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cgal/Packages/Triangulation_3/include/CGAL/Delaunay_triangulation_3.h

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// ============================================================================
//
// Copyright (c) 1999,2000,2001,2002,2003 The CGAL Consortium
//
// This software and related documentation is part of an INTERNAL release
// of the Computational Geometry Algorithms Library (CGAL). It is not
// intended for general use.
//
// ----------------------------------------------------------------------------
//
// release :
// release_date :
//
// file : include/CGAL/Delaunay_triangulation_3.h
// revision : $Revision$
//
// author(s) : Monique Teillaud <Monique.Teillaud@sophia.inria.fr>
// Sylvain Pion <Sylvain.Pion@sophia.inria.fr>
// Andreas Fabri <Andreas.Fabri@sophia.inria.fr>
//
// coordinator : INRIA Sophia Antipolis (<Mariette.Yvinec@sophia.inria.fr>)
//
// ============================================================================
#ifndef CGAL_DELAUNAY_TRIANGULATION_3_H
#define CGAL_DELAUNAY_TRIANGULATION_3_H
#include <CGAL/basic.h>
#include <utility>
#include <vector>
#include <CGAL/Triangulation_short_names_3.h>
#include <CGAL/Triangulation_3.h>
#include <CGAL/Delaunay_remove_tds_3.h>
CGAL_BEGIN_NAMESPACE
template < class Tr > class Natural_neighbors_3;
template < class Gt,
class Tds = Triangulation_data_structure_3 <
Triangulation_vertex_base_3<Gt>,
Triangulation_cell_base_3<Gt> > >
class Delaunay_triangulation_3 : public Triangulation_3<Gt,Tds>
{
friend std::istream& operator >> CGAL_NULL_TMPL_ARGS
(std::istream& is, Triangulation_3<Gt,Tds> &tr);
typedef Delaunay_triangulation_3<Gt, Tds> Self;
typedef Triangulation_3<Gt,Tds> Tr_Base;
friend class Natural_neighbors_3<Self>;
public:
typedef Tds Triangulation_data_structure;
typedef Gt Geom_traits;
typedef typename Gt::Point_3 Point;
typedef typename Gt::Segment_3 Segment;
typedef typename Gt::Triangle_3 Triangle;
typedef typename Gt::Tetrahedron_3 Tetrahedron;
// types for dual:
typedef typename Gt::Line_3 Line;
typedef typename Gt::Ray_3 Ray;
typedef typename Gt::Plane_3 Plane;
typedef typename Gt::Direction_3 Direction;
typedef typename Gt::Object_3 Object;
typedef typename Tr_Base::Cell_handle Cell_handle;
typedef typename Tr_Base::Vertex_handle Vertex_handle;
typedef typename Tr_Base::Cell Cell;
typedef typename Tr_Base::Vertex Vertex;
typedef typename Tr_Base::Facet Facet;
typedef typename Tr_Base::Edge Edge;
typedef typename Tr_Base::Cell_circulator Cell_circulator;
typedef typename Tr_Base::Cell_iterator Cell_iterator;
typedef typename Tr_Base::Facet_iterator Facet_iterator;
typedef typename Tr_Base::Edge_iterator Edge_iterator;
typedef typename Tr_Base::Vertex_iterator Vertex_iterator;
typedef typename Tr_Base::Finite_vertices_iterator Finite_vertices_iterator;
typedef typename Tr_Base::Finite_cells_iterator Finite_cells_iterator;
typedef typename Tr_Base::Finite_facets_iterator Finite_facets_iterator;
typedef typename Tr_Base::Finite_edges_iterator Finite_edges_iterator;
typedef typename Tr_Base::Locate_type Locate_type;
protected:
Oriented_side
side_of_oriented_sphere(const Point &p0, const Point &p1, const Point &p2,
const Point &p3, const Point &t, bool perturb = false) const;
Bounded_side
coplanar_side_of_bounded_circle(const Point &p, const Point &q,
const Point &r, const Point &s, bool perturb = false) const;
// for dual:
Point
construct_circumcenter(const Point &p, const Point &q, const Point &r) const
{
return geom_traits().construct_circumcenter_3_object()(p, q, r);
}
Point
construct_circumcenter(const Point &p, const Point &q,
const Point &r, const Point &s) const
{
return geom_traits().construct_circumcenter_3_object()(p, q, r, s);
}
Line
construct_perpendicular_line(const Plane &pl, const Point &p) const
{
return geom_traits().construct_perpendicular_line_3_object()(pl, p);
}
Plane
construct_plane(const Point &p, const Point &q, const Point &r) const
{
return geom_traits().construct_plane_3_object()(p, q, r);
}
Direction
construct_direction(const Line &l) const
{
return geom_traits().construct_direction_3_object()(l);
}
Ray
construct_ray(const Point &p, const Direction &d) const
{
return geom_traits().construct_ray_3_object()(p, d);
}
Object
construct_object(const Point &p) const
{
return geom_traits().construct_object_3_object()(p);
}
Object
construct_object(const Segment &s) const
{
return geom_traits().construct_object_3_object()(s);
}
Object
construct_object(const Ray &r) const
{
return geom_traits().construct_object_3_object()(r);
}
bool
less_distance(const Point &p, const Point &q, const Point &r) const
{
return geom_traits().compare_distance_3_object()(p, q, r) == SMALLER;
}
public:
Delaunay_triangulation_3(const Gt& gt = Gt())
: Tr_Base(gt)
{}
// copy constructor duplicates vertices and cells
Delaunay_triangulation_3(const Delaunay_triangulation_3 & tr)
: Tr_Base(tr)
{
CGAL_triangulation_postcondition( is_valid() );
}
template < typename InputIterator >
Delaunay_triangulation_3(InputIterator first, InputIterator last,
const Gt& gt = Gt())
: Tr_Base(gt)
{
insert(first, last);
}
template < class InputIterator >
int
insert(InputIterator first, InputIterator last)
{
int n = number_of_vertices();
while(first != last){
insert(*first);
++first;
}
return number_of_vertices() - n;
}
Vertex_handle insert(const Point & p, Cell_handle start = NULL);
Vertex_handle insert(const Point & p, Locate_type lt,
Cell_handle c, int li, int);
// Obsolete.
