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).

1 files changed, 102 insertions, 8 deletions

diff --git a/source/blender/blenkernel/intern/implicit.c b/source/blender/blenkernel/intern/implicit.c
index 72b44ddffb2..689a0f743f5 100644
--- a/source/blender/blenkernel/intern/implicit.c
+++ b/source/blender/blenkernel/intern/implicit.c
@@ -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