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Fixed implementation of the Conjugate Gradient method for the cloth 

solver that properly supports constraints with some degrees-of-freedom.

The previous solver implementation only used the S matrix (constraint
filter matrix) for pinning vertices, in which case all elements are
zero and the error doesn't show up. With partial constraints (useful for
collision contacts) the matrix has non-zero off-diagonal elements and
the algorithm easily diverges.

There are also initial steps for implementing collision prevention as
described in the Baraff/Witkin paper "Large Steps in Cloth Simulation"
(http://www.cs.cmu.edu/~baraff/papers/sig98.pdf).
This commit is contained in:
Lukas Tönne 2014-09-03 23:49:24 +02:00
parent b38663338e
commit c6e5f6afe0
2 changed files with 103 additions and 12 deletions
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5
source/blender/blenkernel/intern/collision.c
View File

@ -1133,9 +1133,6 @@ static CollPair *cloth_point_collpair(float p1[3], float p2[3], MVert *mverts, i
float facenor[3], v1p1[3], v1p2[3];
float w[3];
// if (!isect_line_tri_v3(p1, p2, co1, co2, co3, &lambda, uv))
// return collpair;
if (!cloth_point_face_collision_params(p1, p2, co1, co2, co3, facenor, &lambda, uv))
return collpair;
@ -1159,7 +1156,7 @@ static CollPair *cloth_point_collpair(float p1[3], float p2[3], MVert *mverts, i
*/
copy_v3_v3(collpair->pa, p2);
collpair->distance = distance2;
mul_v3_v3fl(collpair->vector, facenor, distance2);
mul_v3_v3fl(collpair->vector, facenor, -distance2);
w[0] = 1.0f - uv[0] - uv[1];
w[1] = uv[0];

110
source/blender/blenkernel/intern/implicit.c
View File

@ -339,6 +339,15 @@ static void print_fmatrix(float m3[3][3])
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++)
print_fmatrix(m[i].m);
}
}
#endif
/* copy 3x3 matrix */
@ -748,10 +757,11 @@ DO_INLINE void filter(lfVector *V, fmatrix3x3 *S)
unsigned int i=0;
for (i = 0; i < S[0].vcount; i++) {
mul_fvector_fmatrix(V[S[i].r], V[S[i].r], S[i].m);
mul_m3_v3(S[i].m, V[S[i].r]);
}
}
#if 0
static int cg_filtered(lfVector *ldV, fmatrix3x3 *lA, lfVector *lB, lfVector *z, fmatrix3x3 *S)
{
// Solves for unknown X in equation AX=B
@ -816,6 +826,73 @@ static int cg_filtered(lfVector *ldV, fmatrix3x3 *lA, lfVector *lB, lfVector *z
return conjgrad_loopcount<conjgrad_looplimit; // true means we reached desired accuracy in given time - ie stable
}
#else
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 */;
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 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);
delta_target = conjgrad_epsilon*conjgrad_epsilon * dot_lfvector(fB, fB, numverts);
/* 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);
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++;
}
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);
return conjgrad_loopcount < conjgrad_looplimit; // true means we reached desired accuracy in given time - ie stable
}
#endif
#if 0
// block diagonalizer
@ -1686,10 +1763,12 @@ static void setup_constraint_matrix(ClothVertex *verts, int numverts, ColliderCo
/* pinned vertex constraints */
for (i = 0; i < numverts; i++) {
S[i].c = S[i].r = i;
if (verts[i].flags & CLOTH_VERT_FLAG_PINNED)
if (verts[i].flags & CLOTH_VERT_FLAG_PINNED) {
zero_m3(S[i].m);
else
}
else {
unit_m3(S[i].m);
}
}
for (i = 0; i < totcolliders; ++i) {
@ -1697,12 +1776,14 @@ static void setup_constraint_matrix(ClothVertex *verts, int numverts, ColliderCo
for (j = 0; j < ct->totcollisions; ++j) {
CollPair *collpair = &ct->collisions[j];
int v = collpair->face1;
float cmat[3][3];
/* pinned verts handled separately */
if (verts[v].flags & CLOTH_VERT_FLAG_PINNED)
continue;
zero_m3(S[v].m);
mul_fvectorT_fvector(cmat, collpair->normal, collpair->normal);
sub_m3_m3m3(S[v].m, I, cmat);
}
}
}
@ -1853,18 +1934,22 @@ static void cloth_calc_force(ClothModifierData *clmd, float UNUSED(frame), lfVec
cloth_apply_spring_force(clmd, search->link, lF, lX, lV, dFdV, dFdX);
search = search->next;
}
// printf("====== dFdV ======\n");
// print_sparse_matrix(dFdV);
// printf("============\n");
// printf("\n");
}
static void simulate_implicit_euler(Implicit_Data *id, float dt)
static bool simulate_implicit_euler(Implicit_Data *id, float dt)
{
unsigned int numverts = id->dFdV[0].vcount;
bool ok;
lfVector *dFdXmV = create_lfvector(numverts);
zero_lfvector(id->dV, numverts);
cp_bfmatrix(id->A, id->M);
subadd_bfmatrixS_bfmatrixS(id->A, id->dFdV, dt, id->dFdX, (dt*dt));
mul_bfmatrix_lfvector(dFdXmV, id->dFdX, id->V);
@ -1873,7 +1958,7 @@ static void simulate_implicit_euler(Implicit_Data *id, float dt)
// itstart();
cg_filtered(id->dV, id->A, id->B, id->z, id->S); /* conjugate gradient algorithm to solve Ax=b */
ok = cg_filtered(id->dV, id->A, id->B, id->z, id->S); /* conjugate gradient algorithm to solve Ax=b */
// cg_filtered_pre(id->dV, id->A, id->B, id->z, id->S, id->P, id->Pinv, id->bigI);
// itend();
@ -1883,6 +1968,8 @@ static void simulate_implicit_euler(Implicit_Data *id, float dt)
add_lfvector_lfvector(id->Vnew, id->V, id->dV, numverts);
del_lfvector(dFdXmV);
return ok;
}
/* computes where the cloth would be if it were subject to perfectly stiff edges
@ -2032,6 +2119,13 @@ int implicit_solver(Object *ob, float frame, ClothModifierData *clmd, ListBase *
}
copy_v3_v3(verts[i].txold, id->X[i]);
// if (!(verts[i].flags & CLOTH_VERT_FLAG_PINNED) && i > 0)
// BKE_sim_debug_data_add_line(clmd->debug_data, id->Xnew[i], id->Xnew[i-1], 1, 0.5, 0.5, "hair", hash_vertex(4892, i));
// BKE_sim_debug_data_add_vector(clmd->debug_data, id->Xnew[i], id->Vnew[i], 0, 0, 1, "velocity", hash_vertex(3158, i));
if (!(verts[i].flags & CLOTH_VERT_FLAG_PINNED) && i > 0)
BKE_sim_debug_data_add_line(clmd->debug_data, id->X[i], id->X[i-1], 1, 0.5, 0.5, "hair", hash_vertex(4892, i));
BKE_sim_debug_data_add_vector(clmd->debug_data, id->X[i], id->V[i], 0, 0, 1, "velocity", hash_vertex(3158, i));
}
#if 0