Vertex_handle push_back(const Point & p)
{
return insert(p);
}
template <class Out_it_boundary_facets,
class Out_it_cells, class Out_it_internal_facets>
void
find_conflicts(const Point &p, Cell_handle c,
Out_it_boundary_facets bfit, Out_it_cells cit,
Out_it_internal_facets ifit) const
{
CGAL_triangulation_precondition(dimension() >= 2);
std::vector<Cell_handle> cells;
cells.reserve(32);
std::vector<Facet> facets;
facets.reserve(64);
if (dimension() == 2) {
Conflict_tester_2 tester(p, this);
find_conflicts_2(c, tester, std::back_inserter(facets),
std::back_inserter(cells),
ifit);
}
else {
Conflict_tester_3 tester(p, this);
find_conflicts_3(c, tester, std::back_inserter(facets),
std::back_inserter(cells),
ifit);
}
// Reset the conflict flag on the boundary.
for(typename std::vector<Facet>::iterator fit=facets.begin();
fit != facets.end(); ++fit) {
fit->first->neighbor(fit->second)->set_in_conflict_flag(0);
*bfit++ = *fit;
}
// Reset the conflict flag in the conflict cells.
for(typename std::vector<Cell_handle>::iterator ccit=cells.begin();
ccit != cells.end(); ++ccit) {
(*ccit)->set_in_conflict_flag(0);
*cit++ = *ccit;
}
}
// We return bool only for backward compatibility (it's always true).
// The documentation mentions void.
bool remove(Vertex_handle v);
private:
typedef Facet Edge_2D;
void remove_2D(Vertex_handle v);
void make_hole_2D(Vertex_handle v, std::list<Edge_2D> & hole);
void fill_hole_delaunay_2D(std::list<Edge_2D> & hole);
Bounded_side
side_of_sphere(Vertex_handle v0, Vertex_handle v1,
Vertex_handle v2, Vertex_handle v3,
const Point &p, bool perturb) const;
public:
Bounded_side
side_of_sphere( Cell_handle c, const Point & p, bool perturb = false) const
{
return side_of_sphere(c->vertex(0), c->vertex(1),
c->vertex(2), c->vertex(3), p, perturb);
}
Bounded_side
side_of_circle( const Facet & f, const Point & p, bool perturb = false) const
{
return side_of_circle(f.first, f.second, p, perturb);
}
Bounded_side
side_of_circle( Cell_handle c, int i, const Point & p,
bool perturb = false) const;
Vertex_handle
nearest_vertex_in_cell(const Point& p, Cell_handle c) const;
Point dual(Cell_handle c) const;
Object dual(const Facet & f) const
{ return dual( f.first, f.second ); }
Object dual(Cell_handle c, int i) const;
bool is_valid(bool verbose = false, int level = 0) const;
bool is_valid(Cell_handle c, bool verbose = false, int level = 0) const;
template < class Stream>
Stream& draw_dual(Stream & os)
{
Finite_facets_iterator fit = finite_facets_begin();
for (; fit != finite_facets_end(); ++fit) {
Object o = dual(*fit);
Point p;
Ray r;
Segment s;
if (CGAL::assign(p,o)) os << p;
if (CGAL::assign(s,o)) os << s;
if (CGAL::assign(r,o)) os << r;
}
return os;
}
private:
Vertex_handle
nearest_vertex(const Point &p, Vertex_handle v, Vertex_handle w) const
{
CGAL_triangulation_precondition(v != w);
if (is_infinite(v))
return w;
if (is_infinite(w))
return v;
return less_distance(p, v->point(), w->point()) ? v : w;
}
void make_hole_3D_ear( Vertex_handle v,
std::vector<Facet> & boundhole,
std::vector<Cell_handle> & hole);
void fill_hole_3D_ear(const std::vector<Facet> & boundhole);
class Conflict_tester_3
{
const Point &p;
const Self *t;
public:
Conflict_tester_3(const Point &pt, const Self *tr)
: p(pt), t(tr) {}
bool operator()(const Cell_handle c) const
{
return t->side_of_sphere(c, p, true) == ON_BOUNDED_SIDE;
}
};
class Conflict_tester_2
{
const Point &p;
const Self *t;
