/* * This program is free software; you can redistribute it and/or * modify it under the terms of the GNU General Public License * as published by the Free Software Foundation; either version 2 * of the License, or (at your option) any later version. * * This program is distributed in the hope that it will be useful, * but WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the * GNU General Public License for more details. * * You should have received a copy of the GNU General Public License * along with this program; if not, write to the Free Software Foundation, * Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA. * * The Original Code is Copyright (C) Blender Foundation * All rights reserved. */ /** \file * \ingroup sim */ #include "implicit.h" #ifdef IMPLICIT_SOLVER_BLENDER # include "MEM_guardedalloc.h" # include "DNA_meshdata_types.h" # include "DNA_object_force_types.h" # include "DNA_object_types.h" # include "DNA_scene_types.h" # include "DNA_texture_types.h" # include "BLI_math.h" # include "BLI_utildefines.h" # include "BKE_cloth.h" # include "BKE_collision.h" # include "BKE_effect.h" # include "SIM_mass_spring.h" # ifdef __GNUC__ # pragma GCC diagnostic ignored "-Wtype-limits" # endif # ifdef _OPENMP # define CLOTH_OPENMP_LIMIT 512 # endif //#define DEBUG_TIME # ifdef DEBUG_TIME # include "PIL_time.h" # endif static float I[3][3] = {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}; static float ZERO[3][3] = {{0, 0, 0}, {0, 0, 0}, {0, 0, 0}}; # if 0 # define C99 # ifdef C99 # defineDO_INLINE inline # else # defineDO_INLINE static # endif # endif /* if 0 */ struct Cloth; ////////////////////////////////////////// /* fast vector / matrix library, enhancements are welcome :) -dg */ ///////////////////////////////////////// /* DEFINITIONS */ typedef float lfVector[3]; typedef struct fmatrix3x3 { float m[3][3]; /* 3x3 matrix */ unsigned int c, r; /* column and row number */ // int pinned; /* is this vertex allowed to move? */ float n1, n2, n3; /* three normal vectors for collision constrains */ unsigned int vcount; /* vertex count */ unsigned int scount; /* spring count */ } fmatrix3x3; /////////////////////////// /* float[3] vector */ /////////////////////////// /* simple vector code */ /* STATUS: verified */ DO_INLINE void mul_fvector_S(float to[3], const float from[3], float scalar) { to[0] = from[0] * scalar; to[1] = from[1] * scalar; to[2] = from[2] * scalar; } /* simple v^T * v product ("outer product") */ /* STATUS: HAS TO BE verified (*should* work) */ DO_INLINE void mul_fvectorT_fvector(float to[3][3], const float vectorA[3], const float vectorB[3]) { mul_fvector_S(to[0], vectorB, vectorA[0]); mul_fvector_S(to[1], vectorB, vectorA[1]); mul_fvector_S(to[2], vectorB, vectorA[2]); } /* simple v^T * v product with scalar ("outer product") */ /* STATUS: HAS TO BE verified (*should* work) */ DO_INLINE void mul_fvectorT_fvectorS(float to[3][3], float vectorA[3], float vectorB[3], float aS) { mul_fvectorT_fvector(to, vectorA, vectorB); mul_fvector_S(to[0], to[0], aS); mul_fvector_S(to[1], to[1], aS); mul_fvector_S(to[2], to[2], aS); } # if 0 /* printf vector[3] on console: for debug output */ static void print_fvector(float m3[3]) { printf("%f\n%f\n%f\n\n", m3[0], m3[1], m3[2]); } /////////////////////////// /* long float vector float (*)[3] */ /////////////////////////// /* print long vector on console: for debug output */ DO_INLINE void print_lfvector(float (*fLongVector)[3], unsigned int verts) { unsigned int i = 0; for (i = 0; i < verts; i++) { print_fvector(fLongVector[i]); } } # endif /* create long vector */ DO_INLINE lfVector *create_lfvector(unsigned int verts) { /* TODO: check if memory allocation was successful */ return (lfVector *)MEM_callocN(verts * sizeof(lfVector), "cloth_implicit_alloc_vector"); // return (lfVector *)cloth_aligned_malloc(&MEMORY_BASE, verts * sizeof(lfVector)); } /* delete long vector */ DO_INLINE void del_lfvector(float (*fLongVector)[3]) { if (fLongVector != NULL) { MEM_freeN(fLongVector); // cloth_aligned_free(&MEMORY_BASE, fLongVector); } } /* copy long vector */ DO_INLINE void cp_lfvector(float (*to)[3], float (*from)[3], unsigned int verts) { memcpy(to, from, verts * sizeof(lfVector)); } /* init long vector with float[3] */ DO_INLINE void init_lfvector(float (*fLongVector)[3], const float vector[3], unsigned int verts) { unsigned int i = 0; for (i = 0; i < verts; i++) { copy_v3_v3(fLongVector[i], vector); } } /* zero long vector with float[3] */ DO_INLINE void zero_lfvector(float (*to)[3], unsigned int verts) { memset(to, 0.0f, verts * sizeof(lfVector)); } /* Multiply long vector with scalar. */ DO_INLINE void mul_lfvectorS(float (*to)[3], float (*fLongVector)[3], float scalar, unsigned int verts) { unsigned int i = 0; for (i = 0; i < verts; i++) { mul_fvector_S(to[i], fLongVector[i], scalar); } } /* Multiply long vector with scalar. * `A -= B * float` */ DO_INLINE void submul_lfvectorS(float (*to)[3], float (*fLongVector)[3], float scalar, unsigned int verts) { unsigned int i = 0; for (i = 0; i < verts; i++) { VECSUBMUL(to[i], fLongVector[i], scalar); } } /* dot product for big vector */ DO_INLINE float dot_lfvector(float (*fLongVectorA)[3], float (*fLongVectorB)[3], unsigned int verts) { long i = 0; float temp = 0.0; /* XXX brecht, disabled this for now (first schedule line was already disabled), * due to non-commutative nature of floating point ops this makes the sim give * different results each time you run it! * schedule(guided, 2) */ //#pragma omp parallel for reduction(+: temp) if (verts > CLOTH_OPENMP_LIMIT) for (i = 0; i < (long)verts; i++) { temp += dot_v3v3(fLongVectorA[i], fLongVectorB[i]); } return temp; } /* `A = B + C` -> for big vector. */ DO_INLINE void add_lfvector_lfvector(float (*to)[3], float (*fLongVectorA)[3], float (*fLongVectorB)[3], unsigned int verts) { unsigned int i = 0; for (i = 0; i < verts; i++) { add_v3_v3v3(to[i], fLongVectorA[i], fLongVectorB[i]); } } /* `A = B + C * float` -> for big vector. */ DO_INLINE void add_lfvector_lfvectorS(float (*to)[3], float (*fLongVectorA)[3], float (*fLongVectorB)[3], float bS, unsigned int verts) { unsigned int i = 0; for (i = 0; i < verts; i++) { VECADDS(to[i], fLongVectorA[i], fLongVectorB[i], bS); } } /* `A = B * float + C * float` -> for big vector */ DO_INLINE void add_lfvectorS_lfvectorS(float (*to)[3], float (*fLongVectorA)[3], float aS, float (*fLongVectorB)[3], float bS, unsigned int verts) { unsigned int i = 0; for (i = 0; i < verts; i++) { VECADDSS(to[i], fLongVectorA[i], aS, fLongVectorB[i], bS); } } /* `A = B - C * float` -> for big vector. */ DO_INLINE void sub_lfvector_lfvectorS(float (*to)[3], float (*fLongVectorA)[3], float (*fLongVectorB)[3], float bS, unsigned int verts) { unsigned int i = 0; for (i = 0; i < verts; i++) { VECSUBS(to[i], fLongVectorA[i], fLongVectorB[i], bS); } } /* `A = B - C` -> for big vector. */ DO_INLINE void sub_lfvector_lfvector(float (*to)[3], float (*fLongVectorA)[3], float (*fLongVectorB)[3], unsigned int verts) { unsigned int i = 0; for (i = 0; i < verts; i++) { sub_v3_v3v3(to[i], fLongVectorA[i], fLongVectorB[i]); } } /////////////////////////// // 3x3 matrix /////////////////////////// # if 0 /* printf 3x3 matrix on console: for debug output */ static void print_fmatrix(float m3[3][3]) { printf("%f\t%f\t%f\n", m3[0][0], m3[0][1], m3[0][2]); printf("%f\t%f\t%f\n", m3[1][0], m3[1][1], m3[1][2]); printf("%f\t%f\t%f\n\n", m3[2][0], m3[2][1], m3[2][2]); } static