void relabelFaces(Eigen::MatrixXi& aggregated,
const Eigen::MatrixXd& vertices,
const Eigen::MatrixXi& faces,
Eigen::Vector3i& vertexOffset,
int& offset) {
for (int i = 0; i < faces.rows(); i++) {
aggregated.row(offset++) = vertexOffset + Eigen::Vector3i(faces.row(i));
}
int numVerts = vertices.rows();
vertexOffset += Eigen::Vector3i(numVerts, numVerts, numVerts);
}
bool Polygon::convertToInequalityConstraints(Eigen::MatrixXd& A, Eigen::VectorXd& b) const
{
Eigen::MatrixXd V(nVertices(), 2);
for (unsigned int i = 0; i < nVertices(); ++i)
V.row(i) = vertices_[i];
// Create k, a list of indices from V forming the convex hull.
// TODO: Assuming counter-clockwise ordered convex polygon.
// MATLAB: k = convhulln(V);
Eigen::MatrixXi k;
k.resizeLike(V);
for (unsigned int i = 0; i < V.rows(); ++i)
k.row(i) << i, (i+1) % V.rows();
Eigen::RowVectorXd c = V.colwise().mean();
V.rowwise() -= c;
A = Eigen::MatrixXd::Constant(k.rows(), V.cols(), NAN);
unsigned int rc = 0;
for (unsigned int ix = 0; ix < k.rows(); ++ix) {
Eigen::MatrixXd F(2, V.cols());
F.row(0) << V.row(k(ix, 0));
F.row(1) << V.row(k(ix, 1));
Eigen::FullPivLU<Eigen::MatrixXd> luDecomp(F);
if (luDecomp.rank() == F.rows()) {
A.row(rc) = F.colPivHouseholderQr().solve(Eigen::VectorXd::Ones(F.rows()));
++rc;
}
}
A = A.topRows(rc);
b = Eigen::VectorXd::Ones(A.rows());
b = b + A * c.transpose();
return true;
}
void shortest_edge_and_midpoint1(const int e, const Eigen::MatrixXd &V,
const Eigen::MatrixXi &F,
const Eigen::MatrixXi &E,
const Eigen::VectorXi &EMAP,
const Eigen::MatrixXi &EF,
const Eigen::MatrixXi &EI, double &cost,
RowVectorXd &p) {
// vectorsum
const int eflip = E(e, 0) > E(e, 1);
const std::vector<int> nV2Fd =
igl::circulation(e, !eflip, F, E, EMAP, EF, EI);
p = 0.5 * (V.row(E(e, 0)) + V.row(E(e, 1)));
Eigen::RowVectorXd pointy(3);
pointy.setZero();
std::set<int> newEdges;
for (int i = 0; i < nV2Fd.size(); i++) {
for (int j = 0; j < 3; j++) {
int curVert = F.row(nV2Fd[i])[j];
if (curVert != E(e, 0) || curVert != E(e, 1)) {
if (newEdges.insert(curVert).second) {
pointy = (V.row(curVert) - p) + pointy;
}
}
}
}
cost = (pointy).norm();
}
int main(int argc, char *argv[])
{
using namespace Eigen;
using namespace std;
cout<<"Usage:"<<endl;
cout<<"[space] toggle showing input mesh, output mesh or slice "<<endl;
cout<<" through tet-mesh of convex hull."<<endl;
cout<<"'.'/',' push back/pull forward slicing plane."<<endl;
cout<<endl;
// Load mesh: (V,T) tet-mesh of convex hull, F contains facets of input
// surface mesh _after_ self-intersection resolution
igl::readMESH(TUTORIAL_SHARED_PATH "/big-sigcat.mesh",V,T,F);
// Compute barycenters of all tets
igl::barycenter(V,T,BC);
// Compute generalized winding number at all barycenters
cout<<"Computing winding number over all "<<T.rows()<<" tets..."<<endl;
igl::winding_number(V,F,BC,W);
// Extract interior tets
MatrixXi CT((W.array()>0.5).count(),4);
{
size_t k = 0;
for(size_t t = 0;t<T.rows();t++)
{
if(W(t)>0.5)
{
CT.row(k) = T.row(t);
k++;
}
}
}
// find bounary facets of interior tets
igl::boundary_facets(CT,G);
// boundary_facets seems to be reversed...