public:
Conflict_tester_2(const Point &pt, const Self *tr)
: p(pt), t(tr) {}
bool operator()(const Cell_handle c) const
{
return t->side_of_circle(c, 3, p, true) == ON_BOUNDED_SIDE;
}
};
class Perturbation_order {
const Self *t;
public:
Perturbation_order(const Self *tr)
: t(tr) {}
bool operator()(const Point *p, const Point *q) const {
return t->compare_xyz(*p, *q) == SMALLER;
}
};
friend class Perturbation_order;
friend class Conflict_tester_3;
friend class Conflict_tester_2;
};
template < class Gt, class Tds >
typename Delaunay_triangulation_3<Gt,Tds>::Vertex_handle
Delaunay_triangulation_3<Gt,Tds>::
insert(const Point & p, Cell_handle start)
{
Locate_type lt;
int li, lj;
Cell_handle c = locate(p, lt, li, lj, start);
return insert(p, lt, c, li, lj);
}
template < class Gt, class Tds >
typename Delaunay_triangulation_3<Gt,Tds>::Vertex_handle
Delaunay_triangulation_3<Gt,Tds>::
insert(const Point & p, Locate_type lt, Cell_handle c, int li, int)
{
switch (dimension()) {
case 3:
{
if ( lt == Tr_Base::VERTEX )
return c->vertex(li);
Conflict_tester_3 tester(p, this);
Vertex_handle v = insert_conflict_3(c, tester);
v->set_point(p);
return v;
}// dim 3
case 2:
{
switch (lt) {
case Tr_Base::OUTSIDE_CONVEX_HULL:
case Tr_Base::CELL:
case Tr_Base::FACET:
case Tr_Base::EDGE:
{
Conflict_tester_2 tester(p, this);
Vertex_handle v = insert_conflict_2(c, tester);
v->set_point(p);
return v;
}
case Tr_Base::VERTEX:
return c->vertex(li);
case Tr_Base::OUTSIDE_AFFINE_HULL:
// if the 2d triangulation is Delaunay, the 3d
// triangulation will be Delaunay
return Tr_Base::insert_outside_affine_hull(p);
}
}//dim 2
default :
// dimension <= 1
return Tr_Base::insert(p, c);
}
}
template < class Gt, class Tds >
void
Delaunay_triangulation_3<Gt,Tds>::
remove_2D(Vertex_handle v)
{
CGAL_triangulation_precondition(dimension() == 2);
std::list<Edge_2D> hole;
make_hole_2D(v, hole);
fill_hole_delaunay_2D(hole);
tds().delete_vertex(v);
}
template <class Gt, class Tds >
void
Delaunay_triangulation_3<Gt, Tds>::
fill_hole_delaunay_2D(std::list<Edge_2D> & first_hole)
{
typedef std::list<Edge_2D> Hole;
std::vector<Hole> hole_list;
Cell_handle f, ff, fn;
int i, ii, in;
hole_list.push_back(first_hole);
while( ! hole_list.empty())
{
Hole hole = hole_list.back();
hole_list.pop_back();
// if the hole has only three edges, create the triangle
if (hole.size() == 3) {
typename Hole::iterator hit = hole.begin();
f = (*hit).first; i = (*hit).second;
ff = (* ++hit).first; ii = (*hit).second;
fn = (* ++hit).first; in = (*hit).second;
tds().create_face(f, i, ff, ii, fn, in);
continue;
}
// else find an edge with two finite vertices
// on the hole boundary
// and the new triangle adjacent to that edge
// cut the hole and push it back
// first, ensure that a neighboring face
// whose vertices on the hole boundary are finite
// is the first of the hole
while (1) {
ff = (hole.front()).first;
ii = (hole.front()).second;
if ( is_infinite(ff->vertex(cw(ii))) ||
is_infinite(ff->vertex(ccw(ii)))) {
hole.push_back(hole.front());
hole.pop_front();
}
else
break;
}
// take the first neighboring face and pop it;
ff = (hole.front()).first;
ii = (hole.front()).second;
hole.pop_front();
Vertex_handle v0 = ff->vertex(cw(ii));
Vertex_handle v1 = ff->vertex(ccw(ii));
Vertex_handle v2 = infinite_vertex();
const Point &p0 = v0->point();
const Point &p1 = v1->point();
const Point *p2 = NULL; // Initialize to NULL to avoid warning.
