m3m3 remains below 0.4 usec).
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* However, it gives expected results even with non-uniformaly scaled matrices, see T46418 for an example.
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*
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* Based on "Matrix Animation and Polar Decomposition", by Ken Shoemake & Tom Duff
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*
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* @return R the interpolated matrix.
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* @param A the intput matrix which is totally effective with \a t = 0.0.
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* @param B the intput matrix which is totally effective with \a t = 1.0.
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* @param t the interpolation factor.
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*/
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void interp_m3_m3m3(float R[3][3], float A[3][3], float B[3][3], const float t)
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{
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/* 'Rotation' component ('U' part of polar decomposition, the closest orthogonal matrix to M3 rot/scale
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* transformation matrix), spherically interpolated. */
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float U_A[3][3], U_B[3][3], U[3][3];
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float quat_A[4], quat_B[4], quat[4];
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/* 'Scaling' component ('P' part of polar decomposition, i.e. scaling in U-defined space), linearly interpolated. */
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float P_A[3][3], P_B[3][3], P[3][3];
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int i;
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mat3_polar_decompose(A, U_A, P_A);
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mat3_polar_decompose(B, U_B, P_B);
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mat3_to_quat(quat_A, U_A);
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mat3_to_quat(quat_B, U_B);
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interp_qt_qtqt(quat, quat_A, quat_B, t);
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quat_to_mat3(U, quat);
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for (i = 0; i < 3; i++) {
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interp_v3_v3v3(P[i], P_A[i], P_B[i], t);
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}
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/* And we reconstruct rot/scale matrix from interpolated polar components */
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mul_m3_m3m3(R, U, P);
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}
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/**
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* Complete transform matrix interpolation, based on polar-decomposition-based interpolation from interp_m3_m3m3.
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*
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* @return R the interpolated matrix.
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* @param A the intput matrix which is totally effective with \a t = 0.0.
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* @param B the intput matrix which is totally effective with \a t = 1.0.
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* @param t the interpolation factor.
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*/
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void interp_m4_m4m4(float R[4][4], float A[4][4], float B[4][4], const float t)
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{
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float A3[3][3], B3[3][3], R3[3][3];
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/* Location component, linearly interpolated. */
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float loc_A[3], loc_B[3], loc[3];
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copy_v3_v3(loc_A, A[3]);
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copy_v3_v3(loc_B, B[3]);
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interp_v3_v3v3(loc, loc_A, loc_B, t);
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copy_m3_m4(A3, A);
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copy_m3_m4(B3, B);
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interp_m3_m3m3(R3, A3, B3, t);
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copy_m4_m3(R, R3);
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copy_v3_v3(R[3], loc);
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}
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bool is_negative_m3(float mat[3][3])
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{
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float vec[3];
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@ -37,11 +37,11 @@ set(CMAKE_EXE_LINKER_FLAGS_DEBUG "${CMAKE_EXE_LINKER_FLAGS_DEBUG} ${PLATFORM_LIN
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BLENDER_TEST(BLI_stack "bf_blenlib")
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BLENDER_TEST(BLI_math_color "bf_blenlib")
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BLENDER_TEST(BLI_math_geom "bf_blenlib")
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BLENDER_TEST(BLI_math_geom "bf_blenlib;extern_eigen3")
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BLENDER_TEST(BLI_math_base "bf_blenlib")
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BLENDER_TEST(BLI_string "bf_blenlib")
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BLENDER_TEST(BLI_path_util "bf_blenlib;extern_wcwidth;${ZLIB_LIBRARIES}")
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BLENDER_TEST(BLI_polyfill2d "bf_blenlib")
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BLENDER_TEST(BLI_polyfill2d "bf_blenlib;extern_eigen3")
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BLENDER_TEST(BLI_listbase "bf_blenlib")
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BLENDER_TEST(BLI_hash_mm2a "bf_blenlib")
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BLENDER_TEST(BLI_ghash "bf_blenlib")
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