static void meshdeform_matrix_add_cell(MeshDeformBind *mdb, LinearSolver *context, int x, int y, int z)
{
MDefBoundIsect *isect;
float weight, totweight;
int i, a, acenter;
acenter = meshdeform_index(mdb, x, y, z, 0);
if (mdb->tag[acenter] == MESHDEFORM_TAG_EXTERIOR)
return;
EIG_linear_solver_matrix_add(context, mdb->varidx[acenter], mdb->varidx[acenter], 1.0f);
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 || mdb->tag[a] == MESHDEFORM_TAG_EXTERIOR)
continue;
isect = mdb->boundisect[acenter][i - 1];
if (!isect) {
weight = (1.0f / mdb->width[0]) / totweight;
EIG_linear_solver_matrix_add(context, mdb->varidx[acenter], mdb->varidx[a], -weight);
}
}
}
static void laplacian_triangle_weights(LaplacianSystem *sys, int f, int i1, int i2, int i3)
{
float t1, t2, t3;
float *varea = sys->varea, *v1, *v2, *v3;
v1 = sys->verts[i1];
v2 = sys->verts[i2];
v3 = sys->verts[i3];
/* instead of *0.5 we divided by the number of faces of the edge, it still
* needs to be verified that this is indeed the correct thing to do! */
t1 = cotangent_tri_weight_v3(v1, v2, v3) / laplacian_edge_count(sys->edgehash, i2, i3);
t2 = cotangent_tri_weight_v3(v2, v3, v1) / laplacian_edge_count(sys->edgehash, i3, i1);
t3 = cotangent_tri_weight_v3(v3, v1, v2) / laplacian_edge_count(sys->edgehash, i1, i2);
EIG_linear_solver_matrix_add(sys->context, i1, i1, (t2 + t3) * varea[i1]);
EIG_linear_solver_matrix_add(sys->context, i2, i2, (t1 + t3) * varea[i2]);
EIG_linear_solver_matrix_add(sys->context, i3, i3, (t1 + t2) * varea[i3]);
EIG_linear_solver_matrix_add(sys->context, i1, i2, -t3 * varea[i1]);
EIG_linear_solver_matrix_add(sys->context, i2, i1, -t3 * varea[i2]);
EIG_linear_solver_matrix_add(sys->context, i2, i3, -t1 * varea[i2]);
EIG_linear_solver_matrix_add(sys->context, i3, i2, -t1 * varea[i3]);
EIG_linear_solver_matrix_add(sys->context, i3, i1, -t2 * varea[i3]);
EIG_linear_solver_matrix_add(sys->context, i1, i3, -t2 * varea[i1]);
if (sys->storeweights) {
sys->fweights[f][0] = t1 * varea[i1];
sys->fweights[f][1] = t2 * varea[i2];
sys->fweights[f][2] = t3 * varea[i3];
}
}
/**
* 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 no[3];
float w2, w3;
int i = 3, j, ti;
int idv[3];
for (ti = 0; ti < sys->total_tris; ti++) {
const unsigned int *vidt = sys->tris[ti];
const float *co[3];
co[0] = sys->co[vidt[0]];
co[1] = sys->co[vidt[1]];
co[2] = sys->co[vidt[2]];
normal_tri_v3(no, UNPACK3(co));
add_v3_v3(sys->no[vidt[0]], no);
add_v3_v3(sys->no[vidt[1]], no);
add_v3_v3(sys->no[vidt[2]], no);
for (j = 0; j < 3; j++) {
const float *v1, *v2, *v3;
idv[0] = vidt[j];
idv[1] = vidt[(j + 1) % i];
idv[2] = vidt[(j + 2) % i];
v1 = sys->co[idv[0]];
v2 = sys->co[idv[1]];
v3 = sys->co[idv[2]];
w2 = cotangent_tri_weight_v3(v3, v1, v2);
w3 = cotangent_tri_weight_v3(v2, v3, v1);
sys->delta[idv[0]][0] += v1[0] * (w2 + w3);
sys->delta[idv[0]][1] += v1[1] * (w2 + w3);