typename Hole::iterator hdone = hole.end();
typename Hole::iterator hit = hole.begin();
typename Hole::iterator cut_after(hit);
// if tested vertex is c with respect to the vertex opposite
// to NULL neighbor,
// stop at the before last face;
hdone--;
for (; hit != hdone; ++hit) {
fn = hit->first;
in = hit->second;
Vertex_handle vv = fn->vertex(ccw(in));
if (is_infinite(vv)) {
if (is_infinite(v2))
cut_after = hit;
}
else { // vv is a finite vertex
const Point &p = vv->point();
if (coplanar_orientation(p0, p1, p) == COUNTERCLOCKWISE) {
if (is_infinite(v2) ||
coplanar_side_of_bounded_circle(p0, p1, *p2, p, true)
== ON_BOUNDED_SIDE) {
v2 = vv;
p2 = &p;
cut_after = hit;
}
}
}
}
// create new triangle and update adjacency relations
Cell_handle newf;
//update the hole and push back in the Hole_List stack
// if v2 belongs to the neighbor following or preceding *f
// the hole remain a single hole
// otherwise it is split in two holes
fn = (hole.front()).first;
in = (hole.front()).second;
if (fn->has_vertex(v2, i) && i == ccw(in)) {
newf = tds().create_face(ff, ii, fn, in);
hole.pop_front();
hole.push_front(Edge_2D(newf, 1));
hole_list.push_back(hole);
}
else{
fn = (hole.back()).first;
in = (hole.back()).second;
if (fn->has_vertex(v2, i) && i == cw(in)) {
newf = tds().create_face(fn, in, ff, ii);
hole.pop_back();
hole.push_back(Edge_2D(newf, 1));
hole_list.push_back(hole);
}
else{
// split the hole in two holes
newf = tds().create_face(ff, ii, v2);
Hole new_hole;
++cut_after;
while( hole.begin() != cut_after )
{
new_hole.push_back(hole.front());
hole.pop_front();
}
hole.push_front(Edge_2D(newf, 1));
new_hole.push_front(Edge_2D(newf, 0));
hole_list.push_back(hole);
hole_list.push_back(new_hole);
}
}
}
}
template <class Gt, class Tds >
void
Delaunay_triangulation_3<Gt, Tds>::
make_hole_2D(Vertex_handle v, std::list<Edge_2D> & hole)
{
std::vector<Cell_handle> to_delete;
typename Tds::Face_circulator fc = tds().incident_faces(v);
typename Tds::Face_circulator done(fc);
// We prepare for deleting all interior cells.
// We ->set_cell() pointers to cells outside the hole.
// We push the Edges_2D of the boundary (seen from outside) in "hole".
do {
Cell_handle f = fc;
int i = f->index(v);
Cell_handle fn = f->neighbor(i);
int in = fn->index(f);
f->vertex(cw(i))->set_cell(fn);
fn->set_neighbor(in, NULL);
hole.push_back(Edge_2D(fn, in));
to_delete.push_back(f);
++fc;
} while (fc != done);
tds().delete_cells(to_delete.begin(), to_delete.end());
}
template < class Gt, class Tds >
bool
Delaunay_triangulation_3<Gt,Tds>::
remove(Vertex_handle v)
{
CGAL_triangulation_precondition( v != NULL);
CGAL_triangulation_precondition( !is_infinite(v));
CGAL_triangulation_expensive_precondition( tds().is_vertex(v) );
if (dimension() >= 0 && test_dim_down(v)) {
tds().remove_decrease_dimension(v);
// Now try to see if we need to re-orient.
if (dimension() == 2) {
Facet f = *finite_facets_begin();
if (coplanar_orientation(f.first->vertex(0)->point(),
f.first->vertex(1)->point(),
f.first->vertex(2)->point()) == NEGATIVE)
tds().reorient();
}
CGAL_triangulation_expensive_postcondition(is_valid());
return true;
}
if (dimension() == 1) {
tds().remove_from_maximal_dimension_simplex(v);
CGAL_triangulation_expensive_postcondition(is_valid());
return true;
}
if (dimension() == 2) {
remove_2D(v);
CGAL_triangulation_expensive_postcondition(is_valid());
return true;
}
CGAL_triangulation_assertion( dimension() == 3 );
std::vector<Facet> boundhole; // facets on the boundary of the hole
boundhole.reserve(64); // 27 on average.
std::vector<Cell_handle> hole;
hole.reserve(64);
make_hole_3D_ear(v, boundhole, hole);
fill_hole_3D_ear(boundhole);
tds().delete_vertex(v);
tds().delete_cells(hole.begin(), hole.end());
CGAL_triangulation_expensive_postcondition(is_valid());
return true;
}
template < class Gt, class Tds >
Oriented_side
Delaunay_triangulation_3<Gt,Tds>::
side_of_oriented_sphere(const Point &p0, const Point &p1, const Point &p2,
const Point &p3, const Point &p, bool perturb) const
{
CGAL_triangulation_precondition( orientation(p0, p1, p2, p3) == POSITIVE );
Oriented_side os =
geom_traits().side_of_oriented_sphere_3_object()(p0, p1, p2, p3, p);
if (os != ON_ORIENTED_BOUNDARY || !perturb)
return os;
// We are now in a degenerate case => we do a symbolic perturbation.
// We sort the points lexicographically.
#if defined _MSC_VER && _MSC_VER >= 1300 // FIXME : Should use proper macro
std::vector<const Point*> points;
points.push_back(&p0); points.push_back(&p1);
points.push_back(&p2); points.push_back(&p3);
points.push_back(&p);
std::sort(points.begin(), points.end(), Perturbation_order(this));
#else
const Point * points[5] = {&p0, &p1, &p2, &p3, &p};
std::sort(points, points+5, Perturbation_order(this) );
#endif
// We successively look whether the leading monomial, then 2nd monomial
// of the determinant has non null coefficient.
