static void check_neighbour(const std::vector<Vec3ui> &tri, const std::vector<Vec3f> &x,
Array3f &phi, Array3i &closest_tri,
const Vec3f &gx, int i0, int j0, int k0, int i1, int j1, int k1)
{
if(closest_tri(i1,j1,k1)>=0){
unsigned int p, q, r; assign(tri[closest_tri(i1,j1,k1)], p, q, r);
float d=point_triangle_distance(gx, x[p], x[q], x[r]);
if(d<phi(i0,j0,k0)){
phi(i0,j0,k0)=d;
closest_tri(i0,j0,k0)=closest_tri(i1,j1,k1);
}
}
}
void meshsurf3::buildSurface( std::vector<vec3d> &vertices, std::vector<vec3d> &normals, std::vector<vec3i> &faces, const levelset3 *fluid, const levelset3 *solid, bool enclose, FLOAT64 dpx, uint iteration, bool doFit ) {
// Save a reference to the mesher
const mesher3 &g = *this->g;
tick(); dump("Computing levelset for %d nodes...", g.nodes.size());
values.clear();
values.resize(g.nodes.size());
if( values.empty() ) {
email::print("Mesher Uninitialized !\n");
email::send();
exit(0);
}
// Compute levelset for each node
PARALLEL_FOR for( uint n=0; n<g.nodes.size(); n++ ) {
FLOAT64 phi = fluid->evalLevelset(g.nodes[n]);
if( enclose ) phi = fmax(phi,-dpx-solid->evalLevelset(g.nodes[n]));
values[n] = phi;
}
dump("Done. Took %s.\n",stock("meshsurf_levelset_sample"));
// Fill holes
fillHoles(values,solid,g.nodes,g.elements,g.node2node,fluid->dx);
// Calculate intersections on edges
tick(); dump("Computing cut edges for each tet...");
std::vector<vec3d> cutpoints(g.edges.size());
std::vector<int> cutIndices(g.edges.size());
uint index = 0;
for( int n=0; n<g.edges.size(); n++ ) {
FLOAT64 levelsets[2];
for( uint m=0; m<2; m++ ) levelsets[m] = values[g.edges[n][m]];
if( copysign(1.0,levelsets[0]) * copysign(1.0,levelsets[1]) <= 0 ) {
FLOAT64 det = levelsets[0]-levelsets[1];
if( fabs(det) < 1e-16 ) det = copysign(1e-16,det);
FLOAT64 a = fmin(0.99,fmax(0.01,levelsets[0]/det));
vec3d p = (1.0-a)*g.nodes[g.edges[n][0]]+a*g.nodes[g.edges[n][1]];
cutpoints[n] = p;
cutIndices[n] = index++;
} else {
cutIndices[n] = -1;
}
}
// Copy them to packed array
vertices.clear();
vertices.resize(index);
index = 0;
for( uint n=0; n<cutIndices.size(); n++ ) {
if( cutIndices[n] >= 0 ) vertices[index++] = cutpoints[n];
}
dump("Done. Took %s.\n",stock());
// Stitch faces (marching tet)
tick(); dump("Stitching edges...");
std::vector<std::vector<uint> > node_faces;
node_faces.resize(g.nodes.size());
faces.clear();
for( uint n=0; n<g.elements.size(); n++ ) {
std::vector<uint> nv;
for( uint m=0; m<g.element_edges[n].size(); m++ ) {
uint idx = g.element_edges[n][m];
if( cutIndices[idx] >= 0 ) {
nv.push_back(cutIndices[idx]);
}
}
if( nv.size() == 4 ) {
// Triangulate the veritces
int idx0 = -1;
int idx1 = -1;
for( uint m=0; m<g.element_edges[n].size(); m++ ) {
if( cutIndices[g.element_edges[n][m]] >= 0 ) {