G = G.rowwise().reverse().eval();
// normalize
W = (W.array() - W.minCoeff())/(W.maxCoeff()-W.minCoeff());
// Plot the generated mesh
igl::opengl::glfw::Viewer viewer;
update_visualization(viewer);
viewer.callback_key_down = &key_down;
viewer.launch();
}
void igl::polyvector_field_one_ring_matchings(const Eigen::PlainObjectBase<DerivedV> &V,
const Eigen::PlainObjectBase<DerivedF> &F,
const std::vector<std::vector<VFType> >& VF,
const Eigen::MatrixXi& E2F,
const Eigen::MatrixXi& F2E,
const Eigen::PlainObjectBase<DerivedTT>& TT,
const Eigen::PlainObjectBase<DerivedM> &match_ab,
const Eigen::PlainObjectBase<DerivedM> &match_ba,
const int vi,
Eigen::MatrixXi &mvi,
Eigen::VectorXi &fi)
{
int half_degree = match_ab.cols();
mvi.resize(VF[vi].size()+1,half_degree);
fi.resize(VF[vi].size()+1,1);
//start from one face
//first, check if the vertex is on a boundary
//then there must be two faces that are on the boundary
//(other cases not supported)
int fstart = -1;
int ind = 0;
for (int i =0; i<VF[vi].size(); ++i)
{
int fi = VF[vi][i];
for (int j=0; j<3; ++j)
if (F(fi,j)==vi && TT(fi,j) == -1)
{
ind ++;
fstart = fi;
// break;
}
}
if (ind >1 )
{
std::cerr<<"igl::polyvector_field_one_ring_matchings -- vertex "<<vi<< " is on an unusual boundary"<<std::endl;
exit(1);
}
if (fstart == -1)
fstart = VF[vi][0];
int current_face = fstart;
int i =0;
fi[i] = current_face;
for (int j=0; j<half_degree; ++j)
mvi(i,j) = j;
int next_face = -1;
while (next_face != fstart && current_face!=-1)
{
// look for the vertex
int j=-1;
for (unsigned z=0; z<3; ++z)
if (F(current_face,(z+1)%3) == vi)
{
j=z;
break;
}
assert(j!=-1);
next_face = TT(current_face, j);
++i;
if (next_face == -1)
mvi.row(i).setConstant(-1);
else
{
// look at the edge between the two faces
const int ¤t_edge = F2E(current_face,j);
for (int k=0; k<half_degree; ++k)
{
// check its orientation to determine whether match_ab or match_ba should be used
if ((E2F(current_edge,0) == current_face) &&
(E2F(current_edge,1) == next_face) )
{
//look at match_ab
mvi(i,k) = match_ab(current_edge,(mvi(i-1,k))%half_degree);
}
else
{
assert((E2F(current_edge,1) == current_face) &&
(E2F(current_edge,0) == next_face));
//look at match_ba
mvi(i,k) = match_ba(current_edge,(mvi(i-1,k))%half_degree);
}
if (mvi(i-1,k)>=half_degree)
mvi(i,k) = (mvi(i,k)+half_degree)%(2*half_degree);
}
}
current_face = next_face;
fi[i] = current_face;
}
}
void igl::collapse_small_triangles(
const Eigen::MatrixXd & V,
const Eigen::MatrixXi & F,
const double eps,
Eigen::MatrixXi & FF)
{
using namespace Eigen;
using namespace std;
// Compute bounding box diagonal length
double bbd = bounding_box_diagonal(V);
MatrixXd l;
edge_lengths(V,F,l);
VectorXd dblA;
doublearea(l,dblA);
// Minimum area tolerance
const double min_dblarea = 2.0*eps*bbd*bbd;
Eigen::VectorXi FIM = colon<int>(0,V.rows()-1);
int num_edge_collapses = 0;
// Loop over triangles
for(int f = 0;f<F.rows();f++)
{
if(dblA(f) < min_dblarea)
{
double minl = 0;
int minli = -1;
// Find shortest edge
for(int e = 0;e<3;e++)
{
if(minli==-1 || l(f,e)<minl)
{
minli = e;
minl = l(f,e);
}
}
double maxl = 0;
int maxli = -1;
// Find longest edge
for(int e = 0;e<3;e++)
{
if(maxli==-1 || l(f,e)>maxl)
{
maxli = e;
maxl = l(f,e);
}
}
// Be sure that min and max aren't the same
maxli = (minli==maxli?(minli+1)%3:maxli);
// Collapse min edge maintaining max edge: i-->j
// Q: Why this direction?