void print_sparse_matrix(fmatrix3x3 *m) { if (m) { unsigned int i; for (i = 0; i < m[0].vcount + m[0].scount; i++) { printf("%d:\n", i); print_fmatrix(m[i].m); } } } # endif # if 0 static void print_lvector(lfVector *v, int numverts) { int i; for (i = 0; i < numverts; i++) { if (i > 0) { printf("\n"); } printf("%f,\n", v[i][0]); printf("%f,\n", v[i][1]); printf("%f,\n", v[i][2]); } } # endif # if 0 static void print_bfmatrix(fmatrix3x3 *m) { int tot = m[0].vcount + m[0].scount; int size = m[0].vcount * 3; float *t = MEM_callocN(sizeof(float) * size * size, "bfmatrix"); int q, i, j; for (q = 0; q < tot; q++) { int k = 3 * m[q].r; int l = 3 * m[q].c; for (j = 0; j < 3; j++) { for (i = 0; i < 3; i++) { # if 0 if (t[k + i + (l + j) * size] != 0.0f) { printf("warning: overwriting value at %d, %d\n", m[q].r, m[q].c); } # endif if (k == l) { t[k + i + (k + j) * size] += m[q].m[i][j]; } else { t[k + i + (l + j) * size] += m[q].m[i][j]; t[l + j + (k + i) * size] += m[q].m[j][i]; } } } } for (j = 0; j < size; j++) { if (j > 0 && j % 3 == 0) { printf("\n"); } for (i = 0; i < size; i++) { if (i > 0 && i % 3 == 0) { printf(" "); } implicit_print_matrix_elem(t[i + j * size]); } printf("\n"); } MEM_freeN(t); } # endif /* copy 3x3 matrix */ DO_INLINE void cp_fmatrix(float to[3][3], const float from[3][3]) { // memcpy(to, from, sizeof(float[3][3])); copy_v3_v3(to[0], from[0]); copy_v3_v3(to[1], from[1]); copy_v3_v3(to[2], from[2]); } /* copy 3x3 matrix */ DO_INLINE void initdiag_fmatrixS(float to[3][3], float aS) { cp_fmatrix(to, ZERO); to[0][0] = aS; to[1][1] = aS; to[2][2] = aS; } # if 0 /* calculate determinant of 3x3 matrix */ DO_INLINE float det_fmatrix(float m[3][3]) { return m[0][0] * m[1][1] * m[2][2] + m[1][0] * m[2][1] * m[0][2] + m[0][1] * m[1][2] * m[2][0] - m[0][0] * m[1][2] * m[2][1] - m[0][1] * m[1][0] * m[2][2] - m[2][0] * m[1][1] * m[0][2]; } DO_INLINE void inverse_fmatrix(float to[3][3], float from[3][3]) { unsigned int i, j; float d; if ((d = det_fmatrix(from)) == 0) { printf("can't build inverse"); exit(0); } for (i = 0; i < 3; i++) { for (j = 0; j < 3; j++) { int i1 = (i + 1) % 3; int i2 = (i + 2) % 3; int j1 = (j + 1) % 3; int j2 = (j + 2) % 3; /** Reverse indexes i&j to take transpose. */ to[j][i] = (from[i1][j1] * from[i2][j2] - from[i1][j2] * from[i2][j1]) / d; /** * 
       * if (i == j) {
       *     to[i][j] = 1.0f / from[i][j];
       * }
       * else {
       *     to[i][j] = 0;
       * }
       *
*/ } } } # endif /* 3x3 matrix multiplied by a scalar */ /* STATUS: verified */ DO_INLINE void mul_fmatrix_S(float matrix[3][3], float scalar) { mul_fvector_S(matrix[0], matrix[0], scalar); mul_fvector_S(matrix[1], matrix[1], scalar); mul_fvector_S(matrix[2], matrix[2], scalar); } /* a vector multiplied by a 3x3 matrix */ /* STATUS: verified */ DO_INLINE void mul_fvector_fmatrix(float *to, const float *from, const float matrix[3][3]) { to[0] = matrix[0][0] * from[0] + matrix[1][0] * from[1] + matrix[2][0] * from[2]; to[1] = matrix[0][1] * from[0] + matrix[1][1] * from[1] + matrix[2][1] * from[2]; to[2] = matrix[0][2] * from[0] + matrix[1][2] * from[1] + matrix[2][2] * from[2]; } /* 3x3 matrix multiplied by a vector */ /* STATUS: verified */ DO_INLINE void mul_fmatrix_fvector(float *to, const float matrix[3][3], const float from[3]) { to[0] = dot_v3v3(matrix[0], from); to[1] = dot_v3v3(matrix[1], from); to[2] = dot_v3v3(matrix[2], from); } /* 3x3 matrix addition with 3x3 matrix */ DO_INLINE void add_fmatrix_fmatrix(float to[3][3], const float matrixA[3][3], const float matrixB[3][3]) { add_v3_v3v3(to[0], matrixA[0], matrixB[0]); add_v3_v3v3(to[1], matrixA[1], matrixB[1]); add_v3_v3v3(to[2], matrixA[2], matrixB[2]); } /* `A -= B*x + (C * y)` (3x3 matrix sub-addition with 3x3 matrix). */ DO_INLINE void subadd_fmatrixS_fmatrixS( float to[3][3], const float matrixA[3][3], float aS, const float matrixB[3][3], float bS) { VECSUBADDSS(to[0], matrixA[0], aS, matrixB[0], bS); VECSUBADDSS(to[1], matrixA[1], aS, matrixB[1], bS); VECSUBADDSS(to[2], matrixA[2], aS, matrixB[2], bS); } /* `A = B - C` (3x3 matrix subtraction with 3x3 matrix). */ DO_INLINE void sub_fmatrix_fmatrix(float to[3][3], const float matrixA[3][3], const float matrixB[3][3]) { sub_v3_v3v3(to[0], matrixA[0], matrixB[0]); sub_v3_v3v3(to[1], matrixA[1], matrixB[1]); sub_v3_v3v3(to[2], matrixA[2], matrixB[2]); } ///////////////////////////////////////////////////////////////// /* special functions */ ///////////////////////////////////////////////////////////////// /* 3x3 matrix multiplied+added by a vector */ /* STATUS: verified */ DO_INLINE void muladd_fmatrix_fvector(float to[3], const float matrix[3][3], const float from[3]) { to[0] += dot_v3v3(matrix[0], from); to[1] += dot_v3v3(matrix[1], from); to[2] += dot_v3v3(matrix[2], from); } DO_INLINE void muladd_fmatrixT_fvector(float to[3], const float matrix[3][3], const float from[3]) { to[0] += matrix[0][0] * from[0] + matrix[1][0] * from[1] + matrix[2][0] * from[2]; to[1] += matrix[0][1] * from[0] + matrix[1][1] * from[1] + matrix[2][1] * from[2]; to[2] += matrix[0][2] * from[0] + matrix[1][2] * from[1] + matrix[2][2] * from[2]; } BLI_INLINE void outerproduct(float r[3][3], const float a[3], const float b[3]) { mul_v3_v3fl(r[0], a, b[0]); mul_v3_v3fl(r[1], a, b[1]); mul_v3_v3fl(r[2], a, b[2]); } BLI_INLINE void cross_m3_v3m3(float r[3][3], const float v[3], const float m[3][3]) { cross_v3_v3v3(r[0], v, m[0]); cross_v3_v3v3(r[1], v, m[1]); cross_v3_v3v3(r[2], v, m[2]); } BLI_INLINE void cross_v3_identity(float r[3][3], const float v[3]) { r[0][0] = 0.0f; r[1][0] = v[2]; r[2][0] = -v[1]; r[0][1] = -v[2]; r[1][1] = 0.0f; r[2][1] = v[0]; r[0][2] = v[1]; r[1][2] = -v[0]; r[2][2] = 0.0f; } BLI_INLINE void madd_m3_m3fl(float r[3][3], const float m[3][3], float f) { r[0][0] += m[0][0] * f; r[0][1] += m[0][1] * f; r[0][2] += m[0][2] * f; r[1][0] += m[1][0] * f; r[1][1] += m[1][1] * f; r[1][2] += m[1][2] * f; r[2][0] += m[2][0] * f; r[2][1] += m[2][1] * f; r[2][2] += m[2][2] * f; } ///////////////////////////////////////////////////////////////// /////////////////////////// /* SPARSE SYMMETRIC big matrix with 3x3 matrix entries */ /////////////////////////// /* printf a big matrix on console: for debug output */ # if 0 static void print_bfmatrix(fmatrix3x3 *m3) { unsigned int i = 0; for (i = 0; i < m3[0].vcount + m3[0].scount; i++) { print_fmatrix(m3[i].m); } } # endif BLI_INLINE void init_fmatrix(fmatrix3x3 *matrix, int r, int c) { matrix->r = r; matrix->c = c; } /* create big matrix */ DO_INLINE fmatrix3x3 *create_bfmatrix(unsigned int verts, unsigned int springs) { /* TODO: check if memory allocation was successful */ fmatrix3x3 *temp = (fmatrix3x3 *)MEM_callocN(sizeof(fmatrix3x3) * (verts + springs), "cloth_implicit_alloc_matrix"); int i; temp[0].vcount = verts; temp[0].scount = springs; /* vertex part of the matrix is diagonal blocks */ for (i = 0; i < verts; i++) { init_fmatrix(temp + i, i, i); } return temp; } /* delete big matrix */ DO_INLINE void del_bfmatrix(fmatrix3x3 *matrix) { if (matrix != NULL) { MEM_freeN(matrix); } } /* copy big matrix */ DO_INLINE void cp_bfmatrix(fmatrix3x3 *to, fmatrix3x3 *from) { /* TODO: bounds checking. */ memcpy(to, from, sizeof(fmatrix3x3) * (from[0].vcount + from[0].scount)); } /* init big matrix */ /* slow in parallel */ DO_INLINE void init_bfmatrix(fmatrix3x3 *matrix, float m3[3][3]) { unsigned int i; for (i = 0; i < matrix[0].vcount + matrix[0].scount; i++) { cp_fmatrix(matrix[i].m, m3); } } /* init the diagonal of big matrix */ /* slow in parallel */ DO_INLINE void initdiag_bfmatrix(fmatrix3x3 *matrix, float m3[3][3]) { unsigned int i, j; float tmatrix[3][3] = {{0, 0, 0}, {0, 0, 0}, {0, 0, 0}}; for (i = 0; i < matrix[0].vcount; i++) { cp_fmatrix(matrix[i].m, m3); } for (j = matrix[0].vcount; j < matrix[0].vcount + matrix[0].scount; j++) { cp_fmatrix(matrix[j].m, tmatrix); } } /* SPARSE SYMMETRIC multiply big matrix with long vector. */ /* STATUS: verified */ DO_INLINE void mul_bfmatrix_lfvector(float (*to)[3], fmatrix3x3 *from, lfVector *fLongVector) { unsigned int vcount = from[0].vcount; lfVector *temp = create_lfvector(vcount); zero_lfvector(to, vcount); # pragma omp parallel sections if (vcount > CLOTH_OPENMP_LIMIT) { # pragma omp section { for (unsigned int i = from[0].vcount; i < from[0].vcount + from[0].scount; i++) { /* This is the lower triangle of the sparse matrix, * therefore multiplication occurs with transposed submatrices. */ muladd_fmatrixT_fvector(to[from[i].c], from[i].m, fLongVector[from[i].r]); } } # pragma omp section { for (unsigned int i = 0; i < from[0].vcount + from[0].scount; i++) { muladd_fmatrix_fvector(temp[from[i].r], from[i].m, fLongVector[from[i].c]); } } } add_lfvector_lfvector(to, to, temp, from[0].vcount); del_lfvector(temp); } /* SPARSE SYMMETRIC sub big matrix with big matrix. */ /* A -= B * float + C * float --> for big matrix */ /* VERIFIED */ DO_INLINE void subadd_bfmatrixS_bfmatrixS( fmatrix3x3 *to, fmatrix3x3 *from, float aS, fmatrix3x3 *matrix, float bS) { unsigned int i = 0; /* process diagonal elements */ for (i = 0; i < matrix[0].vcount + matrix[0].scount; i++) { subadd_fmatrixS_fmatrixS(to[i].m, from[i].m, aS, matrix[i].m, bS); } } /////////////////////////////////////////////////////////////////// /* simulator start */ /////////////////////////////////////////////////////////////////// typedef struct Implicit_Data { /* inputs */ fmatrix3x3 *bigI; /* identity (constant) */ fmatrix3x3 *tfm; /* local coordinate transform */ fmatrix3x3 *M; /* masses */ lfVector *F; /* forces */ fmatrix3x3 *dFdV, *dFdX; /* force jacobians */ int num_blocks; /* number of off-diagonal blocks (springs) */ /* motion state data */ lfVector *X, *Xnew; /* positions */ lfVector *V, *Vnew; /* velocities */ /* internal solver data */ lfVector *B; /* B for A*dV = B */ fmatrix3x3 *A; /* A for A*dV = B */ lfVector *dV; /* velocity change (solution of A*dV = B) */ lfVector *z; /* target velocity in constrained directions */ fmatrix3x3 *S; /* filtering matrix for constraints */ fmatrix3x3 *P, *Pinv; /* pre-conditioning matrix */ } Implicit_Data; Implicit_Data *SIM_mass_spring_solver_create(int numverts, int numsprings) { Implicit_Data *id = (Implicit_Data *)MEM_callocN(sizeof(Implicit_Data), "implicit vecmat"); /* process diagonal elements */ id->tfm = create_bfmatrix(numverts, 0); id->A = create_bfmatrix(numverts, numsprings); id->dFdV = create_bfmatrix(numverts, numsprings); id->dFdX = create_bfmatrix(numverts, numsprings); id->S = create_bfmatrix(numverts, 0); id->Pinv = create_bfmatrix(numverts, numsprings); id->P = create_bfmatrix(numverts, numsprings); id->bigI = create_bfmatrix(numverts, numsprings); /* TODO: 0 springs. */ id->M = create_bfmatrix(numverts, numsprings); id->X = create_lfvector(numverts); id->Xnew = create_lfvector(numverts); id->V = create_lfvector(numverts); id->Vnew = create_lfvector(numverts); id->F = create_lfvector(numverts); id->B = create_lfvector(numverts); id->dV = create_lfvector(numverts); id->z = create_lfvector(numverts); initdiag_bfmatrix(id->bigI, I); return id; } void SIM_mass_spring_solver_free(Implicit_Data *id) { del_bfmatrix(id->tfm); del_bfmatrix(id->A); del_bfmatrix(id->dFdV); del_bfmatrix(id->dFdX); del_bfmatrix(id->S); del_bfmatrix(id->P); del_bfmatrix(id->Pinv); del_bfmatrix(id->bigI); del_bfmatrix(id->M); del_lfvector(id->X); del_lfvector(id->Xnew); del_lfvector(id->V); del_lfvector(id->Vnew); del_lfvector(id->F); del_lfvector(id->B); del_lfvector(id->dV); del_lfvector(id->z); MEM_freeN(id); } /* ==== Transformation from/to root reference frames ==== */ BLI_INLINE void world_to_root_v3(Implicit_Data *data, int index, float r[3], const float v[3]) { copy_v3_v3(r, v); mul_transposed_m3_v3(data->tfm[index].m, r); } BLI_INLINE void root_to_world_v3(Implicit_Data *data, int index, float r[3], const float v[3]) { mul_v3_m3v3(r, data->tfm[index].m, v); } BLI_INLINE void world_to_root_m3(Implicit_Data *data, int index, float r[3][3], const float m[3][3]) { float trot[3][3]; copy_m3_m3(trot, data->tfm[index].m); transpose_m3(trot); mul_m3_m3m3(r, trot, m); } BLI_INLINE void root_to_world_m3(Implicit_Data *data, int index, float r[3][3], const float m[3][3]) { mul_m3_m3m3(r, data->tfm[index].m, m); } /* ================================ */ DO_INLINE void filter(lfVector *V, fmatrix3x3 *S) { unsigned int i = 0; for (i = 0; i < S[0].vcount; i++) { mul_m3_v3(S[i].m, V[S[i].r]); } } /* this version of the CG algorithm does not work very well with partial constraints * (where S has non-zero elements). */ # if 0 static int cg_filtered(lfVector *ldV, fmatrix3x3 *lA, lfVector *lB, lfVector *z, fmatrix3x3 *S) { /* Solves for unknown X in equation AX=B */ unsigned int conjgrad_loopcount = 0, conjgrad_looplimit = 100; float conjgrad_epsilon = 0.0001f /* , conjgrad_lasterror=0 */ /* UNUSED */; lfVector *q, *d, *tmp, *r; float s, starget, a, s_prev; unsigned int numverts = lA[0].vcount; q = create_lfvector(numverts); d = create_lfvector(numverts); tmp = create_lfvector(numverts); r = create_lfvector(numverts); // zero_lfvector(ldV, CLOTHPARTICLES); filter(ldV, S); add_lfvector_lfvector(ldV, ldV, z, numverts); // r = B - Mul(tmp, A, X); /* just use B if X known to be zero. */ cp_lfvector(r, lB, numverts); mul_bfmatrix_lfvector(tmp, lA, ldV); sub_lfvector_lfvector(r, r, tmp, numverts); filter(r, S); cp_lfvector(d, r, numverts); s = dot_lfvector(r, r, numverts); starget = s * sqrtf(conjgrad_epsilon); while (s > starget && conjgrad_loopcount < conjgrad_looplimit) { // Mul(q, A, d); /* q = A*d; */ mul_bfmatrix_lfvector(q, lA, d); filter(q, S); a = s / dot_lfvector(d, q, numverts); /* X = X + d*a; */ add_lfvector_lfvectorS(ldV, ldV, d, a, numverts); /* r = r - q*a; */ sub_lfvector_lfvectorS(r, r, q, a, numverts); s_prev = s; s = dot_lfvector(r, r, numverts); /* d = r+d*(s/s_prev); */ add_lfvector_lfvectorS(d, r, d, (s / s_prev), numverts); filter(d, S); conjgrad_loopcount++; } /* conjgrad_lasterror = s; */ /* UNUSED */ del_lfvector(q); del_lfvector(d); del_lfvector(tmp); del_lfvector(r); // printf("W/O conjgrad_loopcount: %d\n", conjgrad_loopcount); return conjgrad_loopcount < conjgrad_looplimit; /* true means we reached desired accuracy in given time - ie stable */ } # endif static int cg_filtered(lfVector *ldV, fmatrix3x3 *lA, lfVector *lB, lfVector *z, fmatrix3x3 *S, ImplicitSolverResult *result) { /* Solves for unknown X in equation AX=B */ unsigned int conjgrad_loopcount = 0, conjgrad_looplimit = 100; float conjgrad_epsilon = 0.01f; unsigned int numverts = lA[0].vcount; lfVector *fB = create_lfvector(numverts); lfVector *AdV = create_lfvector(numverts); lfVector *r = create_lfvector(numverts); lfVector *c = create_lfvector(numverts); lfVector *q = create_lfvector(numverts); lfVector *s = create_lfvector(numverts); float bnorm2, delta_new, delta_old, delta_target, alpha; cp_lfvector(ldV, z, numverts); /* d0 = filter(B)^T * P * filter(B) */ cp_lfvector(fB, lB, numverts); filter(fB, S); bnorm2 = dot_lfvector(fB, fB, numverts); delta_target = conjgrad_epsilon * conjgrad_epsilon * bnorm2; /* r = filter(B - A * dV) */ mul_bfmatrix_lfvector(AdV, lA, ldV); sub_lfvector_lfvector(r, lB, AdV, numverts); filter(r, S); /* c = filter(P^-1 * r) */ cp_lfvector(c, r, numverts); filter(c, S); /* delta = r^T * c */ delta_new = dot_lfvector(r, c, numverts); # ifdef IMPLICIT_PRINT_SOLVER_INPUT_OUTPUT printf("==== A ====\n"); print_bfmatrix(lA); printf("==== z ====\n"); print_lvector(z, numverts); printf("==== B ====\n"); print_lvector(lB, numverts); printf("==== S ====\n"); print_bfmatrix(S); # endif while (delta_new > delta_target && conjgrad_loopcount < conjgrad_looplimit) { mul_bfmatrix_lfvector(q, lA, c); filter(q, S); alpha = delta_new / dot_lfvector(c, q, numverts); add_lfvector_lfvectorS(ldV, ldV, c, alpha, numverts); add_lfvector_lfvectorS(r, r, q, -alpha, numverts); /* s = P^-1 * r */ cp_lfvector(s, r, numverts); delta_old = delta_new; delta_new = dot_lfvector(r, s, numverts); add_lfvector_lfvectorS(c, s, c, delta_new / delta_old, numverts); filter(c, S); conjgrad_loopcount++; } # ifdef IMPLICIT_PRINT_SOLVER_INPUT_OUTPUT printf("==== dV ====\n"); print_lvector(ldV, numverts); printf("========\n"); # endif del_lfvector(fB); del_lfvector(AdV); del_lfvector(r); del_lfvector(c); del_lfvector(q); del_lfvector(s); // printf("W/O conjgrad_loopcount: %d\n", conjgrad_loopcount); result->status = conjgrad_loopcount < conjgrad_looplimit ? SIM_SOLVER_SUCCESS : SIM_SOLVER_NO_CONVERGENCE; result->iterations = conjgrad_loopcount; result->error = bnorm2 > 0.0f ? sqrtf(delta_new / bnorm2) : 0.0f; return conjgrad_loopcount < conjgrad_looplimit; /* true means we reached desired accuracy in given time - ie stable */ } # if 0 /* block diagonalizer */ DO_INLINE void BuildPPinv(fmatrix3x3 *lA, fmatrix3x3 *P, fmatrix3x3 *Pinv) { unsigned int i = 0; /* Take only the diagonal blocks of A */ // #pragma omp parallel for private(i) if (lA[0].vcount > CLOTH_OPENMP_LIMIT) for (i = 0; i < lA[0].vcount; i++) { /* block diagonalizer */ cp_fmatrix(P[i].m, lA[i].m); inverse_fmatrix(Pinv[i].m, P[i].m); } } # if 0 /* version 1.3 */ static int cg_filtered_pre(lfVector *dv, fmatrix3x3 *lA, lfVector *lB, lfVector *z, fmatrix3x3 *S, fmatrix3x3 *P, fmatrix3x3 *Pinv) { unsigned int numverts = lA[0].vcount, iterations = 0, conjgrad_looplimit = 100; float delta0 = 0, deltaNew = 0, deltaOld = 0, alpha = 0; float conjgrad_epsilon = 0.0001; /* 0.2 is dt for steps=5 */ lfVector *r = create_lfvector(numverts); lfVector *p = create_lfvector(numverts); lfVector *s = create_lfvector(numverts); lfVector *h = create_lfvector(numverts); BuildPPinv(lA, P, Pinv); filter(dv, S); add_lfvector_lfvector(dv, dv, z, numverts); mul_bfmatrix_lfvector(r, lA, dv); sub_lfvector_lfvector(r, lB, r, numverts); filter(r, S); mul_prevfmatrix_lfvector(p, Pinv, r); filter(p, S); deltaNew = dot_lfvector(r, p, numverts); delta0 = deltaNew * sqrt(conjgrad_epsilon); # ifdef DEBUG_TIME double start = PIL_check_seconds_timer(); # endif while ((deltaNew > delta0) && (iterations < conjgrad_looplimit)) { iterations++; mul_bfmatrix_lfvector(s, lA, p); filter(s, S); alpha = deltaNew / dot_lfvector(p, s, numverts); add_lfvector_lfvectorS(dv, dv, p, alpha, numverts); add_lfvector_lfvectorS(r, r, s, -alpha, numverts); mul_prevfmatrix_lfvector(h, Pinv, r); filter(h, S); deltaOld = deltaNew; deltaNew = dot_lfvector(r, h, numverts); add_lfvector_lfvectorS(p, h, p, deltaNew / deltaOld, numverts); filter(p, S); } # ifdef DEBUG_TIME double end = PIL_check_seconds_timer(); printf("cg_filtered_pre time: %f\n", (float)(end - start)); # endif del_lfvector(h); del_lfvector(s); del_lfvector(p); del_lfvector(r); printf("iterations: %d\n", iterations); return iterations < conjgrad_looplimit; } # endif /* version 1.4 */ static int cg_filtered_pre(lfVector *dv, fmatrix3x3 *lA, lfVector *lB, lfVector *z, fmatrix3x3 *S, fmatrix3x3 *P, fmatrix3x3 *Pinv, fmatrix3x3 *bigI) { unsigned int numverts = lA[0].vcount, iterations = 0, conjgrad_looplimit = 100; float delta0 = 0, deltaNew = 0, deltaOld = 0, alpha = 0, tol = 0; lfVector *r = create_lfvector(numverts); lfVector *p = create_lfvector(numverts); lfVector *s = create_lfvector(numverts); lfVector *h = create_lfvector(numverts); lfVector *bhat = create_lfvector(numverts); lfVector *btemp = create_lfvector(numverts); BuildPPinv(lA, P, Pinv); initdiag_bfmatrix(bigI, I); sub_bfmatrix_Smatrix(bigI, bigI, S); /* x = Sx_0+(I-S)z */ filter(dv, S); add_lfvector_lfvector(dv, dv, z, numverts); /* b_hat = S(b-A(I-S)z) */ mul_bfmatrix_lfvector(r, lA, z); mul_bfmatrix_lfvector(bhat, bigI, r); sub_lfvector_lfvector(bhat, lB, bhat, numverts); /* r = S(b-Ax) */ mul_bfmatrix_lfvector(r, lA, dv); sub_lfvector_lfvector(r, lB, r, numverts); filter(r, S); /* p = SP^-1r */ mul_prevfmatrix_lfvector(p, Pinv, r); filter(p, S); /* delta0 = bhat^TP^-1bhat */ mul_prevfmatrix_lfvector(btemp, Pinv, bhat); delta0 = dot_lfvector(bhat, btemp, numverts); /* deltaNew = r^TP */ deltaNew = dot_lfvector(r, p, numverts); # if 0 filter(dv, S); add_lfvector_lfvector(dv, dv, z, numverts); mul_bfmatrix_lfvector(r, lA, dv); sub_lfvector_lfvector(r, lB, r, numverts); filter(r, S); mul_prevfmatrix_lfvector(p, Pinv, r); filter(p, S); deltaNew = dot_lfvector(r, p, numverts); delta0 = deltaNew * sqrt(conjgrad_epsilon); # endif # ifdef DEBUG_TIME double start = PIL_check_seconds_timer(); # endif tol = (0.01 * 0.2); while ((deltaNew > delta0 * tol * tol) && (iterations < conjgrad_looplimit)) { iterations++; mul_bfmatrix_lfvector(s, lA, p); filter(s, S); alpha = deltaNew / dot_lfvector(p, s, numverts); add_lfvector_lfvectorS(dv, dv, p, alpha, numverts); add_lfvector_lfvectorS(r, r, s, -alpha, numverts); mul_prevfmatrix_lfvector(h, Pinv, r); filter(h, S); deltaOld = deltaNew; deltaNew = dot_lfvector(r, h, numverts); add_lfvector_lfvectorS(p, h, p, deltaNew / deltaOld, numverts); filter(p, S); } # ifdef DEBUG_TIME double end = PIL_check_seconds_timer(); printf("cg_filtered_pre time: %f\n", (float)(end - start)); # endif del_lfvector(btemp); del_lfvector(bhat); del_lfvector(h); del_lfvector(s); del_lfvector(p); del_lfvector(r); // printf("iterations: %d\n", iterations); return iterations < conjgrad_looplimit; } # endif bool SIM_mass_spring_solve_velocities(Implicit_Data *data, float dt, ImplicitSolverResult *result) { unsigned int numverts = data->dFdV[0].vcount; lfVector *dFdXmV = create_lfvector(numverts); zero_lfvector(data->dV, numverts); cp_bfmatrix(data->A, data->M); subadd_bfmatrixS_bfmatrixS(data->A, data->dFdV, dt, data->dFdX, (dt * dt)); mul_bfmatrix_lfvector(dFdXmV, data->dFdX, data->V); add_lfvectorS_lfvectorS(data->B, data->F, dt, dFdXmV, (dt * dt), numverts); # ifdef DEBUG_TIME double start = PIL_check_seconds_timer(); # endif /* Conjugate gradient algorithm to solve Ax=b. */ cg_filtered(data->dV, data->A, data->B, data->z, data->S, result); // cg_filtered_pre(id->dV, id->A, id->B, id->z, id->S, id->P, id->Pinv, id->bigI); # ifdef DEBUG_TIME double end = PIL_check_seconds_timer(); printf("cg_filtered calc time: %f\n", (float)(end - start)); # endif /* advance velocities */ add_lfvector_lfvector(data->Vnew, data->V, data->dV, numverts); del_lfvector(dFdXmV); return result->status == SIM_SOLVER_SUCCESS; } bool SIM_mass_spring_solve_positions(Implicit_Data *data, float dt) { int numverts = data->M[0].vcount; /* advance positions */ add_lfvector_lfvectorS(data->Xnew, data->X, data->Vnew, dt, numverts); return true; } void SIM_mass_spring_apply_result(Implicit_Data *data) { int numverts = data->M[0].vcount; cp_lfvector(data->X, data->Xnew, numverts); cp_lfvector(data->V, data->Vnew, numverts); } void SIM_mass_spring_set_vertex_mass(Implicit_Data *data, int index, float mass) { unit_m3(data->M[index].m); mul_m3_fl(data->M[index].m, mass); } void SIM_mass_spring_set_rest_transform(Implicit_Data *data, int index, float tfm[3][3]) { # ifdef CLOTH_ROOT_FRAME copy_m3_m3(data->tfm[index].m, tfm); # else unit_m3(data->tfm[index].m); (void)tfm; # endif } void SIM_mass_spring_set_motion_state(Implicit_Data *data, int index, const float x[3], const float v[3]) { world_to_root_v3(data, index, data->X[index], x); world_to_root_v3(data, index, data->V[index], v); } void SIM_mass_spring_set_position(Implicit_Data *data, int index, const float x[3]) { world_to_root_v3(data, index, data->X[index], x); } void SIM_mass_spring_set_velocity(Implicit_Data *data, int index, const float v[3]) { world_to_root_v3(data, index, data->V[index], v); } void SIM_mass_spring_get_motion_state(struct Implicit_Data *data, int index, float x[3], float v[3]) { if (x) { root_to_world_v3(data, index, x, data->X[index]); } if (v) { root_to_world_v3(data, index, v, data->V[index]); } } void SIM_mass_spring_get_position(struct Implicit_Data *data, int index, float x[3]) { root_to_world_v3(data, index, x, data->X[index]); } void SIM_mass_spring_get_velocity(struct Implicit_Data *data, int index, float v[3]) { root_to_world_v3(data, index, v, data->V[index]); } void SIM_mass_spring_get_new_position(struct Implicit_Data *data, int index, float x[3]) { root_to_world_v3(data, index, x, data->Xnew[index]); } void SIM_mass_spring_set_new_position(struct Implicit_Data *data, int index, const float x[3]) { world_to_root_v3(data, index, data->Xnew[index], x); } void SIM_mass_spring_get_new_velocity(struct Implicit_Data *data, int index, float v[3]) { root_to_world_v3(data, index, v, data->Vnew[index]); } void SIM_mass_spring_set_new_velocity(struct Implicit_Data *data, int index, const float v[3]) { world_to_root_v3(data, index, data->Vnew[index], v); } /* -------------------------------- */ static int SIM_mass_spring_add_block(Implicit_Data *data, int v1, int v2) { int s = data->M[0].vcount + data->num_blocks; /* index from array start */ BLI_assert(s < data->M[0].vcount + data->M[0].scount); ++data->num_blocks; /* tfm and S don't have spring entries (diagonal blocks only) */ init_fmatrix(data->bigI + s, v1, v2); init_fmatrix(data->M + s, v1, v2); init_fmatrix(data->dFdX + s, v1, v2); init_fmatrix(data->dFdV + s, v1, v2); init_fmatrix(data->A + s, v1, v2); init_fmatrix(data->P + s, v1, v2); init_fmatrix(data->Pinv + s, v1, v2); return s; } void SIM_mass_spring_clear_constraints(Implicit_Data *data) { int i, numverts = data->S[0].vcount; for (i = 0; i < numverts; i++) { unit_m3(data->S[i].m); zero_v3(data->z[i]); } } void SIM_mass_spring_add_constraint_ndof0(Implicit_Data *data, int index, const float dV[3]) { zero_m3(data->S[index].m); world_to_root_v3(data, index, data->z[index], dV); } void SIM_mass_spring_add_constraint_ndof1( Implicit_Data *data, int index, const float c1[3], const float c2[3], const float dV[3]) { float m[3][3], p[3], q[3], u[3], cmat[3][3]; world_to_root_v3(data, index, p, c1); mul_fvectorT_fvector(cmat, p, p); sub_m3_m3m3(m, I, cmat); world_to_root_v3(data, index, q, c2); mul_fvectorT_fvector(cmat, q, q); sub_m3_m3m3(m, m, cmat); /* XXX not sure but multiplication should work here */ copy_m3_m3(data->S[index].m, m); // mul_m3_m3m3(data->S[index].m, data->S[index].m, m); world_to_root_v3(data, index, u, dV); add_v3_v3(data->z[index], u); } void SIM_mass_spring_add_constraint_ndof2(Implicit_Data *data, int index, const float c1[3], const float dV[3]) { float m[3][3], p[3], u[3], cmat[3][3]; world_to_root_v3(data, index, p, c1); mul_fvectorT_fvector(cmat, p, p); sub_m3_m3m3(m, I, cmat); copy_m3_m3(data->S[index].m, m); // mul_m3_m3m3(data->S[index].m, data->S[index].m, m); world_to_root_v3(data, index, u, dV); add_v3_v3(data->z[index], u); } void SIM_mass_spring_clear_forces(Implicit_Data *data) { int numverts = data->M[0].vcount; zero_lfvector(data->F, numverts); init_bfmatrix(data->dFdX, ZERO); init_bfmatrix(data->dFdV, ZERO); data->num_blocks = 0; } void SIM_mass_spring_force_reference_frame(Implicit_Data *data, int index, const float acceleration[3], const float omega[3], const float domega_dt[3], float mass) { # ifdef CLOTH_ROOT_FRAME float acc[3], w[3], dwdt[3]; float f[3], dfdx[3][3], dfdv[3][3]; float euler[3], coriolis[3], centrifugal[3], rotvel[3]; float deuler[3][3], dcoriolis[3][3], dcentrifugal[3][3], drotvel[3][3]; world_to_root_v3(data, index, acc, acceleration); world_to_root_v3(data, index, w, omega); world_to_root_v3(data, index, dwdt, domega_dt); cross_v3_v3v3(euler, dwdt, data->X[index]); cross_v3_v3v3(coriolis, w, data->V[index]); mul_v3_fl(coriolis, 2.0f); cross_v3_v3v3(rotvel, w, data->X[index]); cross_v3_v3v3(centrifugal, w, rotvel); sub_v3_v3v3(f, acc, euler); sub_v3_v3(f, coriolis); sub_v3_v3(f, centrifugal); mul_v3_fl(f, mass); /* F = m * a */ cross_v3_identity(deuler, dwdt); cross_v3_identity(dcoriolis, w); mul_m3_fl(dcoriolis, 2.0f); cross_v3_identity(drotvel, w); cross_m3_v3m3(dcentrifugal, w, drotvel); add_m3_m3m3(dfdx, deuler, dcentrifugal); negate_m3(dfdx); mul_m3_fl(dfdx, mass); copy_m3_m3(dfdv, dcoriolis); negate_m3(dfdv); mul_m3_fl(dfdv, mass); add_v3_v3(data->F[index], f); add_m3_m3m3(data->dFdX[index].m, data->dFdX[index].m, dfdx); add_m3_m3m3(data->dFdV[index].m, data->dFdV[index].m, dfdv); # else (void)data; (void)index; (void)acceleration; (void)omega; (void)domega_dt; # endif } void SIM_mass_spring_force_gravity(Implicit_Data *data, int index, float mass, const float g[3]) { /* force = mass * acceleration (in this case: gravity) */ float f[3]; world_to_root_v3(data, index, f, g); mul_v3_fl(f, mass); add_v3_v3(data->F[index], f); } void SIM_mass_spring_force_drag(Implicit_Data *data, float drag) { int i, numverts = data->M[0].vcount; for (i = 0; i < numverts; i++) { float tmp[3][3]; /* NOTE: Uses root space velocity, no need to transform. */ madd_v3_v3fl(data->F[i], data->V[i], -drag); copy_m3_m3(tmp, I); mul_m3_fl(tmp, -drag); add_m3_m3m3(data->dFdV[i].m, data->dFdV[i].m, tmp); } } void SIM_mass_spring_force_extern( struct Implicit_Data *data, int i, const float f[3], float dfdx[3][3], float dfdv[3][3]) { float tf[3], tdfdx[3][3], tdfdv[3][3]; world_to_root_v3(data, i, tf, f); world_to_root_m3(data, i, tdfdx, dfdx); world_to_root_m3(data, i, tdfdv, dfdv); add_v3_v3(data->F[i], tf); add_m3_m3m3(data->dFdX[i].m, data->dFdX[i].m, tdfdx); add_m3_m3m3(data->dFdV[i].m, data->dFdV[i].m, tdfdv); } static float calc_nor_area_tri(float nor[3], const float v1[3], const float v2[3], const float v3[3]) { float n1[3], n2[3]; sub_v3_v3v3(n1, v1, v2); sub_v3_v3v3(n2, v2, v3); cross_v3_v3v3(nor, n1, n2); return normalize_v3(nor) / 2.0f; } void SIM_mass_spring_force_face_wind( Implicit_Data *data, int v1, int v2, int v3, const float (*winvec)[3]) { /* XXX does not support force jacobians yet, * since the effector system does not provide them either. */ const float effector_scale = 0.02f; const int vs[3] = {v1, v2, v3}; float win[3], nor[3], area; float factor, base_force; float force[3]; /* calculate face normal and area */ area = calc_nor_area_tri(nor, data->X[v1], data->X[v2], data->X[v3]); /* The