// 2 iterations are enough (cf paper)
for (int i=4; i>2; --i) {
if (points[i] == &p)
return ON_NEGATIVE_SIDE; // since p0 p1 p2 p3 are non coplanar
// and positively oriented
Orientation o;
if (points[i] == &p3 && (o = orientation(p0,p1,p2,p)) != COPLANAR )
return Oriented_side(o);
if (points[i] == &p2 && (o = orientation(p0,p1,p3,p)) != COPLANAR )
return Oriented_side(-o);
if (points[i] == &p1 && (o = orientation(p0,p2,p3,p)) != COPLANAR )
return Oriented_side(o);
if (points[i] == &p0 && (o = orientation(p1,p2,p3,p)) != COPLANAR )
return Oriented_side(-o);
}
CGAL_triangulation_assertion(false);
return ON_NEGATIVE_SIDE;
}
template < class Gt, class Tds >
Bounded_side
Delaunay_triangulation_3<Gt,Tds>::
coplanar_side_of_bounded_circle(const Point &p0, const Point &p1,
const Point &p2, const Point &p, bool perturb) const
{
// In dim==2, we should even be able to assert orient == POSITIVE.
CGAL_triangulation_precondition( coplanar_orientation(p0, p1, p2)
!= COLLINEAR );
Bounded_side bs =
geom_traits().coplanar_side_of_bounded_circle_3_object()(p0, p1, p2, p);
if (bs != ON_BOUNDARY || !perturb)
return bs;
// We are now in a degenerate case => we do a symbolic perturbation.
// We sort the points lexicographically.
#if defined _MSC_VER && _MSC_VER >= 1300 // FIXME : should use the right macro
std::vector<const Point*> points;
points.push_back(&p0); points.push_back(&p1);
points.push_back(&p2); points.push_back(&p);
std::sort(points.begin(), points.end(), Perturbation_order(this));
#else
const Point * points[4] = {&p0, &p1, &p2, &p};
std::sort(points, points+4, Perturbation_order(this) );
#endif
Orientation local = coplanar_orientation(p0, p1, p2);
// we successively look whether the leading monomial, then 2nd monimial,
// then 3rd monomial, of the determinant which has non null coefficient
// [syl] : TODO : Probably it can be stopped earlier like the 3D version
for (int i=3; i>0; --i) {
if (points[i] == &p)
return Bounded_side(NEGATIVE); // since p0 p1 p2 are non collinear
// but not necessarily positively oriented
Orientation o;
if (points[i] == &p2
&& (o = coplanar_orientation(p0,p1,p)) != COLLINEAR )
// [syl] : TODO : I'm not sure of the signs here (nor the rest :)
return Bounded_side(o*local);
if (points[i] == &p1
&& (o = coplanar_orientation(p0,p2,p)) != COLLINEAR )
return Bounded_side(-o*local);
if (points[i] == &p0
&& (o = coplanar_orientation(p1,p2,p)) != COLLINEAR )
return Bounded_side(o*local);
}
// case when the first non null coefficient is the coefficient of
// the 4th monomial
// moreover, the tests (points[] == &p) were false up to here, so the
// monomial corresponding to p is the only monomial with non-zero
// coefficient, it is equal to coplanar_orient(p0,p1,p2) == positive
// so, no further test is required
return Bounded_side(-local); //ON_UNBOUNDED_SIDE;
}
template < class Gt, class Tds >
Bounded_side
Delaunay_triangulation_3<Gt,Tds>::
side_of_sphere(Vertex_handle v0, Vertex_handle v1,
Vertex_handle v2, Vertex_handle v3,
const Point &p, bool perturb) const
{
CGAL_triangulation_precondition( dimension() == 3 );
// TODO :
// - avoid accessing points of infinite vertex
// - share the 4 codes below (see old version)
const Point &p0 = v0->point();
const Point &p1 = v1->point();
const Point &p2 = v2->point();
const Point &p3 = v3->point();
if (is_infinite(v0)) {
Orientation o = orientation(p2, p1, p3, p);
if (o != COPLANAR)
return Bounded_side(o);
return coplanar_side_of_bounded_circle(p2, p1, p3, p, perturb);
}
if (is_infinite(v1)) {
Orientation o = orientation(p2, p3, p0, p);
if (o != COPLANAR)
return Bounded_side(o);
return coplanar_side_of_bounded_circle(p2, p3, p0, p, perturb);
}
if (is_infinite(v2)) {