sys->delta[idv[0]][2] += v1[2] * (w2 + w3);
sys->delta[idv[0]][0] -= v2[0] * w2;
sys->delta[idv[0]][1] -= v2[1] * w2;
sys->delta[idv[0]][2] -= v2[2] * w2;
sys->delta[idv[0]][0] -= v3[0] * w3;
sys->delta[idv[0]][1] -= v3[1] * w3;
sys->delta[idv[0]][2] -= v3[2] * w3;
EIG_linear_solver_matrix_add(sys->context, idv[0], idv[1], -w2);
EIG_linear_solver_matrix_add(sys->context, idv[0], idv[2], -w3);
EIG_linear_solver_matrix_add(sys->context, idv[0], idv[0], w2 + w3);
}
}
}
static void fill_laplacian_matrix(LaplacianSystem *sys)
{
int i;
unsigned int idv1, idv2;
for (i = 0; i < sys->numPolys; i++) {
const MPoly *mp = &sys->mpoly[i];
const MLoop *l_next = &sys->mloop[mp->loopstart];
const MLoop *l_term = l_next + mp->totloop;
const MLoop *l_prev = l_term - 2;
const MLoop *l_curr = l_term - 1;
for (;
l_next != l_term;
l_prev = l_curr, l_curr = l_next, l_next++)
{
const unsigned int l_curr_index = l_curr - sys->mloop;
/* Is ring if number of faces == number of edges around vertice*/
if (sys->numNeEd[l_curr->v] == sys->numNeFa[l_curr->v] && sys->zerola[l_curr->v] == 0) {
EIG_linear_solver_matrix_add(sys->context, l_curr->v, l_next->v, sys->fweights[l_curr_index][2] * sys->vweights[l_curr->v]);
EIG_linear_solver_matrix_add(sys->context, l_curr->v, l_prev->v, sys->fweights[l_curr_index][1] * sys->vweights[l_curr->v]);
}
if (sys->numNeEd[l_next->v] == sys->numNeFa[l_next->v] && sys->zerola[l_next->v] == 0) {
EIG_linear_solver_matrix_add(sys->context, l_next->v, l_curr->v, sys->fweights[l_curr_index][2] * sys->vweights[l_next->v]);
EIG_linear_solver_matrix_add(sys->context, l_next->v, l_prev->v, sys->fweights[l_curr_index][0] * sys->vweights[l_next->v]);
}
if (sys->numNeEd[l_prev->v] == sys->numNeFa[l_prev->v] && sys->zerola[l_prev->v] == 0) {
EIG_linear_solver_matrix_add(sys->context, l_prev->v, l_curr->v, sys->fweights[l_curr_index][1] * sys->vweights[l_prev->v]);
EIG_linear_solver_matrix_add(sys->context, l_prev->v, l_next->v, sys->fweights[l_curr_index][0] * sys->vweights[l_prev->v]);
}
}
}
for (i = 0; i < sys->numEdges; i++) {
idv1 = sys->medges[i].v1;
idv2 = sys->medges[i].v2;
/* Is boundary */
if (sys->numNeEd[idv1] != sys->numNeFa[idv1] &&
sys->numNeEd[idv2] != sys->numNeFa[idv2] &&
sys->zerola[idv1] == 0 &&
sys->zerola[idv2] == 0)
{
EIG_linear_solver_matrix_add(sys->context, idv1, idv2, sys->eweights[i] * sys->vlengths[idv1]);
EIG_linear_solver_matrix_add(sys->context, idv2, idv1, sys->eweights[i] * sys->vlengths[idv2]);
}
}
}
static void laplacian_system_construct_end(LaplacianSystem *sys)
{
int (*face)[3];
int a, totvert = sys->totvert, totface = sys->totface;
laplacian_begin_solve(sys, 0);
sys->varea = MEM_callocN(sizeof(float) * totvert, "LaplacianSystemVarea");
sys->edgehash = BLI_edgehash_new_ex(__func__, BLI_EDGEHASH_SIZE_GUESS_FROM_POLYS(sys->totface));
for (a = 0, face = sys->faces; a < sys->totface; a++, face++) {