force is calculated and split up evenly for each of the three face verts */ factor = effector_scale * area / 3.0f; /* Calculate wind pressure at each vertex by projecting the wind field on the normal. */ for (int i = 0; i < 3; i++) { world_to_root_v3(data, vs[i], win, winvec[vs[i]]); force[i] = dot_v3v3(win, nor); } /* Compute per-vertex force values from local pressures. * From integrating the pressure over the triangle and deriving * equivalent vertex forces, it follows that: * * force[idx] = (sum(pressure) + pressure[idx]) * area / 12 * * Effectively, 1/4 of the pressure acts just on its vertex, * while 3/4 is split evenly over all three. */ mul_v3_fl(force, factor / 4.0f); base_force = force[0] + force[1] + force[2]; /* add pressure to each of the face verts */ madd_v3_v3fl(data->F[v1], nor, base_force + force[0]); madd_v3_v3fl(data->F[v2], nor, base_force + force[1]); madd_v3_v3fl(data->F[v3], nor, base_force + force[2]); } void SIM_mass_spring_force_face_extern( Implicit_Data *data, int v1, int v2, int v3, const float (*forcevec)[3]) { const float effector_scale = 0.02f; const int vs[3] = {v1, v2, v3}; float nor[3], area; float factor, base_force[3]; float force[3][3]; /* calculate face normal and area */ area = calc_nor_area_tri(nor, data->X[v1], data->X[v2], data->X[v3]); /* The force is calculated and split up evenly for each of the three face verts */ factor = effector_scale * area / 3.0f; /* Compute common and per-vertex force vectors from the original inputs. */ zero_v3(base_force); for (int i = 0; i < 3; i++) { world_to_root_v3(data, vs[i], force[i], forcevec[vs[i]]); mul_v3_fl(force[i], factor / 4.0f); add_v3_v3(base_force, force[i]); } /* Apply the common and vertex components to all vertices. */ for (int i = 0; i < 3; i++) { add_v3_v3(force[i], base_force); add_v3_v3(data->F[vs[i]], force[i]); } } float SIM_tri_tetra_volume_signed_6x(Implicit_Data *data, int v1, int v2, int v3) { /* The result will be 6x the volume */ return volume_tri_tetrahedron_signed_v3_6x(data->X[v1], data->X[v2], data->X[v3]); } float SIM_tri_area(struct Implicit_Data *data, int v1, int v2, int v3) { float nor[3]; return calc_nor_area_tri(nor, data->X[v1], data->X[v2], data->X[v3]); } void SIM_mass_spring_force_pressure(Implicit_Data *data, int v1, int v2, int v3, float common_pressure, const float *vertex_pressure, const float weights[3]) { float nor[3], area; float factor, base_force; float force[3]; /* calculate face normal and area */ area = calc_nor_area_tri(nor, data->X[v1], data->X[v2], data->X[v3]); /* The force is calculated and split up evenly for each of the three face verts */ factor = area / 3.0f; base_force = common_pressure * factor; /* Compute per-vertex force values from local pressures. * From integrating the pressure over the triangle and deriving * equivalent vertex forces, it follows that: * * force[idx] = (sum(pressure) + pressure[idx]) * area / 12 * * Effectively, 1/4 of the pressure acts just on its vertex, * while 3/4 is split evenly over all three. */ if (vertex_pressure) { copy_v3_fl3(force, vertex_pressure[v1], vertex_pressure[v2], vertex_pressure[v3]); mul_v3_fl(force, factor / 4.0f); base_force += force[0] + force[1] + force[2]; } else { zero_v3(force); } /* add pressure to each of the face verts */ madd_v3_v3fl(data->F[v1], nor, (base_force + force[0]) * weights[0]); madd_v3_v3fl(data->F[v2], nor, (base_force + force[1]) * weights[1]); madd_v3_v3fl(data->F[v3], nor, (base_force + force[2]) * weights[2]); } static void edge_wind_vertex(const float dir[3], float length, float radius, const float wind[3], float f[3], float UNUSED(dfdx[3][3]), float UNUSED(dfdv[3][3])) { const float density = 0.01f; /* XXX arbitrary value, corresponds to effect of air density */ float cos_alpha, sin_alpha, cross_section; float windlen = len_v3(wind); if (windlen == 0.0f) { zero_v3(f); return; } /* angle of wind direction to edge */ cos_alpha = dot_v3v3(wind, dir) / windlen; sin_alpha = sqrtf(1.0f - cos_alpha * cos_alpha); cross_section = radius * ((float)M_PI * radius * sin_alpha + length * cos_alpha); mul_v3_v3fl(f, wind, density * cross_section); } void SIM_mass_spring_force_edge_wind( Implicit_Data *data, int v1, int v2, float radius1, float radius2, const float (*winvec)[3]) { float win[3], dir[3], length; float f[3], dfdx[3][3], dfdv[3][3]; sub_v3_v3v3(dir, data->X[v1], data->X[v2]); length = normalize_v3(dir); world_to_root_v3(data, v1, win, winvec[v1]); edge_wind_vertex(dir, length, radius1, win, f, dfdx, dfdv); add_v3_v3(data->F[v1], f); world_to_root_v3(data, v2, win, winvec[v2]); edge_wind_vertex(dir, length, radius2, win, f, dfdx, dfdv); add_v3_v3(data->F[v2], f); } void SIM_mass_spring_force_vertex_wind(Implicit_Data *data, int v, float UNUSED(radius), const float (*winvec)[3]) { const float density = 0.01f; /* XXX arbitrary value, corresponds to effect of air density */ float wind[3]; float f[3]; world_to_root_v3(data, v, wind, winvec[v]); mul_v3_v3fl(f, wind, density); add_v3_v3(data->F[v], f); } BLI_INLINE void dfdx_spring(float to[3][3], const float dir[3], float length, float L, float k) { /* dir is unit length direction, rest is spring's restlength, k is spring constant. */ // return ( (I-outerprod(dir, dir))*Min(1.0f, rest/length) - I) * -k; outerproduct(to, dir, dir); sub_m3_m3m3(to, I, to); mul_m3_fl(to, (L / length)); sub_m3_m3m3(to, to, I); mul_m3_fl(to, k); } /* unused */ # if 0 BLI_INLINE void dfdx_damp(float to[3][3], const float dir[3], float length, const float vel[3], float rest, float damping) { /* Inner spring damping `vel` is the relative velocity of the endpoints. */ // return (I - outerprod(dir, dir)) * (-damping * -(dot(dir, vel) / Max(length, rest))); mul_fvectorT_fvector(to, dir, dir); sub_fmatrix_fmatrix(to, I, to); mul_fmatrix_S(to, (-damping * -(dot_v3v3(dir, vel) / MAX2(length, rest)))); } # endif BLI_INLINE void dfdv_damp(float to[3][3], const float dir[3], float damping) { /* Derivative of force with regards to velocity. */ outerproduct(to, dir, dir); mul_m3_fl(to, -damping); } BLI_INLINE float fb(float length, float L) { float x = length / L; float xx = x * x; float xxx = xx * x; float xxxx = xxx * x; return (-11.541f * xxxx + 34.193f * xxx - 39.083f * xx + 23.116f * x - 9.713f); } BLI_INLINE float fbderiv(float length, float L) { float x = length / L; float xx = x * x; float xxx = xx * x; return (-46.164f * xxx + 102.579f * xx - 78.166f * x + 23.116f); } BLI_INLINE float fbstar(float length, float L, float kb, float cb) { float tempfb_fl = kb * fb(length, L); float fbstar_fl = cb * (length - L); if (tempfb_fl < fbstar_fl) { return fbstar_fl; } return tempfb_fl; } /* Function to calculate bending spring force (taken from Choi & Co). */ BLI_INLINE float fbstar_jacobi(float length, float L, float kb, float cb) { float tempfb_fl = kb * fb(length, L); float fbstar_fl = cb * (length - L); if (tempfb_fl < fbstar_fl) { return -cb; } return -kb * fbderiv(length, L); } /* calculate elongation */ BLI_INLINE bool spring_length(Implicit_Data *data, int i, int j, float r_extent[3], float r_dir[3], float *r_length, float r_vel[3]) { sub_v3_v3v3(r_extent, data->X[j], data->X[i]); sub_v3_v3v3(r_vel, data->V[j], data->V[i]); *r_length = len_v3(r_extent); if (*r_length > ALMOST_ZERO) { # if 0 if (length > L) { if ((clmd->sim_parms->flags & CSIMSETT_FLAG_TEARING_ENABLED) && (((length - L) * 100.0f / L) > clmd->sim_parms->maxspringlen)) { /* cut spring! */ s->flags |= CSPRING_FLAG_DEACTIVATE; return false; } } # endif mul_v3_v3fl(r_dir, r_extent, 1.0f / (*r_length)); } else { zero_v3(r_dir); } return true; } BLI_INLINE void apply_spring(Implicit_Data *data, int i, int j, const float f[3], const float dfdx[3][3], const float dfdv[3][3]) { int block_ij = SIM_mass_spring_add_block(data, i, j); add_v3_v3(data->F[i], f); sub_v3_v3(data->F[j], f); add_m3_m3m3(data->dFdX[i].m, data->dFdX[i].m, dfdx); add_m3_m3m3(data->dFdX[j].m, data->dFdX[j].m, dfdx); sub_m3_m3m3(data->dFdX[block_ij].m, data->dFdX[block_ij].m, dfdx); add_m3_m3m3(data->dFdV[i].m, data->dFdV[i].m, dfdv); add_m3_m3m3(data->dFdV[j].m, data->dFdV[j].m, dfdv); sub_m3_m3m3(data->dFdV[block_ij].m, data->dFdV[block_ij].m, dfdv); } bool SIM_mass_spring_force_spring_linear(Implicit_Data *data, int i, int j, float restlen, float stiffness_tension, float damping_tension, float stiffness_compression, float damping_compression, bool resist_compress, bool new_compress, float clamp_force) { float extent[3], length, dir[3], vel[3]; float f[3], dfdx[3][3], dfdv[3][3]; float damping = 0; /* calculate elongation */ spring_length(data, i, j, extent, dir, &length, vel); /* This code computes not only the force, but also its derivative. * Zero derivative effectively disables the spring for the implicit solver. * Thus length > restlen makes cloth unconstrained at the start of simulation. */ if ((length >= restlen && length > 0) || resist_compress) { float stretch_force; damping = damping_tension; stretch_force = stiffness_tension * (length - restlen); if (clamp_force > 0.0f && stretch_force > clamp_force) { stretch_force = clamp_force; } mul_v3_v3fl(f, dir, stretch_force); dfdx_spring(dfdx, dir, length, restlen, stiffness_tension); } else if (new_compress) { /* This is based on the Choi and Ko bending model, * which works surprisingly well for compression. */ float kb = stiffness_compression; float cb = kb; /* cb equal to kb seems to work, but a factor can be added if necessary */ damping = damping_compression; mul_v3_v3fl(f, dir, fbstar(length, restlen, kb, cb)); outerproduct(dfdx, dir, dir); mul_m3_fl(dfdx, fbstar_jacobi(length, restlen, kb, cb)); } else { return false; } madd_v3_v3fl(f, dir, damping * dot_v3v3(vel, dir)); dfdv_damp(dfdv, dir, damping); apply_spring(data, i, j, f, dfdx, dfdv); return true; } bool SIM_mass_spring_force_spring_bending( Implicit_Data *data, int i, int j, float restlen, float kb, float cb) { /* See "Stable but Responsive Cloth" (Choi, Ko 2005). */ float extent[3], length, dir[3], vel[3]; /* calculate elongation */ spring_length(data, i, j, extent, dir, &length, vel); if (length < restlen) { float f[3], dfdx[3][3], dfdv[3][3]; mul_v3_v3fl(f, dir, fbstar(length, restlen, kb, cb)); outerproduct(dfdx, dir, dir); mul_m3_fl(dfdx, fbstar_jacobi(length, restlen, kb, cb)); /* XXX damping not supported */ zero_m3(dfdv); apply_spring(data, i, j, f, dfdx, dfdv); return true; } return false; } BLI_INLINE void poly_avg(lfVector *data, const int *inds, int len, float r_avg[3]) { float fact = 1.0f / (float)len; zero_v3(r_avg); for (int i = 0; i < len; i++) { madd_v3_v3fl(r_avg, data[inds[i]], fact); } } BLI_INLINE void poly_norm(lfVector *data, int i, int j, int *inds, int len, float r_dir[3]) { float mid[3]; poly_avg(data, inds, len, mid); normal_tri_v3(r_dir, data[i], data[j], mid); } BLI_INLINE void edge_avg(lfVector *data, int i, int j, float r_avg[3]) { r_avg[0] = (data[i][0] + data[j][0]) * 0.5f; r_avg[1] = (data[i][1] + data[j][1]) * 0.5f; r_avg[2] = (data[i][2] + data[j][2]) * 0.5f; } BLI_INLINE void edge_norm(lfVector *data, int i, int j, float r_dir[3]) { sub_v3_v3v3(r_dir, data[i], data[j]); normalize_v3(r_dir); } BLI_INLINE float bend_angle(const float dir_a[3], const float dir_b[3], const float dir_e[3]) { float cos, sin; float tmp[3]; cos = dot_v3v3(dir_a, dir_b); cross_v3_v3v3(tmp, dir_a, dir_b); sin = dot_v3v3(tmp, dir_e); return atan2f(sin, cos); } BLI_INLINE void spring_angle(Implicit_Data *data, int i, int j, int *i_a, int *i_b, int len_a, int len_b, float r_dir_a[3], float r_dir_b[3], float *r_angle, float r_vel_a[3], float r_vel_b[3]) { float dir_e[3], vel_e[3]; poly_norm(data->X, j, i, i_a, len_a, r_dir_a); poly_norm(data->X, i, j, i_b, len_b, r_dir_b); edge_norm(data->X, i, j, dir_e); *r_angle = bend_angle(r_dir_a, r_dir_b, dir_e); poly_avg(data->V, i_a, len_a, r_vel_a); poly_avg(data->V, i_b, len_b, r_vel_b); edge_avg(data->V, i, j, vel_e); sub_v3_v3(r_vel_a, vel_e); sub_v3_v3(r_vel_b, vel_e); } bool SIM_mass_spring_force_spring_angular(Implicit_Data *data, int i, int j, int *i_a, int *i_b, int len_a, int len_b, float restang, float stiffness, float damping) { float angle, dir_a[3], dir_b[3], vel_a[3], vel_b[3]; float f_a[3], f_b[3], f_e[3]; float force; int x; spring_angle(data, i, j, i_a, i_b, len_a, len_b, dir_a, dir_b, &angle, vel_a, vel_b); /* spring force */ force = stiffness * (angle - restang); /* damping force */ force += -damping * (dot_v3v3(vel_a, dir_a) + dot_v3v3(vel_b, dir_b)); mul_v3_v3fl(f_a, dir_a, force / len_a); mul_v3_v3fl(f_b, dir_b, force / len_b); for (x = 0; x < len_a; x++) { add_v3_v3(data->F[i_a[x]], f_a); } for (x = 0; x < len_b; x++) { add_v3_v3(data->F[i_b[x]], f_b); } mul_v3_v3fl(f_a, dir_a, force * 0.5f); mul_v3_v3fl(f_b, dir_b, force * 0.5f); add_v3_v3v3(f_e, f_a, f_b); sub_v3_v3(data->F[i], f_e); sub_v3_v3(data->F[j], f_e); return true; } /* Jacobian of a direction vector. * Basically the part of the differential orthogonal to the direction, * inversely proportional to the length of the edge. * * dD_ij/dx_i = -dD_ij/dx_j = (D_ij * D_ij^T - I) / len_ij */ BLI_INLINE void spring_grad_dir( Implicit_Data *data, int i, int j, float edge[3], float dir[3], float grad_dir[3][3]) { float length; sub_v3_v3v3(edge, data->X[j], data->X[i]); length = normalize_v3_v3(dir, edge); if (length > ALMOST_ZERO) { outerproduct(grad_dir, dir, dir); sub_m3_m3m3(grad_dir, I, grad_dir); mul_m3_fl(grad_dir, 1.0f / length); } else { zero_m3(grad_dir); } } BLI_INLINE void spring_hairbend_forces(Implicit_Data *data, int i, int j, int k, const float goal[3], float stiffness, float damping, int q, const float dx[3], const float dv[3], float r_f[3]) { float edge_ij[3], dir_ij[3]; float edge_jk[3], dir_jk[3]; float vel_ij[3], vel_jk[3], vel_ortho[3]; float f_bend[3], f_damp[3]; float fk[3]; float dist[3]; zero_v3(fk); sub_v3_v3v3(edge_ij, data->X[j], data->X[i]); if (q == i) { sub_v3_v3(edge_ij, dx); } if (q == j) { add_v3_v3(edge_ij, dx); } normalize_v3_v3(dir_ij, edge_ij); sub_v3_v3v3(edge_jk, data->X[k], data->X[j]); if (q == j) { sub_v3_v3(edge_jk, dx); } if (q == k) { add_v3_v3(edge_jk, dx); } normalize_v3_v3(dir_jk, edge_jk); sub_v3_v3v3(vel_ij, data->V[j], data->V[i]); if (q == i) { sub_v3_v3(vel_ij, dv); } if (q == j) { add_v3_v3(vel_ij, dv); } sub_v3_v3v3(vel_jk, data->V[k], data->V[j]); if (q == j) { sub_v3_v3(vel_jk, dv); } if (q == k) { add_v3_v3(vel_jk, dv); } /* bending force */ sub_v3_v3v3(dist, goal, edge_jk); mul_v3_v3fl(f_bend, dist, stiffness); add_v3_v3(fk, f_bend); /* damping force */ madd_v3_v3v3fl(vel_ortho, vel_jk, dir_jk, -dot_v3v3(vel_jk, dir_jk)); mul_v3_v3fl(f_damp, vel_ortho, damping); sub_v3_v3(fk, f_damp); copy_v3_v3(r_f, fk); } /* Finite Differences method for estimating the jacobian of the force */ BLI_INLINE void spring_hairbend_estimate_dfdx(Implicit_Data *data, int i, int j, int k, const float goal[3], float stiffness, float damping, int q, float dfdx[3][3]) { const