IGL_INLINE void igl::exterior_edges(
const Eigen::MatrixXi & F,
Eigen::MatrixXi & E)
{
using namespace Eigen;
using namespace std;
assert(F.cols() == 3);
const size_t m = F.rows();
MatrixXi all_E,sall_E,sort_order;
// Sort each edge by index
all_edges(F,all_E);
sort(all_E,2,true,sall_E,sort_order);
// Find unique edges
MatrixXi uE;
VectorXi IA,EMAP;
unique_rows(sall_E,uE,IA,EMAP);
VectorXi counts = VectorXi::Zero(uE.rows());
for(size_t a = 0;a<3*m;a++)
{
counts(EMAP(a)) += (sort_order(a)==0?1:-1);
}
E.resize(all_E.rows(),2);
{
int e = 0;
const size_t nue = uE.rows();
// Append each unique edge with a non-zero amount of signed occurances
for(size_t ue = 0; ue<nue; ue++)
{
const int count = counts(ue);
size_t i,j;
if(count == 0)
{
continue;
}else if(count < 0)
{
i = uE(ue,1);
j = uE(ue,0);
}else if(count > 0)
{
i = uE(ue,0);
j = uE(ue,1);
}
// Append edge for every repeated entry
const int abs_count = abs(count);
for(size_t k = 0;k<abs_count;k++)
{
E(e,0) = i;
E(e,1) = j;
e++;
}
}
E.conservativeResize(e,2);
}
}
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);
}