laplacian_increase_edge_count(sys->edgehash, (*face)[0], (*face)[1]);
laplacian_increase_edge_count(sys->edgehash, (*face)[1], (*face)[2]);
laplacian_increase_edge_count(sys->edgehash, (*face)[2], (*face)[0]);
}
if (sys->areaweights)
for (a = 0, face = sys->faces; a < sys->totface; a++, face++)
laplacian_triangle_area(sys, (*face)[0], (*face)[1], (*face)[2]);
for (a = 0; a < totvert; a++) {
if (sys->areaweights) {
if (sys->varea[a] != 0.0f)
sys->varea[a] = 0.5f / sys->varea[a];
}
else
sys->varea[a] = 1.0f;
/* for heat weighting */
if (sys->heat.H)
EIG_linear_solver_matrix_add(sys->context, a, a, sys->heat.H[a]);
}
if (sys->storeweights)
sys->fweights = MEM_callocN(sizeof(float) * 3 * totface, "LaplacianFWeight");
for (a = 0, face = sys->faces; a < totface; a++, face++)
laplacian_triangle_weights(sys, a, (*face)[0], (*face)[1], (*face)[2]);
MEM_freeN(sys->faces);
sys->faces = NULL;
if (sys->varea) {
MEM_freeN(sys->varea);
sys->varea = NULL;
}
BLI_edgehash_free(sys->edgehash, NULL);
sys->edgehash = NULL;
}
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 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;
sys = init_laplacian_system(dm->getNumEdges(dm), dm->getNumPolys(dm), dm->getNumLoops(dm), numVerts);
if (!sys) {
return;
}
sys->mpoly = dm->getPolyArray(dm);
sys->mloop = dm->getLoopArray(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);
sys->context = EIG_linear_least_squares_solver_new(numVerts, numVerts, 3);
init_laplacian_matrix(sys);
for (iter = 0; iter < smd->repeat; iter++) {
for (i = 0; i < numVerts; i++) {
EIG_linear_solver_variable_set(sys->context, 0, i, vertexCos[i][0]);
EIG_linear_solver_variable_set(sys->context, 1, i, vertexCos[i][1]);
EIG_linear_solver_variable_set(sys->context, 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);
}
dv = dvert;
for (i = 0; i < numVerts; i++) {
EIG_linear_solver_right_hand_side_add(sys->context, 0, i, vertexCos[i][0]);
EIG_linear_solver_right_hand_side_add(sys->context, 1, i, vertexCos[i][1]);
EIG_linear_solver_right_hand_side_add(sys->context, 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]) {
EIG_linear_solver_matrix_add(sys->context, i, i, 1.0f + fabsf(smd->lambda) * wpaint);
}
else {
EIG_linear_solver_matrix_add(sys->context, 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]) {
EIG_linear_solver_matrix_add(sys->context, i, i, 1.0f + fabsf(smd->lambda) * wpaint / (4.0f * sys->ring_areas[i]));
}
else {
EIG_linear_solver_matrix_add(sys->context, i, i, 1.0f + fabsf(smd->lambda_border) * wpaint * 2.0f);
}
}
}
else {
EIG_linear_solver_matrix_add(sys->context, i, i, 1.0f);
}
}
}
if (iter == 0) {
fill_laplacian_matrix(sys);
}
if (EIG_linear_solver_solve(sys->context)) {
validate_solution(sys, smd->flag, smd->lambda, smd->lambda_border);
}
}
EIG_linear_solver_delete(sys->context);
sys->context = NULL;
delete_laplacian_system(sys);
}