int i = maxli;
int j = ((minli+1)%3 == maxli ? (minli+2)%3: (minli+1)%3);
assert(i != minli);
assert(j != minli);
assert(i != j);
FIM(F(f,i)) = FIM(F(f,j));
num_edge_collapses++;
}
}
// Reindex faces
MatrixXi rF = F;
// Loop over triangles
for(int f = 0;f<rF.rows();f++)
{
for(int i = 0;i<rF.cols();i++)
{
rF(f,i) = FIM(rF(f,i));
}
}
FF.resize(rF.rows(),rF.cols());
int num_face_collapses=0;
// Only keep uncollapsed faces
{
int ff = 0;
// Loop over triangles
for(int f = 0;f<rF.rows();f++)
{
bool collapsed = false;
// Check if any indices are the same
for(int i = 0;i<rF.cols();i++)
{
for(int j = i+1;j<rF.cols();j++)
{
if(rF(f,i)==rF(f,j))
{
collapsed = true;
num_face_collapses++;
break;
}
}
}
if(!collapsed)
{
FF.row(ff++) = rF.row(f);
}
}
// Use conservative resize
FF.conservativeResize(ff,FF.cols());
}
//cout<<"num_edge_collapses: "<<num_edge_collapses<<endl;
//cout<<"num_face_collapses: "<<num_face_collapses<<endl;
if(num_edge_collapses == 0)
{
// There must have been a "collapsed edge" in the input
assert(num_face_collapses==0);
// Base case
return;
}
//// force base case
//return;
MatrixXi recFF = FF;
return collapse_small_triangles(V,recFF,eps,FF);
}
// A tet is organized in the following fashion:
//
// 0
//
// 3 (3 is in the background; 1 and 2 are in the foreground)
// 2 1
//
// So the faces (with counterclockwise normals) are:
// (0 1 3)
// (0 2 1)
// (3 2 0)
// (1 2 3)
//
//
// This method will perform three steps:
// 1. Add all faces, duplicating ones on the interior
// 2. Remove all duplicate verts (might have been caused during #1)
// 3. Remove all duplicate faces
void marching_tets(
const Eigen::MatrixXd& V,
const Eigen::MatrixXi& T,
const Eigen::VectorXd& H,
double offset,
Eigen::MatrixXd& NV,
Eigen::MatrixXi& NF,
Eigen::VectorXi& I)
{
min_how_much = 1;
max_how_much = 0;
using namespace Eigen;
using namespace std;
// Count the faces.
std::map<std::vector<int>, int> face_counts;
for (int i = 0; i < T.rows(); ++i) {
std::vector<std::vector<int> > fs;
fs.push_back({T(i, 0), T(i, 1), T(i, 3)});
fs.push_back({T(i, 0), T(i, 2), T(i, 1)});
fs.push_back({T(i, 3), T(i, 2), T(i, 0)});
fs.push_back({T(i, 1), T(i, 2), T(i, 3)});
for (auto &f : fs) {
std::sort(f.begin(), f.end());
// Add it to the map.
face_counts[f]++;
}
}
vector<Eigen::RowVector3i> faces;
vector<int> faces_markers;
vector<Eigen::RowVector3d> new_verts;
int times[6];
for (int i = 0; i < 6; i++) {
times[i] = 0;
}
// Create data structure.