float delta = 0.00001f; /* TODO: find a good heuristic for this. */ float dvec_null[3][3], dvec_pos[3][3], dvec_neg[3][3]; float f[3]; int a, b; zero_m3(dvec_null); unit_m3(dvec_pos); mul_m3_fl(dvec_pos, delta * 0.5f); copy_m3_m3(dvec_neg, dvec_pos); negate_m3(dvec_neg); /* XXX TODO: offset targets to account for position dependency. */ for (a = 0; a < 3; a++) { spring_hairbend_forces( data, i, j, k, goal, stiffness, damping, q, dvec_pos[a], dvec_null[a], f); copy_v3_v3(dfdx[a], f); spring_hairbend_forces( data, i, j, k, goal, stiffness, damping, q, dvec_neg[a], dvec_null[a], f); sub_v3_v3(dfdx[a], f); for (b = 0; b < 3; b++) { dfdx[a][b] /= delta; } } } /* Finite Differences method for estimating the jacobian of the force */ BLI_INLINE void spring_hairbend_estimate_dfdv(Implicit_Data *data, int i, int j, int k, const float goal[3], float stiffness, float damping, int q, float dfdv[3][3]) { const float delta = 0.00001f; /* TODO: find a good heuristic for this. */ float dvec_null[3][3], dvec_pos[3][3], dvec_neg[3][3]; float f[3]; int a, b; zero_m3(dvec_null); unit_m3(dvec_pos); mul_m3_fl(dvec_pos, delta * 0.5f); copy_m3_m3(dvec_neg, dvec_pos); negate_m3(dvec_neg); /* XXX TODO: offset targets to account for position dependency. */ for (a = 0; a < 3; a++) { spring_hairbend_forces( data, i, j, k, goal, stiffness, damping, q, dvec_null[a], dvec_pos[a], f); copy_v3_v3(dfdv[a], f); spring_hairbend_forces( data, i, j, k, goal, stiffness, damping, q, dvec_null[a], dvec_neg[a], f); sub_v3_v3(dfdv[a], f); for (b = 0; b < 3; b++) { dfdv[a][b] /= delta; } } } bool SIM_mass_spring_force_spring_bending_hair(Implicit_Data *data, int i, int j, int k, const float target[3], float stiffness, float damping) { /* Angular springs roughly based on the bending model proposed by Baraff and Witkin in * "Large Steps in Cloth Simulation". */ float goal[3]; float fj[3], fk[3]; float dfj_dxi[3][3], dfj_dxj[3][3], dfk_dxi[3][3], dfk_dxj[3][3], dfk_dxk[3][3]; float dfj_dvi[3][3], dfj_dvj[3][3], dfk_dvi[3][3], dfk_dvj[3][3], dfk_dvk[3][3]; const float vecnull[3] = {0.0f, 0.0f, 0.0f}; int block_ij = SIM_mass_spring_add_block(data, i, j); int block_jk = SIM_mass_spring_add_block(data, j, k); int block_ik = SIM_mass_spring_add_block(data, i, k); world_to_root_v3(data, j, goal, target); spring_hairbend_forces(data, i, j, k, goal, stiffness, damping, k, vecnull, vecnull, fk); negate_v3_v3(fj, fk); /* Counter-force. */ spring_hairbend_estimate_dfdx(data, i, j, k, goal, stiffness, damping, i, dfk_dxi); spring_hairbend_estimate_dfdx(data, i, j, k, goal, stiffness, damping, j, dfk_dxj); spring_hairbend_estimate_dfdx(data, i, j, k, goal, stiffness, damping, k, dfk_dxk); copy_m3_m3(dfj_dxi, dfk_dxi); negate_m3(dfj_dxi); copy_m3_m3(dfj_dxj, dfk_dxj); negate_m3(dfj_dxj); spring_hairbend_estimate_dfdv(data, i, j, k, goal, stiffness, damping, i, dfk_dvi); spring_hairbend_estimate_dfdv(data, i, j, k, goal, stiffness, damping, j, dfk_dvj); spring_hairbend_estimate_dfdv(data, i, j, k, goal, stiffness, damping, k, dfk_dvk); copy_m3_m3(dfj_dvi, dfk_dvi); negate_m3(dfj_dvi); copy_m3_m3(dfj_dvj, dfk_dvj); negate_m3(dfj_dvj); /* add forces and jacobians to the solver data */ add_v3_v3(data->F[j], fj); add_v3_v3(data->F[k], fk); add_m3_m3m3(data->dFdX[j].m, data->dFdX[j].m, dfj_dxj); add_m3_m3m3(data->dFdX[k].m, data->dFdX[k].m, dfk_dxk); add_m3_m3m3(data->dFdX[block_ij].m, data->dFdX[block_ij].m, dfj_dxi); add_m3_m3m3(data->dFdX[block_jk].m, data->dFdX[block_jk].m, dfk_dxj); add_m3_m3m3(data->dFdX[block_ik].m, data->dFdX[block_ik].m, dfk_dxi); add_m3_m3m3(data->dFdV[j].m, data->dFdV[j].m, dfj_dvj); add_m3_m3m3(data->dFdV[k].m, data->dFdV[k].m, dfk_dvk); add_m3_m3m3(data->dFdV[block_ij].m, data->dFdV[block_ij].m, dfj_dvi); add_m3_m3m3(data->dFdV[block_jk].m, data->dFdV[block_jk].m, dfk_dvj); add_m3_m3m3(data->dFdV[block_ik].m, data->dFdV[block_ik].m, dfk_dvi); /* XXX analytical calculation of derivatives below is incorrect. * This proved to be difficult, but for now just using the finite difference method for * estimating the jacobians should be sufficient. */ # if 0 float edge_ij[3], dir_ij[3], grad_dir_ij[3][3]; float edge_jk[3], dir_jk[3], grad_dir_jk[3][3]; float dist[3], vel_jk[3], vel_jk_ortho[3], projvel[3]; float target[3]; float tmp[3][3]; float fi[3], fj[3], fk[3]; float dfi_dxi[3][3], dfj_dxi[3][3], dfj_dxj[3][3], dfk_dxi[3][3], dfk_dxj[3][3], dfk_dxk[3][3]; float dfdvi[3][3]; /* TESTING */ damping = 0.0f; zero_v3(fi); zero_v3(fj); zero_v3(fk); zero_m3(dfi_dxi); zero_m3(dfj_dxi); zero_m3(dfk_dxi); zero_m3(dfk_dxj); zero_m3(dfk_dxk); /* jacobian of direction vectors */ spring_grad_dir(data, i, j, edge_ij, dir_ij, grad_dir_ij); spring_grad_dir(data, j, k, edge_jk, dir_jk, grad_dir_jk); sub_v3_v3v3(vel_jk, data->V[k], data->V[j]); /* bending force */ mul_v3_v3fl(target, dir_ij, restlen); sub_v3_v3v3(dist, target, edge_jk); mul_v3_v3fl(fk, dist, stiffness); /* damping force */ madd_v3_v3v3fl(vel_jk_ortho, vel_jk, dir_jk, -dot_v3v3(vel_jk, dir_jk)); madd_v3_v3fl(fk, vel_jk_ortho, damping); /* XXX this only holds true as long as we assume straight rest shape! * eventually will become a bit more involved since the opposite segment * gets its own target, under condition of having equal torque on both sides. */ copy_v3_v3(fi, fk); /* counterforce on the middle point */ sub_v3_v3(fj, fi); sub_v3_v3(fj, fk); /* === derivatives === */ madd_m3_m3fl(dfk_dxi, grad_dir_ij, stiffness * restlen); madd_m3_m3fl(dfk_dxj, grad_dir_ij, -stiffness * restlen); madd_m3_m3fl(dfk_dxj, I, stiffness); madd_m3_m3fl(dfk_dxk, I, -stiffness); copy_m3_m3(dfi_dxi, dfk_dxk); negate_m3(dfi_dxi); /* dfj_dfi == dfi_dfj due to symmetry, * dfi_dfj == dfk_dfj due to fi == fk * XXX see comment above on future bent rest shapes */ copy_m3_m3(dfj_dxi, dfk_dxj); /* dfj_dxj == -(dfi_dxj + dfk_dxj) due to fj == -(fi + fk) */ sub_m3_m3m3(dfj_dxj, dfj_dxj, dfj_dxi); sub_m3_m3m3(dfj_dxj, dfj_dxj, dfk_dxj); /* add forces and jacobians to the solver data */ add_v3_v3(data->F[i], fi); add_v3_v3(data->F[j], fj); add_v3_v3(data->F[k], fk); add_m3_m3m3(data->dFdX[i].m, data->dFdX[i].m, dfi_dxi); add_m3_m3m3(data->dFdX[j].m, data->dFdX[j].m, dfj_dxj); add_m3_m3m3(data->dFdX[k].m, data->dFdX[k].m, dfk_dxk); add_m3_m3m3(data->dFdX[block_ij].m, data->dFdX[block_ij].m, dfj_dxi); add_m3_m3m3(data->dFdX[block_jk].m, data->dFdX[block_jk].m, dfk_dxj); add_m3_m3m3(data->dFdX[block_ik].m, data->dFdX[block_ik].m, dfk_dxi); # endif return true; } bool SIM_mass_spring_force_spring_goal(Implicit_Data *data, int i, const float goal_x[3], const float goal_v[3], float stiffness, float damping) { float root_goal_x[3], root_goal_v[3], extent[3], length, dir[3], vel[3]; float f[3], dfdx[3][3], dfdv[3][3]; /* goal is in world space */ world_to_root_v3(data, i, root_goal_x, goal_x); world_to_root_v3(data, i, root_goal_v, goal_v); sub_v3_v3v3(extent, root_goal_x, data->X[i]); sub_v3_v3v3(vel, root_goal_v, data->V[i]); length = normalize_v3_v3(dir, extent); if (length > ALMOST_ZERO) { mul_v3_v3fl(f, dir, stiffness * length); /* Ascher & Boxman, p.21: Damping only during elongation * something wrong with it. */ madd_v3_v3fl(f, dir, damping * dot_v3v3(vel, dir)); dfdx_spring(dfdx, dir, length, 0.0f, stiffness); dfdv_damp(dfdv, dir, damping); add_v3_v3(data->F[i], f); add_m3_m3m3(data->dFdX[i].m, data->dFdX[i].m, dfdx); add_m3_m3m3(data->dFdV[i].m, data->dFdV[i].m, dfdv); return true; } return false; } #endif /* IMPLICIT_SOLVER_BLENDER */