float
max_dihedral_angle(const TetMesh& mesh)
{
// Measure maximum dihedral angle of tet mesh.
float maxAngle = 0.0f;
for (size_t t = 0; t < mesh.tSize(); ++t) {
std::vector<float> angles;
mesh.getTet(t).dihedralAngles(angles);
for (size_t i = 0; i < angles.size(); ++i) {
if (angles[i] > maxAngle) {
maxAngle = angles[i];
}
}
}
return maxAngle * 180.0f / M_PI;
}
// remove tets with corners where phi=0 but are outside the volume
static void
remove_exterior_tets(TetMesh& mesh,
const std::vector<float> &vphi,
const SDF& sdf)
{
for (size_t t=0; t<mesh.tSize(); ) {
int i, j, k, l; assign(mesh.T(t), i, j, k, l);
assert(vphi[i]<=0 && vphi[j]<=0 && vphi[k]<=0 && vphi[l]<=0);
if (vphi[i]==0 && vphi[j]==0 && vphi[k]==0 && vphi[l]==0
&& sdf((mesh.V(i)+mesh.V(j)+mesh.V(k)+mesh.V(l))/4)>0) {
mesh.T(t) = mesh.tets().back();
mesh.tets().pop_back();
} else {
++t;
}
}
}
// Fix some edge crossings by warping vertices if it's admissible
static void
warp_vertices(const float threshold,
TetMesh& mesh,
std::vector<float>& vphi)
{
assert(threshold>=0 && threshold<=0.5);
std::vector<float> warp(mesh.vSize(), FLT_MAX);
std::vector<int> warp_nbr(mesh.vSize(), -1);
std::vector<Vec3f> d(mesh.vSize(), Vec3f(0,0,0));
// it's wasteful to iterate through tets just to look at edges; oh well
for (size_t t=0; t<mesh.tSize(); ++t) {
for (int u=0; u<3; ++u) {
int i = mesh.T(t)[u];
for (int v=u+1; v<4; ++v) {
int j = mesh.T(t)[v];
if ((vphi[i]<0 && vphi[j]>0) || (vphi[i]>0 && vphi[j]<0)) {
float alpha = vphi[i]/(vphi[i]-vphi[j]);
if (alpha < threshold) { // warp i?
float d2 = alpha*dist2(mesh.V(i), mesh.V(j));
if (d2 < warp[i]) {
warp[i] = d2;
warp_nbr[i] = j;
d[i] = alpha*(mesh.V(j)-mesh.V(i));
}
} else if (alpha > 1-threshold) { // warp j?
float d2 = (1-alpha)*dist2(mesh.V(i), mesh.V(j));
if (d2 < warp[j]) {
warp[j] = d2;
warp_nbr[j] = i;
d[j] = (1-alpha)*(mesh.V(i)-mesh.V(j));
}
}
}
}
}
}
// do the warps (also wasteful to loop over all vertices; oh well)
for (size_t i=0; i<mesh.vSize(); ++i) if(warp_nbr[i]>=0) {
mesh.V(i) += d[i];
vphi[i] = 0;
}
}
void
make_tet_mesh(TetMesh& mesh,
const SDF& sdf,
FeatureSet& featureSet,
bool optimize,
bool intermediate,
bool unsafe)
{
// Initialize exact arithmetic
initialize_exact();
// Initialize mesh from acute lattice.
std::vector<float> vphi; // SDF value at each lattice vertex.
mesh.verts().resize(0);
mesh.tets().resize(0);
std::cout<<" cutting from lattice"<<std::endl;
cut_lattice(sdf, mesh, vphi);
if (intermediate) {
static const char* cutLatticeFile = "1_cut_lattice.tet";
static const char* cutLatticeInfo = "1_cut_lattice.info";
mesh.writeToFile(cutLatticeFile);
mesh.writeInfoToFile(cutLatticeInfo);
std::cout << "Mesh written to " << cutLatticeFile << std::endl;
}
// Warp any vertices close enough to phi=0 to fix sign crossings.
static const float WARP_THRESHOLD = 0.3;
std::cout<<" warping vertices"<<std::endl;
warp_vertices(WARP_THRESHOLD, mesh, vphi);
if (intermediate) {
static const char* warpVerticesFile = "2_warp_vertices.tet";
static const char* warpVerticesInfo = "2_warp_vertices.info";
mesh.writeToFile(warpVerticesFile);
mesh.writeInfoToFile(warpVerticesInfo);
std::cout << "Mesh written to " << warpVerticesFile << std::endl;
}
// Cut through tets that still poke out of the level set
std::cout<<" trimming spikes"<<std::endl;
trim_spikes(mesh, vphi);
if (intermediate) {
static const char* trimSpikesFile = "3_trim_spikes.tet";
static const char* trimSpikesInfo = "3_trim_spikes.info";
mesh.writeToFile(trimSpikesFile);
mesh.writeInfoToFile(trimSpikesInfo);
std::cout << "Mesh written to " << trimSpikesFile << std::endl;
}
// At this point, there could be some bad tets with all four vertices on
// the surface but which lie outside the level set. Get rid of them.
