static void meshdeform_matrix_add_rhs(MeshDeformBind *mdb, int x, int y, int z, int cagevert)
{
MDefBoundIsect *isect;
float rhs, weight, totweight;
int i, a, acenter;
acenter= meshdeform_index(mdb, x, y, z, 0);
if(mdb->tag[acenter] == MESHDEFORM_TAG_EXTERIOR)
return;
totweight= meshdeform_boundary_total_weight(mdb, x, y, z);
for(i=1; i<=6; i++) {
a= meshdeform_index(mdb, x, y, z, i);
if(a == -1)
continue;
isect= mdb->boundisect[acenter][i-1];
if (isect) {
weight= (1.0f/isect->len)/totweight;
rhs= weight*meshdeform_boundary_phi(mdb, isect, cagevert);
nlRightHandSideAdd(0, mdb->varidx[acenter], rhs);
}
}
}
void laplacian_add_right_hand_side(LaplacianSystem *UNUSED(sys), int v, float value)
{
nlRightHandSideAdd(0, v, value);
}
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;
for (iter = 0; iter < smd->repeat; iter++) {
memset_laplacian_system(sys, 0);
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);
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++) {
nlRightHandSideAdd(0, i, vertexCos[i][0]);
nlRightHandSideAdd(1, i, vertexCos[i][1]);
nlRightHandSideAdd(2, i, vertexCos[i][2]);
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);
}
}
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;
}
delete_laplacian_system(sys);
}
/**
* This method computes the Laplacian Matrix and Differential Coordinates for all vertex in the mesh.
* The Linear system is LV = d
* Where L is Laplacian Matrix, V as the vertexes in Mesh, d is the differential coordinates
* The Laplacian Matrix is computes as a
* Lij = sum(Wij) (if i == j)
* Lij = Wij (if i != j)
* Wij is weight between vertex Vi and vertex Vj, we use cotangent weight
*
* The Differential Coordinate is computes as a
* di = Vi * sum(Wij) - sum(Wij * Vj)
* Where :
* di is the Differential Coordinate i
* sum (Wij) is the sum of all weights between vertex Vi and its vertexes neighbors (Vj)
* sum (Wij * Vj) is the sum of the product between vertex neighbor Vj and weight Wij for all neighborhood.
*
* This Laplacian Matrix is described in the paper:
* Desbrun M. et.al, Implicit fairing of irregular meshes using diffusion and curvature flow, SIGGRAPH '99, pag 317-324,
* New York, USA
*
* The computation of Laplace Beltrami operator on Hybrid Triangle/Quad Meshes is described in the paper:
* Pinzon A., Romero E., Shape Inflation With an Adapted Laplacian Operator For Hybrid Quad/Triangle Meshes,
* Conference on Graphics Patterns and Images, SIBGRAPI, 2013
*
* The computation of Differential Coordinates is described in the paper:
* Sorkine, O. Laplacian Surface Editing. Proceedings of the EUROGRAPHICS/ACM SIGGRAPH Symposium on Geometry Processing,
* 2004. p. 179-188.
*/
static void initLaplacianMatrix(LaplacianSystem *sys)
{
float v1[3], v2[3], v3[3], v4[3], no[3];
float w2, w3, w4;
int i, j, fi;
bool has_4_vert;
unsigned int idv1, idv2, idv3, idv4;
for (fi = 0; fi < sys->total_faces; fi++) {
const unsigned int *vidf = sys->faces[fi];
idv1 = vidf[0];
idv2 = vidf[1];
idv3 = vidf[2];
idv4 = vidf[3];
has_4_vert = vidf[3] ? 1 : 0;
if (has_4_vert) {
normal_quad_v3(no, sys->co[idv1], sys->co[idv2], sys->co[idv3], sys->co[idv4]);
add_v3_v3(sys->no[idv4], no);
i = 4;
}
else {
normal_tri_v3(no, sys->co[idv1], sys->co[idv2], sys->co[idv3]);
i = 3;
}
add_v3_v3(sys->no[idv1], no);
add_v3_v3(sys->no[idv2], no);
add_v3_v3(sys->no[idv3], no);
for (j = 0; j < i; j++) {
idv1 = vidf[j];
idv2 = vidf[(j + 1) % i];
idv3 = vidf[(j + 2) % i];
idv4 = has_4_vert ? vidf[(j + 3) % i] : 0;
copy_v3_v3(v1, sys->co[idv1]);
copy_v3_v3(v2, sys->co[idv2]);
copy_v3_v3(v3, sys->co[idv3]);
if (has_4_vert) {
copy_v3_v3(v4, sys->co[idv4]);
}
if (has_4_vert) {
w2 = (cotan_weight(v4, v1, v2) + cotan_weight(v3, v1, v2)) / 2.0f;
w3 = (cotan_weight(v2, v3, v1) + cotan_weight(v4, v1, v3)) / 2.0f;
w4 = (cotan_weight(v2, v4, v1) + cotan_weight(v3, v4, v1)) / 2.0f;
sys->delta[idv1][0] -= v4[0] * w4;
sys->delta[idv1][1] -= v4[1] * w4;
sys->delta[idv1][2] -= v4[2] * w4;
nlRightHandSideAdd(0, idv1, -v4[0] * w4);
nlRightHandSideAdd(1, idv1, -v4[1] * w4);
nlRightHandSideAdd(2, idv1, -v4[2] * w4);
nlMatrixAdd(idv1, idv4, -w4);
}
else {
w2 = cotan_weight(v3, v1, v2);
w3 = cotan_weight(v2, v3, v1);
w4 = 0.0f;
}
sys->delta[idv1][0] += v1[0] * (w2 + w3 + w4);
sys->delta[idv1][1] += v1[1] * (w2 + w3 + w4);
sys->delta[idv1][2] += v1[2] * (w2 + w3 + w4);
sys->delta[idv1][0] -= v2[0] * w2;
sys->delta[idv1][1] -= v2[1] * w2;
sys->delta[idv1][2] -= v2[2] * w2;
sys->delta[idv1][0] -= v3[0] * w3;
sys->delta[idv1][1] -= v3[1] * w3;
sys->delta[idv1][2] -= v3[2] * w3;
nlMatrixAdd(idv1, idv2, -w2);
nlMatrixAdd(idv1, idv3, -w3);
nlMatrixAdd(idv1, idv1, w2 + w3 + w4);
}
}
}