Orientation o = orientation(p1, p0, p3, p);
if (o != COPLANAR)
return Bounded_side(o);
return coplanar_side_of_bounded_circle(p1, p0, p3, p, perturb);
}
if (is_infinite(v3)) {
Orientation o = orientation(p0, p1, p2, p);
if (o != COPLANAR)
return Bounded_side(o);
return coplanar_side_of_bounded_circle(p0, p1, p2, p, perturb);
}
return (Bounded_side) side_of_oriented_sphere(p0, p1, p2, p3, p, perturb);
}
template < class Gt, class Tds >
Bounded_side
Delaunay_triangulation_3<Gt,Tds>::
side_of_circle(Cell_handle c, int i, const Point & p, bool perturb) const
// precondition : dimension >=2
// in dimension 3, - for a finite facet
// returns ON_BOUNDARY if the point lies on the circle,
// ON_UNBOUNDED_SIDE when exterior, ON_BOUNDED_SIDE
// interior
// for an infinite facet, considers the plane defined by the
// adjacent finite facet of the same cell, and does the same as in
// dimension 2 in this plane
// in dimension 2, for an infinite facet
// in this case, returns ON_BOUNDARY if the point lies on the
// finite edge (endpoints included)
// ON_BOUNDED_SIDE for a point in the open half-plane
// ON_UNBOUNDED_SIDE elsewhere
{
CGAL_triangulation_precondition( dimension() >= 2 );
int i3 = 5;
if ( dimension() == 2 ) {
CGAL_triangulation_precondition( i == 3 );
// the triangulation is supposed to be valid, ie the facet
// with vertices 0 1 2 in this order is positively oriented
if ( ! c->has_vertex( infinite_vertex(), i3 ) )
return coplanar_side_of_bounded_circle( c->vertex(0)->point(),
c->vertex(1)->point(),
c->vertex(2)->point(),
p, perturb);
// else infinite facet
// v1, v2 finite vertices of the facet such that v1,v2,infinite
// is positively oriented
Vertex_handle v1 = c->vertex( ccw(i3) ),
v2 = c->vertex( cw(i3) );
CGAL_triangulation_assertion(coplanar_orientation(v1->point(), v2->point(),
(c->mirror_vertex(i3))->point()) == NEGATIVE);
Orientation o = coplanar_orientation(v1->point(), v2->point(), p);
if ( o != COLLINEAR )
return Bounded_side( o );
// because p is in f iff
// it does not lie on the same side of v1v2 as vn
int i_e;
Locate_type lt;
// case when p collinear with v1v2
return side_of_segment( p,
v1->point(), v2->point(),
lt, i_e );
}
// else dimension == 3
CGAL_triangulation_precondition( i >= 0 && i < 4 );
if ( ( ! c->has_vertex(infinite_vertex(),i3) ) || ( i3 != i ) ) {
// finite facet
// initialization of i0 i1 i2, vertices of the facet positively
// oriented (if the triangulation is valid)
int i0 = (i>0) ? 0 : 1;
int i1 = (i>1) ? 1 : 2;
int i2 = (i>2) ? 2 : 3;
CGAL_triangulation_precondition( coplanar( c->vertex(i0)->point(),
c->vertex(i1)->point(),
c->vertex(i2)->point(),
p ) );
return coplanar_side_of_bounded_circle( c->vertex(i0)->point(),
c->vertex(i1)->point(),
c->vertex(i2)->point(),
p, perturb);
}
//else infinite facet
// v1, v2 finite vertices of the facet such that v1,v2,infinite
// is positively oriented
Vertex_handle v1 = c->vertex( next_around_edge(i3,i) ),
v2 = c->vertex( next_around_edge(i,i3) );
Orientation o = (Orientation)
(coplanar_orientation( v1->point(), v2->point(),
c->vertex(i)->point()) *
coplanar_orientation( v1->point(), v2->point(), p ));
// then the code is duplicated from 2d case
if ( o != COLLINEAR )
return Bounded_side( -o );
// because p is in f iff
// it is not on the same side of v1v2 as c->vertex(i)
int i_e;
Locate_type lt;
// case when p collinear with v1v2
return side_of_segment( p,
v1->point(), v2->point(),
lt, i_e );
}
template < class Gt, class Tds >
typename Delaunay_triangulation_3<Gt,Tds>::Vertex_handle
Delaunay_triangulation_3<Gt,Tds>::
nearest_vertex_in_cell(const Point& p, Cell_handle c) const
// Returns the finite vertex of the cell c which is the closest to p.
