void MeshPara::LSCM()
{
is_Parameterized = true;
int nb_vertices = mesh_.n_vertices();
nlNewContext();
nlSolverParameteri(NL_SOLVER, NL_CG);
nlSolverParameteri(NL_PRECONDITIONER, NL_PRECOND_JACOBI);
nlSolverParameteri(NL_NB_VARIABLES, 2 * nb_vertices);
nlSolverParameteri(NL_LEAST_SQUARES, NL_TRUE);
nlSolverParameteri(NL_MAX_ITERATIONS, 5 * nb_vertices);
nlSolverParameterd(NL_THRESHOLD, 1e-10);
nlBegin(NL_SYSTEM);
init_slover();
nlBegin(NL_MATRIX);
setup_LSCM();
nlEnd(NL_MATRIX);
nlEnd(NL_SYSTEM);
std::cout << "Solving ..." << std::endl;
nlSolve();
// Get results
get_result();
// Display time and iter_num
double time;
NLint iterations;
nlGetDoublev(NL_ELAPSED_TIME, &time);
nlGetIntergerv(NL_USED_ITERATIONS, &iterations);
std::cout << "Solver time: " << time << std::endl;
std::cout << "Used iterations: " << iterations << std::endl;
nlDeleteContext(nlGetCurrent());
}
int laplacian_system_solve(LaplacianSystem *sys)
{
nlEnd(NL_MATRIX);
nlEnd(NL_SYSTEM);
sys->nlbegun = 0;
//nlPrintMatrix();
return nlSolveAdvanced(NULL, NL_TRUE);
}
// LSCM equation, geometric form :
// (Z1 - Z0)(U2 - U0) = (Z2 - Z0)(U1 - U0)
// Where Uk = uk + i.vk is the complex number
// corresponding to (u,v) coords
// Zk = xk + i.yk is the complex number
// corresponding to local (x,y) coords
void MeshPara::setup_conformal_map_relations(Mesh::FHandle fh)
{
int id[3];
Vec3f p[3];
auto fv = mesh_.fv_begin(fh);
for (int i = 0; i < 3; i++, fv++)
{
p[i] = mesh_.point(*fv);
id[i] = (*fv).idx();
}
Vec2f z[3];
project_triangle(p[0], p[1], p[2], z[0], z[1], z[2]);
Vec2f z01 = z[1] - z[0];
Vec2f z02 = z[2] - z[0];
double a = z01[0];
double b = z01[1];
double c = z02[0];
double d = z02[1];
assert(b == 0.0);
// Note : 2*id + 0 --> u
// 2*id + 1 --> v
int u0_id = 2 * id[0];
int v0_id = 2 * id[0] + 1;
int u1_id = 2 * id[1];
int v1_id = 2 * id[1] + 1;
int u2_id = 2 * id[2];
int v2_id = 2 * id[2] + 1;
// Note : b = 0
// Real part
nlBegin(NL_ROW);
nlCoefficient(u0_id, -a + c);
nlCoefficient(v0_id, b - d);
nlCoefficient(u1_id, -c);
nlCoefficient(v1_id, d);
nlCoefficient(u2_id, a);
nlEnd(NL_ROW);
// Imaginary part
nlBegin(NL_ROW);
nlCoefficient(u0_id, -b + d);
nlCoefficient(v0_id, -a + c);
nlCoefficient(u1_id, -d);
nlCoefficient(v1_id, -c);
nlCoefficient(v2_id, a);
nlEnd(NL_ROW);
}
void leastSquaresSystem::solve(double *vs)
{
int i;
Node *n;
coeffIndexPair *f;
nlNewContext();
nlSolverParameteri(NL_SOLVER, NL_PERM_SUPERLU_EXT);
nlSolverParameteri(NL_NB_VARIABLES, num_variables);
nlSolverParameteri(NL_LEAST_SQUARES, NL_TRUE) ;
nlSolverParameteri(NL_MAX_ITERATIONS, 1000) ;
nlSolverParameterd(NL_THRESHOLD, 1e-10) ;
nlBegin(NL_SYSTEM);
for (i=0; i<num_variables; i++)
{
nlSetVariable(i, vs[i]);
if (locks[i]) nlLockVariable(i);
}
nlBegin(NL_MATRIX);
for (i=0; i<num_equations; i++)
{
nlRowParameterd(NL_RIGHT_HAND_SIDE, known_term[0][i]);
nlBegin(NL_ROW);
for (n=rows[i].cips.head(); n!=NULL; n=n->next())
{
f = (coeffIndexPair *)n->data;
nlCoefficient(f->index, f->coeff);
}
nlEnd(NL_ROW);
}
nlEnd(NL_MATRIX);
nlEnd(NL_SYSTEM);
nlSolve();
for (i=0; i<num_variables; i++) vs[i] = nlGetVariable(i);