idx0 = g.element_edges[n][m];
break;
}
}
// If found one intersection edge
if( idx0 >= 0 ) {
for( uint m=0; m<g.element_edges[n].size(); m++ ) {
uint opID = g.element_edges[n][m];
if( cutIndices[opID] >= 0 && isOpEdge(idx0,opID)) {
idx1 = opID;
break;
}
}
// If found opposite intersection edge
if( idx1 >= 0 ) {
vec3i v;
v[0] = cutIndices[idx0];
v[1] = cutIndices[idx1];
for( uint m=0; m<g.element_edges[n].size(); m++ ) {
uint idx2 = g.element_edges[n][m];
if( cutIndices[idx2] >= 0 && idx2 != idx0 && idx2 != idx1 ) {
v[2] = cutIndices[idx2];
faces.push_back(v);
for( uint m=0; m<g.elements[n].size(); m++ ) {
node_faces[g.elements[n][m]].push_back(faces.size()-1);
}
}
}
} else {
dump( "Opposite edge was not found !\n");
exit(0);
}
} else {
dump( "Ground edge was not found !\n");
exit(0);
}
} else if( nv.size() == 3 ) {
faces.push_back(vec3i(nv[0],nv[1],nv[2]));
for( uint m=0; m<g.elements[n].size(); m++ ) {
node_faces[g.elements[n][m]].push_back(faces.size()-1);
}
} else if( nv.size() == 0 ) {
// Empty surface. Do nothing...
} else {
dump( "\nBad stitch encounrtered: Element - edge count = %d.\n", g.element_edges[n].size() );
dump( "Unknown set found N(%e,%e,%e,%e) = %d.\n",
values[g.elements[n][0]], values[g.elements[n][1]], values[g.elements[n][2]], values[g.elements[n][3]], nv.size());
for( uint k=0; k<g.element_edges[n].size(); k++ ) {
uint vidx[2] = { g.edges[g.element_edges[n][k]][0], g.edges[g.element_edges[n][k]][1] };
dump( "Edge info[%d] = edge(%d,%d) = (%e,%e) = (%f,%f)\n", k, vidx[0], vidx[1], values[vidx[0]], values[vidx[1]], copysign(1.0,values[vidx[0]]), copysign(1.0,values[vidx[1]]) );
}
}
}
dump("Done. Took %s.\n",stock("meshsurf_stitch_mesh"));
// Find closest position
tick(); dump("Finding closest surface position at surface tets...");
surfacePos.clear();
surfacePos.resize(g.nodes.size());
for( uint n=0; n<g.nodes.size(); n++ ) {
FLOAT64 dist = 1e8;
vec3d p = g.nodes[n];
for( uint m=0; m<node_faces[n].size(); m++ ) {
vec3d p0 = vertices[faces[node_faces[n][m]][0]];
vec3d p1 = vertices[faces[node_faces[n][m]][1]];
vec3d p2 = vertices[faces[node_faces[n][m]][2]];
vec3d out = g.nodes[n];
vec3d src = out;
FLOAT64 d = fmax(1e-8,point_triangle_distance(src,p0,p1,p2,out));
if( d < dist ) {
p = out;
dist = d;
}
}
if( dist < 1.0 ) {
values[n] = (values[n]>=0 ? 1.0 : -1.0) * dist;
surfacePos[n].push_back(g.nodes[n]);
surfacePos[n].push_back(p);
} else {
values[n] = (values[n]>=0 ? 1.0 : -1.0) * 1e8;
}
}
dump("Done. Took %s.\n",stock("meshsurf_find_close_pos1"));
if( extrapolate_dist ) {
// Fast march
tick();
std::vector<fastmarch3<FLOAT64>::node3 *> fnodes(g.nodes.size());
for( uint n=0; n<g.nodes.size(); n++ ) fnodes[n] = new fastmarch3<FLOAT64>::node3;
for( uint n=0; n<g.nodes.size(); n++ ) {
vec3d p = g.nodes[n];