MarchingTetsDat dd(V, H, faces, faces_markers, face_counts, new_verts, offset);
int numEq = 0;
// Check each tet face, add as needed.
for (int i = 0; i < T.rows(); ++i) {
// See if the tet is entirely inside.
vector<int> inside, outside, inside_t, outside_t, identical;
for (int j = 0; j < T.cols(); ++j) {
//if (H(T(i, j)) > offset + 1e-4) {
if (H(T(i, j)) > offset) {
outside.push_back(j);
} else if (H(T(i, j)) < offset) {
inside.push_back(j);
} else {
numEq++;
identical.push_back(j);
}
if (H(T(i, j)) == GLOBAL::outside_temp) {
outside_t.push_back(j);
} else if (H(T(i, j)) == GLOBAL::inside_temp) {
inside_t.push_back(j);
}
}
// Ignore this tet if it's entirely outside.
if (outside.size() == 4) {
continue;
}
if (outside.size() == 0 && inside.size() == 0) {
// degenerate, ignore.
printf("WARNING: degenerate tet face found!!\n");
} else if (inside.size() == 0 && identical.size() < 3) {
// Nothing to add.
} else if (identical.size() == 3) {
//addOrig(T.row(i), 7, dd.faces, dd.faces_markers);
// Ignore it if there's only one on the outside.
//if (inside.size() == 0) continue;
if (outside.size() == 0) continue;
times[1]++;
// Add just a single face (always)
int i1 = T(i,identical[0]), i2 = T(i,identical[1]), i3 = T(i,identical[2]);
Eigen::RowVector3i f({i1, i2, i3});
dd.faces.push_back(f);
dd.faces_markers.push_back(1);
} else if (outside.size() == 0) {
// (these are colored blue)
times[0]++;
// (A) Takes care of:
// inside: 1, identical: 3 (remove three duplicated faces later)
// inside: 2, identical: 2 (remove all four duplicated faces later)
// inside: 3, identical: 1 (remove all four duplicated faces later)
// inside: 4, identical: 0 (remove all four duplicated faces later)
case0Out(dd, T.row(i), inside, outside, identical, inside_t, outside_t);
} else if (inside.size() == 1) {
// (these are colored green)
times[2]++;
// (B) Takes care of:
// inside: 1 outside: 3
// inside: 1 outside: 2 identical: 1
// inside: 1 outside: 1 identical: 2
//
case1In(dd, T.row(i), inside, outside, identical, inside_t, outside_t);
} else if (inside.size() == 3 && outside.size() == 1) {
// (these are colored orange)
times[3]++;
// (C) takes care of:
// inside: 3 outside: 1
//
case3In1Out(dd, T.row(i), inside, outside, identical, inside_t, outside_t);
} else if (inside.size() == 2 && outside.size() >= 1) {
// (these are colored red)
times[4]++;
// (D) takes care of:
// inside: 2 outside: 1 identical: 1
// inside: 2 outside: 2 identical: 0
//
case2In2Out(dd, T.row(i), inside, outside, identical, inside_t, outside_t);
} else {
times[5]++;
fprintf(stderr, "WARN: marching tets found something weird, with in:%lu out:%lu\n",
inside.size(), outside.size());
}
}
printf("Finished marching tets with usages:\n");
for (int i = 0; i < 6; ++i) {
printf(" %d: %d\n", i, times[i]);
}
printf("how_much is %lf and EPS is %lf\n", min_how_much, GLOBAL::EPS);
printf(" max is %lf\n", max_how_much);
printf("Num equal is %d\n", numEq);
// Copy verts
NV.resize(V.rows() + new_verts.size(), 3);
