// Remove small triangles with different semantics
void remove_singularSemantics(Polyhedron& exteriorPolyhe) {
double SMALL_TRIANGLE_LIMIT = 0.1;
Polyhedron::Facet_iterator exfIt; // Iterate over exterior faces
while (true) {
bool newSemFound = false;
for (exfIt = exteriorPolyhe.facets_begin(); exfIt != exteriorPolyhe.facets_end(); ++exfIt) {
if (exfIt->area < SMALL_TRIANGLE_LIMIT) {
std::map<std::string,double> semCountList;
std::map<std::string,double>::iterator semCount;
Polyhedron::Facet::Halfedge_around_facet_circulator itHDS = exfIt->facet_begin();
double maxArea = 0;
std::string newSem;
do {
if (is_coplanar(itHDS,false)) {
std::string otherSem = itHDS->opposite()->facet()->semanticBLA;
// Compute sum of area
if (is_coplanar(itHDS->opposite()->next(),true) ||
is_coplanar(itHDS->opposite()->prev(),true)) {
semCount = semCountList.find(otherSem);
if (semCount == semCountList.end())
semCountList[otherSem] = 1; // Might not be needed
else
++(semCountList[otherSem]);
}
}
} while (++itHDS != exfIt->facet_begin());
for (semCount = semCountList.begin();semCount!=semCountList.end();++semCount) {
if (semCount->second > maxArea) {
maxArea = semCount->second;
newSem = semCount->first;
} else if (semCount->second == maxArea &&
((exfIt->semanticBLA=="Anything"&&semCount->first!="Anything")||semCount->first==exfIt->semanticBLA))
newSem = semCount->first;
}
if (maxArea > 0 && newSem!=exfIt->semanticBLA) {
exfIt->semanticBLA = newSem;
newSemFound = true;
break; // Dafuq? is this correct?
}
}
}
if (!newSemFound) break; // Really?
}
}
double lloyd_step (std::vector<Point> &points)
{
std::vector<Plane> planes;
for (size_t i = 0; i < points.size(); ++i)
planes.push_back(tangent_plane(points[i]));
Polyhedron P;
CGAL::internal::halfspaces_intersection(planes.begin(),
planes.end(), P, K());
size_t N = points.size();
points.clear();
double totarea = 0.0;
double vararea = 0.0;
for (Polyhedron::Facet_iterator it = P.facets_begin();
it != P.facets_end(); ++it)
{
Polyhedron::Halfedge_around_facet_circulator
h0 = it->facet_begin(), hf = h0--, hs = hf;
hs ++;
double farea = 0.0;
Vector fcentroid (CGAL::NULL_VECTOR);
while(1)
{
const Point &a = h0->vertex()->point(),
&b = hf->vertex()->point(),
&c = hs->vertex()->point();
Vector v =
CGAL::cross_product(b -a, c - a);
double tarea = .5 * sqrt(v.squared_length());
farea += tarea;
fcentroid = fcentroid + (tarea/3.0) * ((a - CGAL::ORIGIN) +
(b - CGAL::ORIGIN) +
(c - CGAL::ORIGIN));
if (hs == h0)
break;
++hs; ++hf;
}
totarea += farea;
vararea += pow(4.0 * M_PI / N - farea, 2.0);
fcentroid = fcentroid/farea;
points.push_back(project_back(CGAL::ORIGIN + fcentroid));
}
std::cerr << "area = " << totarea << ", "
<< "vararea = " << vararea << "\n";
return vararea/totarea;
}
void Polyhedra::Initialize(){
if (init) return;
bool isRandom = false;
//get vertices
int N = (int) v.size();
if (N==0) {
//generate randomly
while ((int) v.size()<4) GenerateRandomGeometry();
N = (int) v.size();
isRandom = true;
}
//compute convex hull of vertices
std::vector<CGALpoint> points;
points.resize(v.size());
for(int i=0;i<N;i++) {
points[i] = CGALpoint(v[i][0],v[i][1],v[i][2]);
}
CGAL::convex_hull_3(points.begin(), points.end(), P);
//connect triagular facets if possible
std::transform(P.facets_begin(), P.facets_end(), P.planes_begin(),Plane_equation());
P = Simplify(P, 1E-9);
//modify order of v according to CGAl polyhedron
int i = 0;
v.clear();
for (Polyhedron::Vertex_iterator vIter = P.vertices_begin(); vIter != P.vertices_end(); ++vIter, i++){
v.push_back(Vector3r(vIter->point().x(),vIter->point().y(),vIter->point().z()));
}
//list surface triangles for plotting
faceTri.clear();
std::transform(P.facets_begin(), P.facets_end(), P.planes_begin(),Plane_equation());
for (Polyhedron::Facet_iterator fIter = P.facets_begin(); fIter != P.facets_end(); fIter++){