std::cout<<" removing exterior tets"<<std::endl;
remove_exterior_tets(mesh, vphi, sdf);
// Compact mesh and clear away unused vertices.
std::cout<<" compacting mesh"<<std::endl;
mesh.compactMesh();
if (intermediate) {
static const char* removeExtFile = "4_remove_exterior.tet";
static const char* removeExtInfo = "4_remove_exterior.info";
static const char* removeExtObj = "4_remove_exterior.obj";
mesh.writeToFile(removeExtFile);
mesh.writeInfoToFile(removeExtInfo);
std::vector<Vec3f> objVerts;
std::vector<Vec3i> objTris;
mesh.getBoundary(objVerts, objTris);
write_objfile(objVerts, objTris, removeExtObj);
std::cout << "Mesh written to " << removeExtFile << std::endl;
}
// Compute maximum dihedral angle of mesh (unoptimized, no features).
std::cout << " Maximum dihedral angle = " << max_dihedral_angle(mesh)
<< std::endl;
if (featureSet.numFeatures() > 0 || optimize)
{
// Identify boundary vertices
std::vector<int> boundary_verts;
std::vector<Vec3i> boundary_tris;
std::cout << " identifying boundary" << std::endl;
mesh.getBoundary(boundary_verts, boundary_tris);
assert(!boundary_verts.empty());
// Snap vertices to given features
std::vector<int> feature_endpoints;
std::map<int, int> vertex_feature_map;
if (featureSet.numFeatures() > 0)
{
// Move vertices to match desired features
std::cout << " matching features" << std::endl;
clock_t featureTime = clock();
match_features(mesh, featureSet, sdf.dx,
boundary_verts, boundary_tris,
feature_endpoints, vertex_feature_map,
unsafe);
featureTime = clock() - featureTime;
std::cout << " features matched in "
<< ((float)featureTime)/CLOCKS_PER_SEC
<< " seconds." << std::endl;
std::cout << " Maximum dihedral angle = "
<< max_dihedral_angle(mesh) << std::endl;
if (optimize && intermediate)
{
static const char* matchFeaturesFile = "5_match_features.tet";
static const char* matchFeaturesInfo = "5_match_features.info";
mesh.writeToFile(matchFeaturesFile);
mesh.writeInfoToFile(matchFeaturesInfo);
std::cout << "Mesh written to " << matchFeaturesFile
<< std::endl;
}
}
// Finish by optimizing the tetmesh, if desired.
if (optimize)
{
std::cout << " optimizing mesh" << std::endl;
clock_t optTime = clock();
optimize_tet_mesh(mesh, sdf,
boundary_verts,
featureSet,
feature_endpoints,
vertex_feature_map);
optTime = clock() - optTime;
std::cout << " Mesh optimization completed in "
<< ((float)optTime)/CLOCKS_PER_SEC
<< " seconds." << std::endl;
std::cout<< " Maximum dihedral angle = "
<< max_dihedral_angle(mesh) << std::endl;
}
// DEBUGGING
// Check for inverted tets
for (size_t t = 0; t < mesh.tSize(); ++t)
{
Tet tet = mesh.getTet(t);
float signedVolume = tet.volume();
if (signedVolume <= 0.0)
{
std::cerr << "Tet #" << t << " is inverted! " <<
"Volume = " << signedVolume << "; " <<
"Aspect = " << tet.aspectRatio() << std::endl <<
"{" << tet[0] << "} {" << tet[1] << "} {" << tet[2] <<
"} {" << tet[3] << "}" << std::endl;
}
}
}
}
// Find all tets with vertices where a corner has vphi>0 and trim them back.
static void
trim_spikes(TetMesh& mesh,
std::vector<float> &vphi)
{
// keep track of edges we cut - store the index of the new vertex
std::map<Vec2i,int> cut_map;
// we have a separate list for the results of trimming tets
std::vector<Vec4i> new_tets;
// go through the existing tets to see what we have to trim
for (int t=0; t<(int)mesh.tSize(); ++t) {
int p, q, r, s; assign(mesh.T(t), p, q, r, s);
if (vphi[p]<=0 && vphi[q]<=0 && vphi[r]<=0 && vphi[s]<=0)
continue; // this tet doesn't stick out
// We have a plethora of cases to deal with. Let's sort the vertices
// by their phi values and break ties with index, remembering if we
// have switched orientation or not, to cut down on the number of
// cases to handle. Use a sorting network to do the job.
