//**********************************************************************************
//test of polyhedron intersection callable from python shell
bool do_Polyhedras_Intersect(const shared_ptr<Shape>& cm1,const shared_ptr<Shape>& cm2,const State& state1,const State& state2){
const Se3r& se31=state1.se3;
const Se3r& se32=state2.se3;
Polyhedra* A = static_cast<Polyhedra*>(cm1.get());
Polyhedra* B = static_cast<Polyhedra*>(cm2.get());
//move and rotate 1st the CGAL structure Polyhedron
Matrix3r rot_mat = (se31.orientation).toRotationMatrix();
Vector3r trans_vec = se31.position;
Transformation t_rot_trans(rot_mat(0,0),rot_mat(0,1),rot_mat(0,2), trans_vec[0],rot_mat(1,0),rot_mat(1,1),rot_mat(1,2),trans_vec[1],rot_mat(2,0),rot_mat(2,1),rot_mat(2,2),trans_vec[2],1.);
Polyhedron PA = A->GetPolyhedron();
std::transform( PA.points_begin(), PA.points_end(), PA.points_begin(), t_rot_trans);
//move and rotate 2st the CGAL structure Polyhedron
rot_mat = (se32.orientation).toRotationMatrix();
trans_vec = se32.position;
t_rot_trans = Transformation(rot_mat(0,0),rot_mat(0,1),rot_mat(0,2), trans_vec[0],rot_mat(1,0),rot_mat(1,1),rot_mat(1,2),trans_vec[1],rot_mat(2,0),rot_mat(2,1),rot_mat(2,2),trans_vec[2],1.);
Polyhedron PB = B->GetPolyhedron();
std::transform( PB.points_begin(), PB.points_end(), PB.points_begin(), t_rot_trans);
//calculate plane equations
std::transform( PA.facets_begin(), PA.facets_end(), PA.planes_begin(),Plane_equation());
std::transform( PB.facets_begin(), PB.facets_end(), PB.planes_begin(),Plane_equation());
//call test
return do_intersect(PA,PB);
}
void mergeCoplanar(Polyhedron& p,bool step2) {
int facetsBefore = p.size_of_facets();
p.normalize_border();
if(!p.size_of_border_halfedges()) {
// Calculate normals only once in advace! so all tris should be coplanar with the original
std::transform( p.facets_begin(), p.facets_end(),p.planes_begin(),Plane_equation()); // Calculate plane equations (only works on tri<- = bs)=true
bool coplanarFound = true;
std::vector<Polyhedron::Halfedge_handle> skipHEs;
while (coplanarFound) {
coplanarFound = false; // Set coplanarFound false
int percCount = 1;
for (Polyhedron::Halfedge_iterator hit = p.halfedges_begin(); hit != p.halfedges_end(); ++hit,++percCount){ // Loop through all halfedges
if (is_coplanar(hit,true)){ // If coplanar and equals semantics
Polyhedron::Halfedge_handle removeMe = hit;
while (CGAL::circulator_size(removeMe->vertex_begin()) < 3) // Mover handle to beginning of linestring
removeMe = removeMe->next();
bool jcnh = false;
if (!step2) jcnh = joinCreatesNoHole (hit);
else jcnh = joinCreatesNoHole2(hit);
if (jcnh){ // If no holes will be created
std::cout << "\rFacets before/after: "<<facetsBefore<<" -> "<< p.size_of_facets()<<". ("<<100*percCount/p.size_of_halfedges()<<"%)";
while (CGAL::circulator_size(removeMe->opposite()->vertex_begin()) < 3) // Join vertexes until at the other end of linestring
if (removeMe->facet_degree()>3 && removeMe->opposite()->facet_degree()>3)
removeMe = (p.join_vertex(removeMe))->next()->opposite();
else // One of the faces turned into a triangle ->remove center vertex
break;
if (CGAL::circulator_size(removeMe->opposite()->vertex_begin()) < 3) // Remove remained of the border
p.erase_center_vertex(removeMe->opposite()); // if two segments remain remove center point
else
p.join_facet(removeMe); // if one segment remains join facets
coplanarFound = true;
break;
} else { // simplify border, but how to do this safely? not optimal solution implemented. Should do: add inward offseted point of intersection etc.
