static void validate_solution(LaplacianSystem *sys, short flag, float lambda, float lambda_border)
{
int i;
float lam;
float vini, vend;
if (flag & MOD_LAPLACIANSMOOTH_PRESERVE_VOLUME) {
vini = compute_volume(sys->vert_centroid, sys->vertexCos, sys->mpoly, sys->numPolys, sys->mloop);
}
for (i = 0; i < sys->numVerts; i++) {
if (sys->zerola[i] == 0) {
lam = sys->numNeEd[i] == sys->numNeFa[i] ? (lambda >= 0.0f ? 1.0f : -1.0f) : (lambda_border >= 0.0f ? 1.0f : -1.0f);
if (flag & MOD_LAPLACIANSMOOTH_X) {
sys->vertexCos[i][0] += lam * ((float)EIG_linear_solver_variable_get(sys->context, 0, i) - sys->vertexCos[i][0]);
}
if (flag & MOD_LAPLACIANSMOOTH_Y) {
sys->vertexCos[i][1] += lam * ((float)EIG_linear_solver_variable_get(sys->context, 1, i) - sys->vertexCos[i][1]);
}
if (flag & MOD_LAPLACIANSMOOTH_Z) {
sys->vertexCos[i][2] += lam * ((float)EIG_linear_solver_variable_get(sys->context, 2, i) - sys->vertexCos[i][2]);
}
}
}
if (flag & MOD_LAPLACIANSMOOTH_PRESERVE_VOLUME) {
vend = compute_volume(sys->vert_centroid, sys->vertexCos, sys->mpoly, sys->numPolys, sys->mloop);
volume_preservation(sys, vini, vend, flag);
}
}
float laplacian_system_get_solution(LaplacianSystem *sys, int v)
{
return EIG_linear_solver_variable_get(sys->context, 0, v);
}
static void meshdeform_matrix_solve(MeshDeformModifierData *mmd, MeshDeformBind *mdb)
{
LinearSolver *context;
float vec[3], gridvec[3];
int a, b, x, y, z, totvar;
char message[256];
/* setup variable indices */
mdb->varidx = MEM_callocN(sizeof(int) * mdb->size3, "MeshDeformDSvaridx");
for (a = 0, totvar = 0; a < mdb->size3; a++)
mdb->varidx[a] = (mdb->tag[a] == MESHDEFORM_TAG_EXTERIOR) ? -1 : totvar++;
if (totvar == 0) {
MEM_freeN(mdb->varidx);
return;
}
progress_bar(0, "Starting mesh deform solve");
/* setup linear solver */
context = EIG_linear_solver_new(totvar, totvar, 1);
/* build matrix */
for (z = 0; z < mdb->size; z++)
for (y = 0; y < mdb->size; y++)
for (x = 0; x < mdb->size; x++)
meshdeform_matrix_add_cell(mdb, context, x, y, z);
/* solve for each cage vert */
for (a = 0; a < mdb->totcagevert; a++) {
/* fill in right hand side and solve */
for (z = 0; z < mdb->size; z++)
for (y = 0; y < mdb->size; y++)
for (x = 0; x < mdb->size; x++)
meshdeform_matrix_add_rhs(mdb, context, x, y, z, a);
if (EIG_linear_solver_solve(context)) {
for (z = 0; z < mdb->size; z++)
for (y = 0; y < mdb->size; y++)
for (x = 0; x < mdb->size; x++)
meshdeform_matrix_add_semibound_phi(mdb, x, y, z, a);
for (z = 0; z < mdb->size; z++)
for (y = 0; y < mdb->size; y++)
for (x = 0; x < mdb->size; x++)
meshdeform_matrix_add_exterior_phi(mdb, x, y, z, a);
for (b = 0; b < mdb->size3; b++) {
if (mdb->tag[b] != MESHDEFORM_TAG_EXTERIOR)
mdb->phi[b] = EIG_linear_solver_variable_get(context, 0, mdb->varidx[b]);
mdb->totalphi[b] += mdb->phi[b];
}
if (mdb->weights) {
/* static bind : compute weights for each vertex */
for (b = 0; b < mdb->totvert; b++) {
if (mdb->inside[b]) {
copy_v3_v3(vec, mdb->vertexcos[b]);
gridvec[0] = (vec[0] - mdb->min[0] - mdb->halfwidth[0]) / mdb->width[0];
gridvec[1] = (vec[1] - mdb->min[1] - mdb->halfwidth[1]) / mdb->width[1];
gridvec[2] = (vec[2] - mdb->min[2] - mdb->halfwidth[2]) / mdb->width[2];
mdb->weights[b * mdb->totcagevert + a] = meshdeform_interp_w(mdb, gridvec, vec, a);
}
}
}
else {
MDefBindInfluence *inf;
/* dynamic bind */
for (b = 0; b < mdb->size3; b++) {
if (mdb->phi[b] >= MESHDEFORM_MIN_INFLUENCE) {
inf = BLI_memarena_alloc(mdb->memarena, sizeof(*inf));