bool fixed = fabs(values[n]) < 1.0;
fnodes[n]->p = p;
fnodes[n]->fixed = fixed;
fnodes[n]->levelset = values[n];
fnodes[n]->value = 0.0;
fnodes[n]->p2p.resize(g.node2node[n].size());
for( uint m=0; m<g.node2node[n].size(); m++ ) {
fnodes[n]->p2p[m] = fnodes[g.node2node[n][m]];
}
}
fastmarch3<FLOAT64>::fastMarch(fnodes,extrapolate_dist,-extrapolate_dist,1);
// Pick up values
for( uint n=0; n<g.nodes.size(); n++ ) {
values[n] = fnodes[n]->levelset;
delete fnodes[n];
}
stock("meshsurf_fastmarch");
}
// Compute normal
tick(); dump("Computing normals...");
computeNormals(vertices,normals,faces,cutIndices);
dump("Done. Took %s.\n",stock("meshsurf_normal"));
// Flip facet rotation if necessary
flipFacet(vertices,normals,faces,0.1*fluid->dx);
#if 1
// Fit surface
if( doFit ) {
tick(); dump("Fitting %d surface vertices...", vertices.size() );
for( uint k=0; k<1; k++ ) {
smoothMesh(vertices,normals,faces,solid,dpx,1);
PARALLEL_FOR for( uint n=0; n<vertices.size(); n++ ) {
vec3d out = vertices[n];
if( solid->evalLevelset(out) > dpx && fluid->getClosestSurfacePos(out) ) {
vertices[n] = out;
}
}
}
dump("Done. Took %s.\n",stock("meshsurf_fit"));
}
#endif
// Smooth mesh
#if 1
tick(); dump("Smoothing faces...");
smoothMesh(vertices,normals,faces,solid,dpx,iteration);
dump("Done. Took %s.\n",stock("meshsurf_smooth"));
#endif
// Find closest position again
tick(); dump("Finding closest surface position at surface tets again...");
surfacePos.clear();
surfacePos.resize(g.nodes.size());
for( uint n=0; n<g.nodes.size(); n++ ) {
FLOAT64 dist = 1e8;
vec3d p = g.nodes[n];
for( uint m=0; m<node_faces[n].size(); m++ ) {
vec3d p0 = vertices[faces[node_faces[n][m]][0]];
vec3d p1 = vertices[faces[node_faces[n][m]][1]];
vec3d p2 = vertices[faces[node_faces[n][m]][2]];
vec3d out = g.nodes[n];
vec3d src = out;
FLOAT64 d = fmax(1e-8,point_triangle_distance(src,p0,p1,p2,out));
if( d < dist ) {
p = out;
dist = d;
}
}
if( dist < 1.0 ) {
values[n] = (values[n]>=0 ? 1.0 : -1.0) * dist;
}
}
dump("Done. Took %s.\n",stock("meshsurf_find_close_pos2"));
// Flip again
flipFacet(vertices,normals,faces,0.1*fluid->dx);
}
Array3i make_level_set3(const std::vector<Vec3ui> &tri,
const std::vector<Vec3f> &x,
const Vec3f &origin,
float dx, float dy, float dz,
int ni, int nj, int nk,
Array3f &phi,
const int exact_band)
{
phi.resize(ni, nj, nk);
phi.assign(ni*dx+nj*dy+nk*dz); // upper bound on distance
Array3i closest_tri(ni, nj, nk, -1);
Array3i intersection_count(ni, nj, nk, 0); // intersection_count(i,j,k) is # of tri intersections in (i-1,i]x{j}x{k}
// we begin by initializing distances near the mesh, and figuring out intersection counts
Vec3f ijkmin, ijkmax;
for(unsigned int t=0; t<tri.size(); ++t){
unsigned int p, q, r; assign(tri[t], p, q, r);