nlDeleteContext(nlGetCurrent());
}
void sparse3System::solve(double *vs)
{
int i, j;
Node *n;
coeffIndexPair *f;
for (j=0; j<3; j++)
{
nlNewContext();
nlSolverParameteri(NL_SOLVER, NL_PERM_SUPERLU_EXT);
nlSolverParameteri(NL_NB_VARIABLES, num_variables);
nlBegin(NL_SYSTEM);
for (i=0; i<num_variables; i++)
{
nlSetVariable(i, vs[i*3 + j]);
if (locks[i]) nlLockVariable(i);
}
nlBegin(NL_MATRIX);
for (i=0; i<num_equations; i++)
{
nlRowParameterd(NL_RIGHT_HAND_SIDE, known_term[j][i]);
nlBegin(NL_ROW);
for (n=rows[i].cips.head(); n!=NULL; n=n->next())
{
f = (coeffIndexPair *)n->data;
nlCoefficient(f->index, f->coeff);
}
nlEnd(NL_ROW);
}
nlEnd(NL_MATRIX);
nlEnd(NL_SYSTEM);
nlSolve();
for (i=0; i<num_variables; i++) vs[i*3 + j] = nlGetVariable(i);
nlDeleteContext(nlGetCurrent());
}
}
// Solves the system for j'th component of B
bool sparseSystem::solve(double *x, int j)
{
int i;
Node *n;
coeffIndexPair *f;
nlNewContext();
nlSolverParameteri(NL_SOLVER, NL_PERM_SUPERLU_EXT);
nlSolverParameteri(NL_NB_VARIABLES, num_variables);
nlBegin(NL_SYSTEM);
for (i=0; i<num_variables; i++) nlSetVariable(i, x[i]);
nlBegin(NL_MATRIX);
for (i=0; i<num_equations; i++)
{
nlRowParameterd(NL_RIGHT_HAND_SIDE, known_term[j][i]);
nlBegin(NL_ROW);
for (n=rows[i].cips.head(); n!=NULL; n=n->next())
{
f = (coeffIndexPair *)n->data;
nlCoefficient(f->index, f->coeff);
}
nlEnd(NL_ROW);
}
nlEnd(NL_MATRIX);
nlEnd(NL_SYSTEM);
bool success = (bool)nlSolve();
if (success) for (i=0; i<num_variables; i++) x[i] = nlGetVariable(i);
nlDeleteContext(nlGetCurrent());
return success;
}
static void laplaciansmoothModifier_do(
LaplacianSmoothModifierData *smd, Object *ob, DerivedMesh *dm,
float (*vertexCos)[3], int numVerts)
{
LaplacianSystem *sys;
MDeformVert *dvert = NULL;
MDeformVert *dv = NULL;
float w, wpaint;
int i, iter;
int defgrp_index;
DM_ensure_tessface(dm);
sys = init_laplacian_system(dm->getNumEdges(dm), dm->getNumTessFaces(dm), numVerts);
if (!sys) {
return;
}
sys->mfaces = dm->getTessFaceArray(dm);
sys->medges = dm->getEdgeArray(dm);
sys->vertexCos = vertexCos;
sys->min_area = 0.00001f;
modifier_get_vgroup(ob, dm, smd->defgrp_name, &dvert, &defgrp_index);
sys->vert_centroid[0] = 0.0f;
sys->vert_centroid[1] = 0.0f;
sys->vert_centroid[2] = 0.0f;
memset_laplacian_system(sys, 0);
#ifdef OPENNL_THREADING_HACK
modifier_opennl_lock();
#endif
nlNewContext();
sys->context = nlGetCurrent();
nlSolverParameteri(NL_NB_VARIABLES, numVerts);
nlSolverParameteri(NL_LEAST_SQUARES, NL_TRUE);
nlSolverParameteri(NL_NB_ROWS, numVerts);
nlSolverParameteri(NL_NB_RIGHT_HAND_SIDES, 3);
init_laplacian_matrix(sys);
for (iter = 0; iter < smd->repeat; iter++) {
nlBegin(NL_SYSTEM);
for (i = 0; i < numVerts; i++) {
nlSetVariable(0, i, vertexCos[i][0]);
nlSetVariable(1, i, vertexCos[i][1]);
nlSetVariable(2, i, vertexCos[i][2]);
if (iter == 0) {
add_v3_v3(sys->vert_centroid, vertexCos[i]);
}
}
if (iter == 0 && numVerts > 0) {
mul_v3_fl(sys->vert_centroid, 1.0f / (float)numVerts);
}
nlBegin(NL_MATRIX);
dv = dvert;
for (i = 0; i < numVerts; i++) {
nlRightHandSideSet(0, i, vertexCos[i][0]);