{
CGAL_triangulation_precondition(dimension() >= 1);
Vertex_handle nearest = nearest_vertex(p, c->vertex(0), c->vertex(1));
if (dimension() >= 2) {
nearest = nearest_vertex(p, nearest, c->vertex(2));
if (dimension() == 3)
nearest = nearest_vertex(p, nearest, c->vertex(3));
}
return nearest;
}
template < class Gt, class Tds >
typename Delaunay_triangulation_3<Gt,Tds>::Point
Delaunay_triangulation_3<Gt,Tds>::
dual(Cell_handle c) const
{
CGAL_triangulation_precondition(dimension()==3);
CGAL_triangulation_precondition( ! is_infinite(c) );
return construct_circumcenter( c->vertex(0)->point(),
c->vertex(1)->point(),
c->vertex(2)->point(),
c->vertex(3)->point() );
}
template < class Gt, class Tds >
typename Delaunay_triangulation_3<Gt,Tds>::Object
Delaunay_triangulation_3<Gt,Tds>::
dual(Cell_handle c, int i) const
{
CGAL_triangulation_precondition(dimension()>=2);
CGAL_triangulation_precondition( ! is_infinite(c,i) );
if ( dimension() == 2 ) {
CGAL_triangulation_precondition( i == 3 );
return construct_object( construct_circumcenter(c->vertex(0)->point(),
c->vertex(1)->point(),
c->vertex(2)->point()) );
}
// dimension() == 3
Cell_handle n = c->neighbor(i);
if ( ! is_infinite(c) && ! is_infinite(n) )
return construct_object(construct_segment( dual(c), dual(n) ));
// either n or c is infinite
int in;
if ( is_infinite(c) )
in = n->index(c);
else {
n = c;
in = i;
}
// n now denotes a finite cell, either c or c->neighbor(i)
unsigned char ind[3] = {(in+1)&3,(in+2)&3,(in+3)&3};
if ( (in&1) == 1 )
std::swap(ind[0], ind[1]);
const Point& p = n->vertex(ind[0])->point();
const Point& q = n->vertex(ind[1])->point();
const Point& r = n->vertex(ind[2])->point();
Line l = construct_perpendicular_line( construct_plane(p,q,r),
construct_circumcenter(p,q,r) );
return construct_object(construct_ray( dual(n),
construct_direction(l)));
}
template < class Gt, class Tds >
bool
Delaunay_triangulation_3<Gt,Tds>::
is_valid(bool verbose, int level) const
{
if ( ! tds().is_valid(verbose,level) ) {
if (verbose)
std::cerr << "invalid data structure" << std::endl;
CGAL_triangulation_assertion(false);
return false;
}
if ( infinite_vertex() == NULL ) {
if (verbose)
std::cerr << "no infinite vertex" << std::endl;
CGAL_triangulation_assertion(false);
return false;
}
switch ( dimension() ) {
case 3:
{
Finite_cells_iterator it;
for ( it = finite_cells_begin(); it != finite_cells_end(); ++it ) {
is_valid_finite(it);
for (int i=0; i<4; i++ ) {
if ( side_of_sphere (it,
it->vertex(it->neighbor(i)->index(it))->point())
== ON_BOUNDED_SIDE ) {
if (verbose)
std::cerr << "non-empty sphere " << std::endl;
CGAL_triangulation_assertion(false);
return false;
}
}
}
break;
}
case 2:
{
Finite_facets_iterator it;
for ( it = finite_facets_begin(); it != finite_facets_end(); ++it ) {
is_valid_finite((*it).first);
for (int i=0; i<2; i++ ) {
if ( side_of_circle ( (*it).first, 3,
(*it).first->vertex( (((*it).first)->neighbor(i))
->index((*it).first) )->point() )
== ON_BOUNDED_SIDE ) {
if (verbose)
std::cerr << "non-empty circle " << std::endl;
CGAL_triangulation_assertion(false);
return false;
}
}
}
break;
}
case 1:
{
Finite_edges_iterator it;
for ( it = finite_edges_begin(); it != finite_edges_end(); ++it )
is_valid_finite((*it).first);
break;
}
}
if (verbose)
std::cerr << "Delaunay valid triangulation" << std::endl;
return true;
}
template < class Gt, class Tds >
bool
Delaunay_triangulation_3<Gt,Tds>::
is_valid(Cell_handle c, bool verbose, int level) const
{
if ( ! c->is_valid(dimension(),verbose,level) ) {
if (verbose) {
std::cerr << "combinatorically invalid cell" ;
for (int i=0; i <= dimension(); i++ )
std::cerr << c->vertex(i)->point() << ", " ;
std::cerr << std::endl;
}
CGAL_triangulation_assertion(false);
return false;
}
switch ( dimension() ) {
case 3:
{
if ( ! is_infinite(c) ) {
is_valid_finite(c,verbose,level);
for (int i=0; i<4; i++ ) {
if (side_of_sphere(c, c->vertex((c->neighbor(i))->index(c))->point())
== ON_BOUNDED_SIDE ) {
if (verbose)
std::cerr << "non-empty sphere " << std::endl;
CGAL_triangulation_assertion(false);
return false;
}
}
}
break;
}
case 2:
{
if ( ! is_infinite(c,3) ) {
for (int i=0; i<2; i++ ) {
if (side_of_circle(c, 3, c->vertex(c->neighbor(i)->index(c))->point())
== ON_BOUNDED_SIDE ) {
if (verbose)
std::cerr << "non-empty circle " << std::endl;
CGAL_triangulation_assertion(false);
return false;
}
}
}
break;
}
}
if (verbose)
std::cerr << "Delaunay valid cell" << std::endl;
return true;
}
template < class Gt, class Tds >
void
Delaunay_triangulation_3<Gt,Tds>::
make_hole_3D_ear( Vertex_handle v,
std::vector<Facet> & boundhole,
std::vector<Cell_handle> & hole)
{
CGAL_triangulation_expensive_precondition( ! test_dim_down(v) );
incident_cells(v, std::back_inserter(hole));
for (typename std::vector<Cell_handle>::iterator cit = hole.begin();
cit != hole.end(); ++cit) {
int indv = (*cit)->index(v);
Cell_handle opp_cit = (*cit)->neighbor( indv );
boundhole.push_back(Facet( opp_cit, opp_cit->index(*cit)) );
for (int i=0; i<4; i++)
if ( i != indv )
(*cit)->vertex(i)->set_cell(opp_cit);
}
}
template < class Gt, class Tds >
void
Delaunay_triangulation_3<Gt,Tds>::
fill_hole_3D_ear(const std::vector<Facet> & boundhole)
{
typedef Delaunay_remove_tds_3_2<Delaunay_triangulation_3> Surface;
typedef typename Surface::Face_3_2 Face_3_2;
typedef typename Surface::Face_handle_3_2 Face_handle_3_2;
typedef typename Surface::Vertex_handle_3_2 Vertex_handle_3_2;
Surface surface(boundhole);
Face_handle_3_2 f = surface.faces_begin();
Face_handle_3_2 last_op = f; // This is where the last ear was inserted
int k = -1;
// This is a loop over the halfedges of the surface of the hole
// As edges are not explicitely there, we loop over the faces instead,
// and an index.