for (int i = 0; i < V.rows(); ++i) {
NV.row(i) = V.row(i);
}
for (int i = 0; i < new_verts.size(); ++i) {
NV.row(i + V.rows()) = new_verts[i];
}
// Set I
I.resize(NV.rows());
for (int i = 0; i < I.rows(); ++i) {
if (i < V.rows()) {
I(i) = i;
} else {
I(i) = -1;
}
}
Eigen::VectorXi facesMarkers;
facesMarkers.resize(faces.size());
// Copy faces
NF.resize(faces.size(), 3);
for (int i = 0; i < faces.size(); ++i) {
NF.row(i) = faces[i];
facesMarkers(i) = faces_markers[i];
}
Eigen::MatrixXd newV;
Eigen::MatrixXi newF;
Eigen::VectorXi SVJ, SVI, I2;
// Helpers::viewTriMesh(NV, NF, facesMarkers);
//igl::writeOFF("offset_mesh.off", NV, NF)
Helpers::writeMeshWithMarkers("offset_mesh", NV, NF, facesMarkers);
/*
igl::collapse_small_triangles(NV, NF, 1e-8, newF);
printf("Collapsed %d small triangles\n", NF.rows() - newF.rows());
NF = newF;
*/
///*
igl::remove_duplicate_vertices(NV, NF, 1e-20, newV, SVI, SVJ, newF);
I2.resize(newV.rows());
I2.setConstant(-1);
for (int i = 0; i < NV.rows(); ++i) {
if (I2(SVJ(i)) == -1) {
I2(SVJ(i)) = I(i);
} else {
I2(SVJ(i)) = std::min(I2(SVJ(i)), I(i));
}
}
NF = newF;
NV = newV;
I = I2;
// Now see if we have duplicated faces.
//igl::resolve_duplicated_faces(NF, newF, SVJ);
//NF = newF;
//*/
// Other option is to do these two:
// These are bad because sometimes the "small" triangles are not area zero,
// and doing the removeDuplicates will delete these triangles and make the
// mesh non-manifold. Better to wait for remeshing later.
//Helpers::removeDuplicates(NV, NF, I);
//Helpers::collapseSmallTriangles(NV, NF);
igl::remove_unreferenced(NV, NF, newV, newF, SVI, SVJ);
I2.resize(newV.rows());
I2.setConstant(-1);
for (int i = 0; i < I2.rows(); ++i) {
I2(i) = I(SVJ(i));
}
I = I2;
NV = newV;
NF = newF;
// orient everything correctly.
Eigen::VectorXi C;
igl::orientable_patches(NF, C);
igl::bfs_orient(NF, newF, C);
NF = newF;
igl::orient_outward(NV, NF, C, newF, SVJ);
NF = newF;
//igl::writeOFF("offset_mesh_normals.off", NV, NF);
#ifdef DEBUG_MESH
if (!Helpers::isMeshOkay(NV, NF)) {
printf("Error: Mesh is not okay at first...\n");
}
if (!Helpers::isManifold(NV, NF, I)) {
printf("Error: Mesh from marching tets not manifold!\n");
Eigen::VectorXi temp;
temp.resize(I.rows());
temp.setZero();
Helpers::isManifold(NV, NF, temp, true);
Helpers::viewTriMesh(NV, NF, temp);
Helpers::writeMeshWithMarkers("marching_tets_manifold", NV, NF, temp);
cout << "See marching_tets_manifold.off for problems.\n";
exit(1);
}
#endif
}
IGL_INLINE bool igl::decimate(
const Eigen::MatrixXd & OV,
const Eigen::MatrixXi & OF,
const std::function<void(
const int,
const Eigen::MatrixXd &,
const Eigen::MatrixXi &,
const Eigen::MatrixXi &,
const Eigen::VectorXi &,
const Eigen::MatrixXi &,
const Eigen::MatrixXi &,
double &,
Eigen::RowVectorXd &)> & cost_and_placement,
const std::function<bool(
const Eigen::MatrixXd &,
const Eigen::MatrixXi &,
const Eigen::MatrixXi &,
const Eigen::VectorXi &,
const Eigen::MatrixXi &,
const Eigen::MatrixXi &,
const std::set<std::pair<double,int> > &,