if (std::find(skipHEs.begin(), skipHEs.end(),hit)!=skipHEs.end()) { // Skip if hit in skipList
while (CGAL::circulator_size(removeMe->opposite()->vertex_begin()) < 3) { // Join vertexes until at the other end of linestring
if (removeMe->facet_degree()>3 && removeMe->opposite()->facet_degree()>3)
if (triDoesNotIntersectFacet(removeMe)) // if tri reMe,reME->prev does not intersect left or right facet
removeMe = (p.join_vertex(removeMe))->next()->opposite(); // remove removeME
else {
skipHEs.push_back(removeMe);
skipHEs.push_back(removeMe->opposite());
removeMe = removeMe->prev(); // move removeME one halfedge back
}
else break; // stop if only a triangle remains or at other end
}
skipHEs.push_back(removeMe);
skipHEs.push_back(removeMe->opposite());
} } } } } }
//if (!step2) mergeCoplanar(p,true);
//else
std::cout << "\rFacets before/after: "<<facetsBefore<<" -> "<< p.size_of_facets()<<". (100%)"<<std::endl;
}
int main() {
Point_3 p( 1, 0, 0);
Point_3 q( 0, 1, 0);
Point_3 r( 0, 0, 1);
Point_3 s( 0, 0, 0);
Polyhedron P;
P.make_tetrahedron( p, q, r, s);
std::transform( P.facets_begin(), P.facets_end(), P.planes_begin(),
Plane_equation());
CGAL::set_pretty_mode( std::cout);
std::copy( P.planes_begin(), P.planes_end(),
std::ostream_iterator<Plane_3>( std::cout, "\n"));
return 0;
}
int main(int argc, char* argv[]) {
CGAL_assertion(argc==2);
std::ifstream in1(argv[1]);
Polyhedron P1;
in1 >> P1;
std::transform( P1.facets_begin(), P1.facets_end(), P1.planes_begin(),
Plane_equation());
CGAL_assertion(is_strongly_convex_3(P1));
Gausian_map G1(P1);
G1.visualize();
}
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;
}
void set_semantic_AABB_C2V(Polyhedron& exteriorPolyhe,PolVector& polyVec) {
if (exteriorPolyhe.is_pure_triangle()) {
std::transform( exteriorPolyhe.facets_begin(), exteriorPolyhe.facets_end(),exteriorPolyhe.planes_begin(),Plane_equation());
std::vector<std::string> semList;
std::vector<std::shared_ptr<AAbbTree>> treeList;
// Build Trees. One for each semantic
for(PolVector::iterator pvIt = polyVec.begin();pvIt!=polyVec.end();++pvIt) {// Get AABB trees of all semantics
if (pvIt->is_pure_triangle()) {
std::string semP = pvIt->facets_begin()->semanticBLA;
std::vector<std::string>::iterator strIt = std::find(semList.begin(), semList.end(),semP);
if (strIt==semList.end()) { // If new sematic
semList.push_back(semP); // Add sem
std::shared_ptr<AAbbTree> tree = std::make_shared<AAbbTree>(pvIt->facets_begin(),pvIt->facets_end()); // Create tree
tree->accelerate_distance_queries(); // accelerate
treeList.push_back(tree); // Add tree
} else // If not new
treeList[strIt-semList.begin()]->insert(pvIt->facets_begin(),pvIt->facets_end()); // Append to tree
} else std::cerr << "ERROR: Not pure triangle (set_semantic_AABB2C2V)" << std::endl;
}
// For each facet calculate the least distance to each tree
std::string semListStr = boost::algorithm::join((semList), " ");
int percCount = 1;
Polyhedron::Facet_iterator exfIt; // Iterate over exterior faces
for (exfIt = exteriorPolyhe.facets_begin(); exfIt != exteriorPolyhe.facets_end(); ++exfIt,++percCount) {
std::cout << "\r"<<semListStr<<". ("<<100*percCount/exteriorPolyhe.size_of_facets()<<"%)";
Vector_3 orthVec = exfIt->plane().orthogonal_vector();
normalizeVector(orthVec); //if (!normalizeVector(ortVec)) continue;
std::vector<distSemFace> dsfList(semList.size());
Point_3 centerPoint = comp_facetCentroid(exfIt); // Compute centroid
std::vector<Kernel::FT> leastSemDistances;
for (int intIt=0;intIt<(int)treeList.size();++intIt) { // Loop over all trees
AAbbTree::Point_and_primitive_id pp = treeList[intIt]->closest_point_and_primitive(centerPoint);
dsfList[intIt].dist = CGAL::squared_distance(centerPoint,pp.first); // Store distance semantic and facet for each tree
dsfList[intIt].sem = semList[intIt];
dsfList[intIt].fh = pp.second;
}
std::sort(dsfList.begin(),dsfList.end(),by_dist());
exfIt->leastSqDistance = dsfList[0].dist; // least sqrt distance
if (exfIt->isMinkFacet = dsfList[0].dist > SEMANTIC_DISTANCE_THRESHOLD) {
exfIt->semanticBLA = TO_DIST_SEMANTIC; // Default semantic if too distant
continue;
} else
exfIt->semanticBLA = dsfList[0].sem; // Semantics of closest
Vector_3 faceNormal;
Kernel::FT faceSqArea;
double minAngle = 10;
Kernel::FT maxArea= 0;