// The current face is f, the current index is k = -1, 0, 1, 2
for(;;) {
next_edge: ;
k++;
if(k == 3) {
// The faces form a circular list. With f->n() we go to the next face.
f = f->n();
CGAL_assertion_msg(f != last_op, "Unable to find an ear");
k = 0;
}
// The edges are marked, if they are a candidate for an ear.
// This saves time, for example an edge gets not considered
// from both adjacent faces.
if (!f->is_halfedge_marked(k))
continue;
Vertex_handle_3_2 w0, w1, w2, w3;
Vertex_handle v0, v1, v2, v3;
int i = ccw(k);
int j = cw(k);
Face_handle_3_2 n = f->neighbor(k);
int fi = n->index(f);
w1 = f->vertex(i);
w2 = f->vertex(j);
v1 = w1->info();
v2 = w2->info();
if( is_infinite(v1) || is_infinite(v2) ){
// there will be another ear, so let's ignore this one,
// because it is complicated to treat
continue;
}
w0 = f->vertex(k);
w3 = n->vertex(fi);
v0 = w0->info();
v3 = w3->info();
if( !is_infinite(v0) && !is_infinite(v3) &&
orientation(v0->point(), v1->point(),
v2->point(), v3->point()) != POSITIVE)
continue;
// the two faces form a concavity, in which we might plug a cell
// we now look at all vertices that are on the boundary of the hole
for(typename Surface::Vertex_iterator vit = surface.vertices_begin();
vit != surface.vertices_end(); ++vit) {
Vertex_handle v = vit->info();
if (is_infinite(v) || v == v0 || v == v1 || v == v2 || v == v3)
continue;
if (side_of_sphere(v0,v1,v2,v3, v->point(), true) == ON_BOUNDED_SIDE)
goto next_edge;
}
// we looked at all vertices
Face_handle_3_2 m_i = f->neighbor(i);
Face_handle_3_2 m_j = f->neighbor(j);
bool neighbor_i = m_i == n->neighbor(cw(fi));
bool neighbor_j = m_j == n->neighbor(ccw(fi));
// Test if the edge that would get introduced is on the surface
if ( !neighbor_i && !neighbor_j &&
surface.is_edge(f->vertex(k), n->vertex(fi)))
continue;
// none of the vertices violates the Delaunay property
// We are ready to plug a new cell
Cell_handle ch = tds().create_cell(v0, v1, v2, v3);
// The new cell touches the faces that form the ear
Facet fac = n->info();
tds().set_adjacency(ch, 0, fac.first, fac.second);
fac = f->info();
tds().set_adjacency(ch, 3, fac.first, fac.second);
// It may touch another face,
// or even two other faces if it is the last cell
if(neighbor_i) {
fac = m_i->info();
tds().set_adjacency(ch, 1, fac.first, fac.second);
}
if(neighbor_j) {
fac = m_j->info();
tds().set_adjacency(ch, 2, fac.first, fac.second);
}
if( !neighbor_i && !neighbor_j) {
surface.flip(f,k);
int fi = n->index(f);
int ni = f->index(n);
// The flipped edge is not a concavity
f->unmark_edge(ni);
// The adjacent edges may be a concavity
// that is they are candidates for an ear
// In the list of faces they get moved behind f
f->mark_edge(cw(ni), f);
f->mark_edge(ccw(ni), f);
n->mark_edge(cw(fi), f);
n->mark_edge(ccw(fi), f);
f->set_info(Facet(ch,2));
n->set_info(Facet(ch,1));
} else if (neighbor_i && (! neighbor_j)) {
surface.remove_degree_3(f->vertex(j), f);
// all three edges adjacent to f are
// candidate for an ear
f->mark_adjacent_edges();
f->set_info(Facet(ch,2));
} else if ((! neighbor_i) && neighbor_j) {
surface.remove_degree_3(f->vertex(i), f);
f->mark_adjacent_edges();
f->set_info(Facet(ch,1));
} else {
CGAL_assertion(surface.number_of_vertices() == 4);
// when we leave the function the vertices and faces of the surface
// are deleted by the destructor
return;
}
// we successfully inserted a cell
last_op = f;
// we have to reconsider all edges incident to f
k = -1;
} // for(;;)
}
CGAL_END_NAMESPACE
#endif // CGAL_DELAUNAY_TRIANGULATION_3_H
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