inf->vertex = a;
inf->weight = mdb->phi[b];
inf->next = mdb->dyngrid[b];
mdb->dyngrid[b] = inf;
}
}
}
}
else {
modifier_setError(&mmd->modifier, "Failed to find bind solution (increase precision?)");
error("Mesh Deform: failed to find bind solution.");
break;
}
BLI_snprintf(message, sizeof(message), "Mesh deform solve %d / %d |||", a + 1, mdb->totcagevert);
progress_bar((float)(a + 1) / (float)(mdb->totcagevert), message);
}
#if 0
/* sanity check */
for (b = 0; b < mdb->size3; b++)
if (mdb->tag[b] != MESHDEFORM_TAG_EXTERIOR)
if (fabsf(mdb->totalphi[b] - 1.0f) > 1e-4f)
printf("totalphi deficiency [%s|%d] %d: %.10f\n",
(mdb->tag[b] == MESHDEFORM_TAG_INTERIOR) ? "interior" : "boundary", mdb->semibound[b], mdb->varidx[b], mdb->totalphi[b]);
#endif
/* free */
MEM_freeN(mdb->varidx);
EIG_linear_solver_delete(context);
}
static void laplacianDeformPreview(LaplacianSystem *sys, float (*vertexCos)[3])
{
int vid, i, j, n, na;
n = sys->total_verts;
na = sys->total_anchors;
if (!sys->is_matrix_computed) {
sys->context = EIG_linear_least_squares_solver_new(n + na, n, 3);
for (i = 0; i < n; i++) {
EIG_linear_solver_variable_set(sys->context, 0, i, sys->co[i][0]);
EIG_linear_solver_variable_set(sys->context, 1, i, sys->co[i][1]);
EIG_linear_solver_variable_set(sys->context, 2, i, sys->co[i][2]);
}
for (i = 0; i < na; i++) {
vid = sys->index_anchors[i];
EIG_linear_solver_variable_set(sys->context, 0, vid, vertexCos[vid][0]);
EIG_linear_solver_variable_set(sys->context, 1, vid, vertexCos[vid][1]);
EIG_linear_solver_variable_set(sys->context, 2, vid, vertexCos[vid][2]);
}
initLaplacianMatrix(sys);
computeImplictRotations(sys);
for (i = 0; i < n; i++) {
EIG_linear_solver_right_hand_side_add(sys->context, 0, i, sys->delta[i][0]);
EIG_linear_solver_right_hand_side_add(sys->context, 1, i, sys->delta[i][1]);
EIG_linear_solver_right_hand_side_add(sys->context, 2, i, sys->delta[i][2]);
}
for (i = 0; i < na; i++) {
vid = sys->index_anchors[i];
EIG_linear_solver_right_hand_side_add(sys->context, 0, n + i, vertexCos[vid][0]);
EIG_linear_solver_right_hand_side_add(sys->context, 1, n + i, vertexCos[vid][1]);
EIG_linear_solver_right_hand_side_add(sys->context, 2, n + i, vertexCos[vid][2]);
EIG_linear_solver_matrix_add(sys->context, n + i, vid, 1.0f);
}
if (EIG_linear_solver_solve(sys->context)) {
sys->has_solution = true;
for (j = 1; j <= sys->repeat; j++) {
rotateDifferentialCoordinates(sys);
for (i = 0; i < na; i++) {
vid = sys->index_anchors[i];
EIG_linear_solver_right_hand_side_add(sys->context, 0, n + i, vertexCos[vid][0]);
EIG_linear_solver_right_hand_side_add(sys->context, 1, n + i, vertexCos[vid][1]);
EIG_linear_solver_right_hand_side_add(sys->context, 2, n + i, vertexCos[vid][2]);
}
if (!EIG_linear_solver_solve(sys->context)) {
sys->has_solution = false;
break;
}
}
if (sys->has_solution) {
for (vid = 0; vid < sys->total_verts; vid++) {
vertexCos[vid][0] = EIG_linear_solver_variable_get(sys->context, 0, vid);
vertexCos[vid][1] = EIG_linear_solver_variable_get(sys->context, 1, vid);
vertexCos[vid][2] = EIG_linear_solver_variable_get(sys->context, 2, vid);
}
}
else {
sys->has_solution = false;
}
}
else {
sys->has_solution = false;
}
sys->is_matrix_computed = true;
}
else if (sys->has_solution) {
for (i = 0; i < n; i++) {
EIG_linear_solver_right_hand_side_add(sys->context, 0, i, sys->delta[i][0]);
EIG_linear_solver_right_hand_side_add(sys->context, 1, i, sys->delta[i][1]);