// coordinates in grid to high precision
double fip=((double)x[p][0]-origin[0])/dx, fjp=((double)x[p][1]-origin[1])/dy, fkp=((double)x[p][2]-origin[2])/dz;
double fiq=((double)x[q][0]-origin[0])/dx, fjq=((double)x[q][1]-origin[1])/dy, fkq=((double)x[q][2]-origin[2])/dz;
double fir=((double)x[r][0]-origin[0])/dx, fjr=((double)x[r][1]-origin[1])/dy, fkr=((double)x[r][2]-origin[2])/dz;
// do distances nearby
int i0=clamp(int(min(fip,fiq,fir))-exact_band, 0, ni-1), i1=clamp(int(max(fip,fiq,fir))+exact_band+1, 0, ni-1);
int j0=clamp(int(min(fjp,fjq,fjr))-exact_band, 0, nj-1), j1=clamp(int(max(fjp,fjq,fjr))+exact_band+1, 0, nj-1);
int k0=clamp(int(min(fkp,fkq,fkr))-exact_band, 0, nk-1), k1=clamp(int(max(fkp,fkq,fkr))+exact_band+1, 0, nk-1);
for(int k=k0; k<=k1; ++k) for(int j=j0; j<=j1; ++j) for(int i=i0; i<=i1; ++i){
Vec3f gx(i*dx+origin[0], j*dy+origin[1], k*dz+origin[2]);
float d=point_triangle_distance(gx, x[p], x[q], x[r]);
if(d<phi(i,j,k)){
phi(i,j,k)=d;
closest_tri(i,j,k)=t;
}
}
// and do intersection counts
j0=clamp((int)std::ceil(min(fjp,fjq,fjr)), 0, nj-1);
j1=clamp((int)std::floor(max(fjp,fjq,fjr)), 0, nj-1);
k0=clamp((int)std::ceil(min(fkp,fkq,fkr)), 0, nk-1);
k1=clamp((int)std::floor(max(fkp,fkq,fkr)), 0, nk-1);
for(int k=k0; k<=k1; ++k) for(int j=j0; j<=j1; ++j){
double a, b, c;
if(point_in_triangle_2d(j, k, fjp, fkp, fjq, fkq, fjr, fkr, a, b, c)){
double fi=a*fip+b*fiq+c*fir; // intersection i coordinate
int i_interval=int(std::ceil(fi)); // intersection is in (i_interval-1,i_interval]
if(i_interval<0) ++intersection_count(0, j, k); // we enlarge the first interval to include everything to the -x direction
else if(i_interval<ni) ++intersection_count(i_interval,j,k);
// we ignore intersections that are beyond the +x side of the grid
}
}
}
// and now we fill in the rest of the distances with fast sweeping
for(unsigned int pass=0; pass<2; ++pass){
sweep(tri, x, phi, closest_tri, origin, dx, dy, dz, +1, +1, +1);
sweep(tri, x, phi, closest_tri, origin, dx, dy, dz, -1, -1, -1);
sweep(tri, x, phi, closest_tri, origin, dx, dy, dz, +1, +1, -1);
sweep(tri, x, phi, closest_tri, origin, dx, dy, dz, -1, -1, +1);
sweep(tri, x, phi, closest_tri, origin, dx, dy, dz, +1, -1, +1);
sweep(tri, x, phi, closest_tri, origin, dx, dy, dz, -1, +1, -1);
sweep(tri, x, phi, closest_tri, origin, dx, dy, dz, +1, -1, -1);
sweep(tri, x, phi, closest_tri, origin, dx, dy, dz, -1, +1, +1);
}
// then figure out signs (inside/outside) from intersection counts
for(int k=0; k<nk; ++k) for(int j=0; j<nj; ++j){
int total_count=0;
for(int i=0; i<ni; ++i){
total_count+=intersection_count(i,j,k);
if(total_count%2==1){ // if parity of intersections so far is odd,
phi(i,j,k)=-phi(i,j,k); // we are inside the mesh
}
}
}
return closest_tri;
}