Polyhedron::Halfedge_around_facet_circulator hfc0;
int n = fIter->facet_degree();
hfc0 = fIter->facet_begin();
int a = std::distance(P.vertices_begin(), hfc0->vertex());
for (int i=2; i<n; i++){
++hfc0;
faceTri.push_back(a);
faceTri.push_back(std::distance(P.vertices_begin(), hfc0->vertex()));
faceTri.push_back(std::distance(P.vertices_begin(), hfc0->next()->vertex()));
}
}
//compute centroid and volume
P_volume_centroid(P, &volume, ¢roid);
//check vierd behavior of CGAL in tessalation
if(isRandom && volume*1.75<4./3.*3.14*size[0]/2.*size[1]/2.*size[2]/2.) {
v.clear();
seed = rand();
Initialize();
}
Vector3r translation((-1)*centroid);
//set centroid to be [0,0,0]
for(int i=0;i<N;i++) {
v[i] = v[i]-centroid;
}
if(isRandom) centroid = Vector3r::Zero();
Vector3r origin(0,0,0);
//move and rotate also the CGAL structure Polyhedron
Transformation t_trans(1.,0.,0.,translation[0],0.,1.,0.,translation[1],0.,0.,1.,translation[2],1.);
std::transform( P.points_begin(), P.points_end(), P.points_begin(), t_trans);
//compute inertia
Real vtet;
Vector3r ctet;
Matrix3r Itet1, Itet2;
Matrix3r inertia_tensor(Matrix3r::Zero());
for(int i=0; i<(int) faceTri.size(); i+=3){
vtet = std::abs((origin-v[faceTri[i+2]]).dot((v[faceTri[i]]-v[faceTri[i+2]]).cross(v[faceTri[i+1]]-v[faceTri[i+2]]))/6.);
ctet = (origin+v[faceTri[i]]+v[faceTri[i+1]]+v[faceTri[i+2]]) / 4.;
Itet1 = TetraInertiaTensor(origin-ctet, v[faceTri[i]]-ctet, v[faceTri[i+1]]-ctet, v[faceTri[i+2]]-ctet);
ctet = ctet-origin;
Itet2<<
ctet[1]*ctet[1]+ctet[2]*ctet[2], -ctet[0]*ctet[1], -ctet[0]*ctet[2],
-ctet[0]*ctet[1], ctet[0]*ctet[0]+ctet[2]*ctet[2], -ctet[2]*ctet[1],
-ctet[0]*ctet[2], -ctet[2]*ctet[1], ctet[1]*ctet[1]+ctet[0]*ctet[0];
inertia_tensor = inertia_tensor + Itet1 + Itet2*vtet;
}
if(std::abs(inertia_tensor(0,1))+std::abs(inertia_tensor(0,2))+std::abs(inertia_tensor(1,2)) < 1E-13){
// no need to rotate, inertia already diagonal
orientation = Quaternionr::Identity();
inertia = Vector3r(inertia_tensor(0,0),inertia_tensor(1,1),inertia_tensor(2,2));
}else{
// calculate eigenvectors of I
Vector3r rot;
Matrix3r I_rot(Matrix3r::Zero()), I_new(Matrix3r::Zero());
matrixEigenDecomposition(inertia_tensor,I_rot,I_new);
// I_rot = eigenvectors of inertia_tensors in columns
// I_new = eigenvalues on diagonal
// set positove direction of vectors - otherwise reloading does not work
Matrix3r sign(Matrix3r::Zero());
Real max_v_signed = I_rot(0,0);
Real max_v = std::abs(I_rot(0,0));
if (max_v < std::abs(I_rot(1,0))) {max_v_signed = I_rot(1,0); max_v = std::abs(I_rot(1,0));}
if (max_v < std::abs(I_rot(2,0))) {max_v_signed = I_rot(2,0); max_v = std::abs(I_rot(2,0));}
sign(0,0) = max_v_signed/max_v;
max_v_signed = I_rot(0,1);
max_v = std::abs(I_rot(0,1));
if (max_v < std::abs(I_rot(1,1))) {max_v_signed = I_rot(1,1); max_v = std::abs(I_rot(1,1));}
if (max_v < std::abs(I_rot(2,1))) {max_v_signed = I_rot(2,1); max_v = std::abs(I_rot(2,1));}
sign(1,1) = max_v_signed/max_v;
sign(2,2) = 1.;
I_rot = I_rot*sign;
// force the eigenvectors to be right-hand oriented
Vector3r third = (I_rot.col(0)).cross(I_rot.col(1));
I_rot(0,2) = third[0];
I_rot(1,2) = third[1];
I_rot(2,2) = third[2];
inertia = Vector3r(I_new(0,0),I_new(1,1),I_new(2,2));
orientation = Quaternionr(I_rot);
//rotate the voronoi cell so that x - is maximal inertia axis and z - is minimal inertia axis
//orientation.normalize(); //not needed
for(int i=0; i< (int) v.size();i++) {
v[i] = orientation.conjugate()*v[i];
}
//rotate also the CGAL structure Polyhedron
Matrix3r rot_mat = (orientation.conjugate()).toRotationMatrix();
Transformation t_rot(rot_mat(0,0),rot_mat(0,1),rot_mat(0,2),rot_mat(1,0),rot_mat(1,1),rot_mat(1,2),rot_mat(2,0),rot_mat(2,1),rot_mat(2,2),1.);
std::transform( P.points_begin(), P.points_end(), P.points_begin(), t_rot);
}
//initialization done
init = 1;
}