nlRightHandSideSet(1, i, vertexCos[i][1]);
nlRightHandSideSet(2, i, vertexCos[i][2]);
if (iter == 0) {
if (dv) {
wpaint = defvert_find_weight(dv, defgrp_index);
dv++;
}
else {
wpaint = 1.0f;
}
if (sys->zerola[i] == 0) {
if (smd->flag & MOD_LAPLACIANSMOOTH_NORMALIZED) {
w = sys->vweights[i];
sys->vweights[i] = (w == 0.0f) ? 0.0f : -fabsf(smd->lambda) * wpaint / w;
w = sys->vlengths[i];
sys->vlengths[i] = (w == 0.0f) ? 0.0f : -fabsf(smd->lambda_border) * wpaint * 2.0f / w;
if (sys->numNeEd[i] == sys->numNeFa[i]) {
nlMatrixAdd(i, i, 1.0f + fabsf(smd->lambda) * wpaint);
}
else {
nlMatrixAdd(i, i, 1.0f + fabsf(smd->lambda_border) * wpaint * 2.0f);
}
}
else {
w = sys->vweights[i] * sys->ring_areas[i];
sys->vweights[i] = (w == 0.0f) ? 0.0f : -fabsf(smd->lambda) * wpaint / (4.0f * w);
w = sys->vlengths[i];
sys->vlengths[i] = (w == 0.0f) ? 0.0f : -fabsf(smd->lambda_border) * wpaint * 2.0f / w;
if (sys->numNeEd[i] == sys->numNeFa[i]) {
nlMatrixAdd(i, i, 1.0f + fabsf(smd->lambda) * wpaint / (4.0f * sys->ring_areas[i]));
}
else {
nlMatrixAdd(i, i, 1.0f + fabsf(smd->lambda_border) * wpaint * 2.0f);
}
}
}
else {
nlMatrixAdd(i, i, 1.0f);
}
}
}
if (iter == 0) {
fill_laplacian_matrix(sys);
}
nlEnd(NL_MATRIX);
nlEnd(NL_SYSTEM);
if (nlSolveAdvanced(NULL, NL_TRUE)) {
validate_solution(sys, smd->flag, smd->lambda, smd->lambda_border);
}
}
nlDeleteContext(sys->context);
sys->context = NULL;
#ifdef OPENNL_THREADING_HACK
modifier_opennl_unlock();
#endif
delete_laplacian_system(sys);
}
static void meshdeform_matrix_solve(MeshDeformBind *mdb)
{
NLContext *context;
float vec[3], gridvec[3];
int a, b, x, y, z, totvar;
char message[1024];
/* 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 opennl solver */
nlNewContext();
context= nlGetCurrent();
nlSolverParameteri(NL_NB_VARIABLES, totvar);
nlSolverParameteri(NL_NB_ROWS, totvar);
nlSolverParameteri(NL_NB_RIGHT_HAND_SIDES, 1);
nlBegin(NL_SYSTEM);
nlBegin(NL_MATRIX);
/* 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, x, y, z);
/* solve for each cage vert */
for(a=0; a<mdb->totcagevert; a++) {
if(a != 0) {
nlBegin(NL_SYSTEM);
nlBegin(NL_MATRIX);
}
/* 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, x, y, z, a);
nlEnd(NL_MATRIX);
nlEnd(NL_SYSTEM);
#if 0
nlPrintMatrix();
#endif
if(nlSolveAdvanced(NULL, NL_TRUE)) {
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]= nlGetVariable(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 {
error("Mesh Deform: failed to find solution.");
break;
}
sprintf(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(fabs(mdb->totalphi[b] - 1.0f) > 1e-4)
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);
nlDeleteContext(context);
}
static void laplacianDeformPreview(LaplacianSystem *sys, float (*vertexCos)[3])
{
int vid, i, j, n, na;
n = sys->total_verts;
na = sys->total_anchors;
#ifdef OPENNL_THREADING_HACK
modifier_opennl_lock();
#endif
if (!sys->is_matrix_computed) {
nlNewContext();
sys->context = nlGetCurrent();
nlSolverParameteri(NL_NB_VARIABLES, n);
nlSolverParameteri(NL_SYMMETRIC, NL_FALSE);
nlSolverParameteri(NL_LEAST_SQUARES, NL_TRUE);