bool flipped=false;
if (vphi[p]<vphi[q] || (vphi[p]==vphi[q] && p<q)) {
std::swap(p, q);
flipped = !flipped;
}
if (vphi[r]<vphi[s] || (vphi[r]==vphi[s] && r<s)) {
std::swap(r, s);
flipped = !flipped;
}
if (vphi[p]<vphi[r] || (vphi[p]==vphi[r] && p<r)) {
std::swap(p, r);
flipped = !flipped;
}
if (vphi[q]<vphi[s] || (vphi[q]==vphi[s] && q<s)) {
std::swap(q, s);
flipped = !flipped;
}
if (vphi[q]<vphi[r] || (vphi[q]==vphi[r] && q<r)) {
std::swap(q, r);
flipped = !flipped;
}
// sanity checks
assert(vphi[p]>=vphi[q] && vphi[q]>=vphi[r] && vphi[r]>=vphi[s]); //sort
assert(vphi[p]>0); // we already skipped interior tets
assert(vphi[s]<=0); // we never generate tets with all positive phi
// now do the actual trimming
if (vphi[s]==0) { // +++0 entirely outside
mesh.T(t)=mesh.tets().back(); // overwrite with last tet
mesh.tets().pop_back(); // get rid of the last one
--t; // decrement to cancel the next for-loop increment
} else if (vphi[r]>0) { // +++- just one vertex inside, three out
// replace this tet with one clipped back to the isosurface
int ps = cut_edge(p, s, mesh, vphi, cut_map),
qs = cut_edge(q, s, mesh, vphi, cut_map),
rs = cut_edge(r, s, mesh, vphi, cut_map);
if (flipped)
mesh.T(t) = Vec4i(qs, ps, rs, s);
else
mesh.T(t) = Vec4i(ps, qs, rs, s);
} else if(vphi[q]<0) { // +--- just one vertex outside, three in
// Have to tetrahedralize the resulting triangular prism.
// Note that the quad faces have to be split in a way that will
// be consistent with face-adjacent tets: our sort of pqrs with
// consistently broken ties makes this work. We cut the quad to the
// deepest vertex (phi as negative as possible).
int pq = cut_edge(p, q, mesh, vphi, cut_map),
pr = cut_edge(p, r, mesh, vphi, cut_map),
ps = cut_edge(p, s, mesh, vphi, cut_map);
if (flipped) {
mesh.T(t) = Vec4i(q, pq, r, s);
new_tets.push_back(Vec4i(r, pq, pr, s));
new_tets.push_back(Vec4i(s, pq, pr, ps));
} else {
mesh.T(t)=Vec4i(pq, q, r, s);
new_tets.push_back(Vec4i(pq, r, pr, s));
new_tets.push_back(Vec4i(pq, s, pr, ps));
}
} else if (vphi[q]>0 && vphi[r]<0) { // ++-- two vertices out, two in
int pr = cut_edge(p, r, mesh, vphi, cut_map),
ps = cut_edge(p, s, mesh, vphi, cut_map),
qr = cut_edge(q, r, mesh, vphi, cut_map),
qs = cut_edge(q, s, mesh, vphi, cut_map);
if (flipped) {
mesh.T(t) = Vec4i(qr, pr, r, s);
new_tets.push_back(Vec4i(qs, pr, qr, s));
new_tets.push_back(Vec4i(ps, pr, qs, s));
} else {
mesh.T(t) = Vec4i(pr, qr, r, s);
new_tets.push_back(Vec4i(pr, qs, qr, s));
new_tets.push_back(Vec4i(pr, ps, qs, s));
}
} else if (vphi[q]==0 && vphi[r]==0) { // +00- 1 out, 1 in, 2 surface
int ps = cut_edge(p, s, mesh, vphi, cut_map);
if (flipped)
mesh.T(t) = Vec4i(q, ps, r, s);
else
mesh.T(t) = Vec4i(ps, q, r, s);
} else if (vphi[q]==0) { // +0-- 1 out, 2 in, 1 surface
int pr = cut_edge(p, r, mesh, vphi, cut_map),
ps = cut_edge(p, s, mesh, vphi, cut_map);
if (flipped) {
mesh.T(t) = Vec4i(q, pr, r, s);
new_tets.push_back(Vec4i(q, ps, pr, s));
} else {
mesh.T(t) = Vec4i(pr, q, r, s);
new_tets.push_back(Vec4i(ps, q, pr, s));
}
} else { // ++0- two out, one in, one surface
int ps = cut_edge(p, s, mesh, vphi, cut_map),
qs = cut_edge(q, s, mesh, vphi, cut_map);
if (flipped)
mesh.T(t) = Vec4i(qs, ps, r, s);
else
mesh.T(t) = Vec4i(ps, qs, r, s);
}
}
// append all the remaining new tets
for (size_t t=0; t<new_tets.size(); ++t)
mesh.tets().push_back(new_tets[t]);
}