// 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;
}
}
// 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]);
}