EIG_linear_solver_right_hand_side_add(sys->context, 2, i, sys->delta[i][2]);
}
for (i = 0; i < na; i++) {
vid = sys->index_anchors[i];
EIG_linear_solver_right_hand_side_add(sys->context, 0, n + i, vertexCos[vid][0]);
EIG_linear_solver_right_hand_side_add(sys->context, 1, n + i, vertexCos[vid][1]);
EIG_linear_solver_right_hand_side_add(sys->context, 2, n + i, vertexCos[vid][2]);
EIG_linear_solver_matrix_add(sys->context, n + i, vid, 1.0f);
}
if (EIG_linear_solver_solve(sys->context)) {
sys->has_solution = true;
for (j = 1; j <= sys->repeat; j++) {
rotateDifferentialCoordinates(sys);
for (i = 0; i < na; i++) {
vid = sys->index_anchors[i];
EIG_linear_solver_right_hand_side_add(sys->context, 0, n + i, vertexCos[vid][0]);
EIG_linear_solver_right_hand_side_add(sys->context, 1, n + i, vertexCos[vid][1]);
EIG_linear_solver_right_hand_side_add(sys->context, 2, n + i, vertexCos[vid][2]);
}
if (!EIG_linear_solver_solve(sys->context)) {
sys->has_solution = false;
break;
}
}
if (sys->has_solution) {
for (vid = 0; vid < sys->total_verts; vid++) {
vertexCos[vid][0] = EIG_linear_solver_variable_get(sys->context, 0, vid);
vertexCos[vid][1] = EIG_linear_solver_variable_get(sys->context, 1, vid);
vertexCos[vid][2] = EIG_linear_solver_variable_get(sys->context, 2, vid);
}
}
else {
sys->has_solution = false;
}
}
else {
sys->has_solution = false;
}
}
}
static void rotateDifferentialCoordinates(LaplacianSystem *sys)
{
float alpha, beta, gamma;
float pj[3], ni[3], di[3];
float uij[3], dun[3], e2[3], pi[3], fni[3], vn[3][3];
int i, j, num_fni, k, fi;
int *fidn;
for (i = 0; i < sys->total_verts; i++) {
copy_v3_v3(pi, sys->co[i]);
copy_v3_v3(ni, sys->no[i]);
k = sys->unit_verts[i];
copy_v3_v3(pj, sys->co[k]);
sub_v3_v3v3(uij, pj, pi);
mul_v3_v3fl(dun, ni, dot_v3v3(uij, ni));
sub_v3_v3(uij, dun);
normalize_v3(uij);
cross_v3_v3v3(e2, ni, uij);
copy_v3_v3(di, sys->delta[i]);
alpha = dot_v3v3(ni, di);
beta = dot_v3v3(uij, di);
gamma = dot_v3v3(e2, di);
pi[0] = EIG_linear_solver_variable_get(sys->context, 0, i);
pi[1] = EIG_linear_solver_variable_get(sys->context, 1, i);
pi[2] = EIG_linear_solver_variable_get(sys->context, 2, i);
zero_v3(ni);
num_fni = sys->ringf_map[i].count;
for (fi = 0; fi < num_fni; fi++) {
const unsigned int *vin;
fidn = sys->ringf_map[i].indices;
vin = sys->tris[fidn[fi]];
for (j = 0; j < 3; j++) {
vn[j][0] = EIG_linear_solver_variable_get(sys->context, 0, vin[j]);
vn[j][1] = EIG_linear_solver_variable_get(sys->context, 1, vin[j]);
vn[j][2] = EIG_linear_solver_variable_get(sys->context, 2, vin[j]);
if (vin[j] == sys->unit_verts[i]) {
copy_v3_v3(pj, vn[j]);
}
}
normal_tri_v3(fni, UNPACK3(vn));
add_v3_v3(ni, fni);
}
normalize_v3(ni);
sub_v3_v3v3(uij, pj, pi);
mul_v3_v3fl(dun, ni, dot_v3v3(uij, ni));
sub_v3_v3(uij, dun);
normalize_v3(uij);
cross_v3_v3v3(e2, ni, uij);
fni[0] = alpha * ni[0] + beta * uij[0] + gamma * e2[0];
fni[1] = alpha * ni[1] + beta * uij[1] + gamma * e2[1];
fni[2] = alpha * ni[2] + beta * uij[2] + gamma * e2[2];
if (len_squared_v3(fni) > FLT_EPSILON) {
EIG_linear_solver_right_hand_side_add(sys->context, 0, i, fni[0]);
EIG_linear_solver_right_hand_side_add(sys->context, 1, i, fni[1]);
EIG_linear_solver_right_hand_side_add(sys->context, 2, i, fni[2]);
}
else {
EIG_linear_solver_right_hand_side_add(sys->context, 0, i, sys->delta[i][0]);
EIG_linear_solver_right_hand_side_add(sys->context, 1, i, sys->delta[i][1]);
EIG_linear_solver_right_hand_side_add(sys->context, 2, i, sys->delta[i][2]);
}
}
}