const std::vector<std::set<std::pair<double,int> >::iterator > &,
const Eigen::MatrixXd &,
const int,
const int,
const int,
const int,
const int)> & stopping_condition,
const std::function<bool(
const Eigen::MatrixXd & ,/*V*/
const Eigen::MatrixXi & ,/*F*/
const Eigen::MatrixXi & ,/*E*/
const Eigen::VectorXi & ,/*EMAP*/
const Eigen::MatrixXi & ,/*EF*/
const Eigen::MatrixXi & ,/*EI*/
const std::set<std::pair<double,int> > & ,/*Q*/
const std::vector<std::set<std::pair<double,int> >::iterator > &,/*Qit*/
const Eigen::MatrixXd & ,/*C*/
const int /*e*/
)> & pre_collapse,
const std::function<void(
const Eigen::MatrixXd & , /*V*/
const Eigen::MatrixXi & , /*F*/
const Eigen::MatrixXi & , /*E*/
const Eigen::VectorXi & ,/*EMAP*/
const Eigen::MatrixXi & , /*EF*/
const Eigen::MatrixXi & , /*EI*/
const std::set<std::pair<double,int> > & , /*Q*/
const std::vector<std::set<std::pair<double,int> >::iterator > &, /*Qit*/
const Eigen::MatrixXd & , /*C*/
const int , /*e*/
const int , /*e1*/
const int , /*e2*/
const int , /*f1*/
const int , /*f2*/
const bool /*collapsed*/
)> & post_collapse,
const Eigen::MatrixXi & OE,
const Eigen::VectorXi & OEMAP,
const Eigen::MatrixXi & OEF,
const Eigen::MatrixXi & OEI,
Eigen::MatrixXd & U,
Eigen::MatrixXi & G,
Eigen::VectorXi & J,
Eigen::VectorXi & I
)
{
// Decimate 1
using namespace Eigen;
using namespace std;
// Working copies
Eigen::MatrixXd V = OV;
Eigen::MatrixXi F = OF;
Eigen::MatrixXi E = OE;
Eigen::VectorXi EMAP = OEMAP;
Eigen::MatrixXi EF = OEF;
Eigen::MatrixXi EI = OEI;
typedef std::set<std::pair<double,int> > PriorityQueue;
PriorityQueue Q;
std::vector<PriorityQueue::iterator > Qit;
Qit.resize(E.rows());
// If an edge were collapsed, we'd collapse it to these points:
MatrixXd C(E.rows(),V.cols());
for(int e = 0;e<E.rows();e++)
{
double cost = e;
RowVectorXd p(1,3);
cost_and_placement(e,V,F,E,EMAP,EF,EI,cost,p);
C.row(e) = p;
Qit[e] = Q.insert(std::pair<double,int>(cost,e)).first;
}
int prev_e = -1;
bool clean_finish = false;
while(true)
{
if(Q.empty())
{
break;
}
if(Q.begin()->first == std::numeric_limits<double>::infinity())
{
// min cost edge is infinite cost
break;
}
int e,e1,e2,f1,f2;
if(collapse_edge(
cost_and_placement, pre_collapse, post_collapse,
V,F,E,EMAP,EF,EI,Q,Qit,C,e,e1,e2,f1,f2))
{
if(stopping_condition(V,F,E,EMAP,EF,EI,Q,Qit,C,e,e1,e2,f1,f2))
{
clean_finish = true;
break;
}
}else
{
if(prev_e == e)
{
assert(false && "Edge collapse no progress... bad stopping condition?");
break;
}
// Edge was not collapsed... must have been invalid. collapse_edge should
// have updated its cost to inf... continue
}
prev_e = e;
}
// remove all IGL_COLLAPSE_EDGE_NULL faces
MatrixXi F2(F.rows(),3);
J.resize(F.rows());
int m = 0;
for(int f = 0;f<F.rows();f++)
{
if(
F(f,0) != IGL_COLLAPSE_EDGE_NULL ||
F(f,1) != IGL_COLLAPSE_EDGE_NULL ||
F(f,2) != IGL_COLLAPSE_EDGE_NULL)
{
F2.row(m) = F.row(f);
J(m) = f;
m++;
}
}
F2.conservativeResize(m,F2.cols());
J.conservativeResize(m);
VectorXi _1;
remove_unreferenced(V,F2,U,G,_1,I);
return clean_finish;
}