for (std::vector<distSemFace>::iterator slIt = dsfList.begin();slIt != dsfList.end();++slIt)// HANDLE ANYTHING AS LESS IMPORTANT
if (slIt->dist < dsfList[0].dist+OVERLAP_DIST_THRESHOLD) { // Check if Equidistant
pointVector facetPoints = comp_facetPoints(exfIt);
CGAL::normal_vector_newell_3(facetPoints.begin(),facetPoints.end(),faceNormal); // Calculate normal vector, ortVec set to zero in newell
double angle = comp_angle(orthVec,faceNormal);
if (angle!=-1 && angle < minAngle+OVERLAP_ANGLE_THRESHOLD) {
if (minAngle >= angle+OVERLAP_ANGLE_THRESHOLD) exfIt->equidistSems.clear();
if (angle < minAngle) minAngle = angle;
faceSqArea = comp_facetSquaredArea(facetPoints);
if (faceSqArea>maxArea-OVERLAP_AREA_THRESHOLD) {
if (maxArea<=faceSqArea-OVERLAP_AREA_THRESHOLD) exfIt->equidistSems.clear();
if (faceSqArea>maxArea) maxArea = faceSqArea;
exfIt->equidistSems.push_back(slIt->sem); // Add equidist semantics
}
}
}
}
std::cout << "\r"<<semListStr<<". (100%)" << std::endl;
}else std::cerr << "ERROR: Not pure triangle (set_semantic_AABB2C2V)" << std::endl;
}
//**********************************************************************************
//generate "packing" of non-overlapping balls
vector<Vector3r> fillBoxByBalls_cpp(Vector3r minCoord, Vector3r maxCoord, Vector3r sizemin, Vector3r sizemax, Vector3r ratio, int seed, shared_ptr<Material> mat, int NumPoints){
vector<Vector3r> v;
Polyhedra trialP;
Polyhedron trial, trial_moved;
srand(seed);
int it = 0;
vector<Polyhedron> polyhedrons;
vector<vector<Vector3r> > vv;
Vector3r position;
bool intersection;
int count = 0;
Vector3r radii;
bool fixed_ratio = 0;
if (ratio[0] > 0 && ratio[1] > 0 && ratio[2]>0){
fixed_ratio = 1;
sizemax[0] = min(min(sizemax[0]/ratio[0], sizemax[1]/ratio[1]), sizemax[2]/ratio[2]);
sizemin[0] = max(max(sizemin[0]/ratio[0], sizemin[1]/ratio[1]), sizemin[2]/ratio[2]);
}
fixed_ratio = 1; //force spherical
//it - number of trials to make packing possibly more/less dense
Vector3r random_size;
while (it<1000){
it = it+1;
if (it == 1){
if (fixed_ratio) {
double rrr = (rand()*(sizemax[0]-sizemin[0])/RAND_MAX + sizemin[0])/2.;
radii = Vector3r(rrr,rrr,rrr);
}else {
radii = Vector3r(rand()*(sizemax[0]-sizemin[0])/2.,rand()*(sizemax[1]-sizemin[1])/2.,rand()*(sizemax[2]-sizemin[2])/2.)/RAND_MAX + sizemin/2.;
}
trialP.v = BallPoints(radii,NumPoints,rand());
trialP.Initialize();
trial = trialP.GetPolyhedron();
Matrix3r rot_mat = (trialP.GetOri()).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( trial.points_begin(), trial.points_end(), trial.points_begin(), t_rot);
}
position = Vector3r(rand()*(maxCoord[0]-minCoord[0]),rand()*(maxCoord[1]-minCoord[1]),rand()*(maxCoord[2]-minCoord[2]))/RAND_MAX + minCoord;
//move CGAL structure Polyhedron
Transformation transl(CGAL::TRANSLATION, ToCGALVector(position));
trial_moved = trial;
std::transform( trial_moved.points_begin(), trial_moved.points_end(), trial_moved.points_begin(), transl);
//calculate plane equations
std::transform( trial_moved.facets_begin(), trial_moved.facets_end(), trial_moved.planes_begin(),Plane_equation());
intersection = false;
//call test with boundary
for(Polyhedron::Vertex_iterator vi = trial_moved.vertices_begin(); (vi != trial_moved.vertices_end()) && (!intersection); vi++){
intersection = (vi->point().x()<minCoord[0]) || (vi->point().x()>maxCoord[0]) || (vi->point().y()<minCoord[1]) || (vi->point().y()>maxCoord[1]) || (vi->point().z()<minCoord[2]) || (vi->point().z()>maxCoord[2]);
}
//call test with other polyhedrons
for(vector<Polyhedron>::iterator a = polyhedrons.begin(); (a != polyhedrons.end()) && (!intersection); a++){
intersection = do_intersect(*a,trial_moved);
if (intersection) break;
}
if (!intersection){
polyhedrons.push_back(trial_moved);
v.clear();
for(Polyhedron::Vertex_iterator vi = trial_moved.vertices_begin(); vi != trial_moved.vertices_end(); vi++){
v.push_back(FromCGALPoint(vi->point()));
}
vv.push_back(v);
it = 0;
count ++;
}
}
cout << "generated " << count << " polyhedrons"<< endl;
//can't be used - no information about material
Scene* scene=Omega::instance().getScene().get();
for(vector<vector<Vector3r> >::iterator p=vv.begin(); p!=vv.end(); ++p){
shared_ptr<Body> BP = NewPolyhedra(*p, mat);
BP->shape->color = Vector3r(double(rand())/RAND_MAX,double(rand())/RAND_MAX,double(rand())/RAND_MAX);
scene->bodies->insert(BP);
}
return v;
}