nlSolverParameteri(NL_NB_ROWS, n + na);
nlSolverParameteri(NL_NB_RIGHT_HAND_SIDES, 3);
nlBegin(NL_SYSTEM);
for (i = 0; i < n; i++) {
nlSetVariable(0, i, sys->co[i][0]);
nlSetVariable(1, i, sys->co[i][1]);
nlSetVariable(2, i, sys->co[i][2]);
}
for (i = 0; i < na; i++) {
vid = sys->index_anchors[i];
nlSetVariable(0, vid, vertexCos[vid][0]);
nlSetVariable(1, vid, vertexCos[vid][1]);
nlSetVariable(2, vid, vertexCos[vid][2]);
}
nlBegin(NL_MATRIX);
initLaplacianMatrix(sys);
computeImplictRotations(sys);
for (i = 0; i < n; i++) {
nlRightHandSideSet(0, i, sys->delta[i][0]);
nlRightHandSideSet(1, i, sys->delta[i][1]);
nlRightHandSideSet(2, i, sys->delta[i][2]);
}
for (i = 0; i < na; i++) {
vid = sys->index_anchors[i];
nlRightHandSideSet(0, n + i, vertexCos[vid][0]);
nlRightHandSideSet(1, n + i, vertexCos[vid][1]);
nlRightHandSideSet(2, n + i, vertexCos[vid][2]);
nlMatrixAdd(n + i, vid, 1.0f);
}
nlEnd(NL_MATRIX);
nlEnd(NL_SYSTEM);
if (nlSolveAdvanced(NULL, NL_TRUE)) {
sys->has_solution = true;
for (j = 1; j <= sys->repeat; j++) {
nlBegin(NL_SYSTEM);
nlBegin(NL_MATRIX);
rotateDifferentialCoordinates(sys);
for (i = 0; i < na; i++) {
vid = sys->index_anchors[i];
nlRightHandSideSet(0, n + i, vertexCos[vid][0]);
nlRightHandSideSet(1, n + i, vertexCos[vid][1]);
nlRightHandSideSet(2, n + i, vertexCos[vid][2]);
}
nlEnd(NL_MATRIX);
nlEnd(NL_SYSTEM);
if (!nlSolveAdvanced(NULL, NL_FALSE)) {
sys->has_solution = false;
break;
}
}
if (sys->has_solution) {
for (vid = 0; vid < sys->total_verts; vid++) {
vertexCos[vid][0] = nlGetVariable(0, vid);
vertexCos[vid][1] = nlGetVariable(1, vid);
vertexCos[vid][2] = nlGetVariable(2, vid);
}
}
else {
sys->has_solution = false;
}
}
else {
sys->has_solution = false;
}
sys->is_matrix_computed = true;
}
else if (sys->has_solution) {
nlBegin(NL_SYSTEM);
nlBegin(NL_MATRIX);
for (i = 0; i < n; i++) {
nlRightHandSideSet(0, i, sys->delta[i][0]);
nlRightHandSideSet(1, i, sys->delta[i][1]);
nlRightHandSideSet(2, i, sys->delta[i][2]);
}
for (i = 0; i < na; i++) {
vid = sys->index_anchors[i];
nlRightHandSideSet(0, n + i, vertexCos[vid][0]);
nlRightHandSideSet(1, n + i, vertexCos[vid][1]);
nlRightHandSideSet(2, n + i, vertexCos[vid][2]);
nlMatrixAdd(n + i, vid, 1.0f);
}
nlEnd(NL_MATRIX);
nlEnd(NL_SYSTEM);
if (nlSolveAdvanced(NULL, NL_FALSE)) {
sys->has_solution = true;
for (j = 1; j <= sys->repeat; j++) {
nlBegin(NL_SYSTEM);
nlBegin(NL_MATRIX);
rotateDifferentialCoordinates(sys);
for (i = 0; i < na; i++) {
vid = sys->index_anchors[i];
nlRightHandSideSet(0, n + i, vertexCos[vid][0]);
nlRightHandSideSet(1, n + i, vertexCos[vid][1]);
nlRightHandSideSet(2, n + i, vertexCos[vid][2]);
}
nlEnd(NL_MATRIX);
nlEnd(NL_SYSTEM);
if (!nlSolveAdvanced(NULL, NL_FALSE)) {
sys->has_solution = false;
break;
}
}
if (sys->has_solution) {
for (vid = 0; vid < sys->total_verts; vid++) {
vertexCos[vid][0] = nlGetVariable(0, vid);
vertexCos[vid][1] = nlGetVariable(1, vid);
vertexCos[vid][2] = nlGetVariable(2, vid);
}
}
else {
sys->has_solution = false;
}
}
else {
sys->has_solution = false;
}
}
#ifdef OPENNL_THREADING_HACK
modifier_opennl_unlock();
#endif
}
