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1822 1823 1824 1825 1826 1827 1828 1829 1830 1831 1832 1833 1834 1835 1836 1837 1838 1839 1840 1841 1842 1843 1844 1845 1846 1847 1848 1849 1850 1851 1852 1853 1854 1855 1856 1857 1858 1859 1860 1861 1862 1863 1864 1865 1866 1867 1868 1869 1870 1871 1872 1873 1874 1875 1876 1877 1878 1879 1880 1881 1882 1883 1884 1885 1886 1887 1888 1889 1890 1891 1892 1893 1894 1895 1896 1897 1898 1899 1900 1901 1902 1903 1904 1905 1906 1907 1908 1909 1910 1911 1912 1913 1914 1915 1916 1917 | // Copyright (c) 1997, 2012 INRIA Sophia-Antipolis (France).
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org).
// You can redistribute it and/or modify it under the terms of the GNU
// General Public License as published by the Free Software Foundation,
// either version 3 of the License, or (at your option) any later version.
//
// Licensees holding a valid commercial license may use this file in
// accordance with the commercial license agreement provided with the so
//
// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
//
// $URL$
// $Id$
//
//
// Author(s) : Tran Kai Frank DA <Frank.Da@sophia.inria.fr>
// Andreas Fabri <Andreas.Fabri@geometryfactory.com>
// Mariette Yvinec <Mariette.Yvinec@sophia.inria.fr>
#ifndef CGAL_ALPHA_SHAPE_3_H
#define CGAL_ALPHA_SHAPE_3_H
#include <CGAL/basic.h>
#include <set>
#include <map>
#include <list>
#include <vector>
#include <algorithm>
#include <utility>
#include <iostream>
#include <CGAL/Triangulation_utils_3.h>
#include <CGAL/Object.h>
#include <CGAL/Unique_hash_map.h>
#include <CGAL/Compact_container.h>
#include <CGAL/Alpha_shape_vertex_base_3.h>
#include <CGAL/Alpha_shape_cell_base_3.h>
#include <CGAL/internal/Lazy_alpha_nt_3.h>
#ifdef CGAL_USE_GEOMVIEW
#include <CGAL/IO/Geomview_stream.h> // TBC
#endif
//-------------------------------------------------------------------
namespace CGAL {
//-------------------------------------------------------------------
template < class Dt, class ExactAlphaComparisonTag = Tag_false >
class Alpha_shape_3 : public Dt
{
// DEFINITION The class Alpha_shape_3<Dt> represents the family
// of alpha-shapes for a set of points (or a set of weighted points)
// for all possible values of alpha. The alphashape is defined through
// the Delaunay tetrahedralization of the points
// (or the Regular tetrahedralization in case of weighted points)
// and depends on the value of a parameter called alpha.
// The alpha_shape is the domain of a subcomplex of this triangulation
// called the Alpha_complex. The alpha_complex includes any simplex
// having a circumscribing sphere (an orthogonal sphere
// in case of weighted points) empty of other points
// (or suborthogonal to other sites in case of weighted points)
// with squared radius equal or less than alpha
// The alpha_shapes comes in two versions : GENERAL or REGULARIZED
// where the REGULARIZED version is onbtaining by restricting the
// alpha complex ti is pure 3D component.
// The cells of the triangulation are classified as INTERIOR
// or EXTERIOR according to the value alpha_cell of their circumsphere
// squared radius compared to alpha.
// In GENERAL mode each k-dimensional simplex of the triangulation
// for (k=0,1,2)
// can be classified as EXTERIOR, SINGULAR, REGULAR
// or INTERIOR with respect to the alpha shape.
// In GENERAL mode a $k$ simplex is REGULAR if it is on the boundary
// of the alpha_complex and belongs to a $k+1$ simplex in the complex
// and it is SINGULAR simplex if it is a boundary simplex tht is not
// included in a $k+1$ simplex of the complex.
// In REGULARIZED mode each k-dimensional simplex of the triangulation
// for (k=0,1,2)
// can be classified as EXTERIOR, REGULAR
// or INTERIOR with respect to the alpha shape.
// A $k$ simplex is REGULAR if it is on the boundary of alpha complex
// and belong to a tetrahedral cell of the complex.
// Roughly, the Alpha_shapes data structure computes and stores,
// for each simplex
// the at most three critical value (alpha_min, alpha_mid and alpha_max)
// which compared to the actual alpha value
// determine the classification of the simplex.
//------------------------- TYPES ------------------------------------
public:
typedef Dt Triangulation;
typedef typename Dt::Geom_traits Gt;
typedef typename Dt::Triangulation_data_structure Tds;
//extra the type used for representing alpha according to ExactAlphaComparisonTag
typedef typename internal::Alpha_nt_selector_3<Gt,ExactAlphaComparisonTag,typename Dt::Weighted_tag>::Type_of_alpha NT;
typedef typename internal::Alpha_nt_selector_3<Gt,ExactAlphaComparisonTag,typename Dt::Weighted_tag>::Compute_squared_radius_3 Compute_squared_radius_3;
typedef NT FT;
typedef typename Gt::FT Coord_type;
//checks whether tags are correctly set in Vertex and Cell classes
CGAL_static_assertion( (boost::is_same<NT,typename Dt::Cell::NT>::value) );
CGAL_static_assertion( (boost::is_same<NT,typename Dt::Vertex::Alpha_status::NT>::value) );
typedef typename Gt::Point_3 Point;
typedef typename Dt::Cell_handle Cell_handle;
typedef typename Dt::Vertex_handle Vertex_handle;
typedef typename Dt::Facet Facet;
typedef typename Dt::Edge Edge;
typedef typename Dt::Cell_circulator Cell_circulator;
typedef typename Dt::Facet_circulator Facet_circulator;
typedef typename Dt::Cell_iterator Cell_iterator;
typedef typename Dt::Facet_iterator Facet_iterator;
typedef typename Dt::Edge_iterator Edge_iterator;
typedef typename Dt::Vertex_iterator Vertex_iterator;
typedef typename Dt::Finite_cells_iterator Finite_cells_iterator;
typedef typename Dt::Finite_facets_iterator Finite_facets_iterator;
typedef typename Dt::Finite_edges_iterator Finite_edges_iterator;
typedef typename Dt::Finite_vertices_iterator Finite_vertices_iterator;
typedef typename Dt::size_type size_type;
typedef typename Dt::Locate_type Locate_type;
typedef typename Dt::Weighted_tag Weighted_tag;
using Dt::dimension;
using Dt::finite_facets_begin;
using Dt::finite_facets_end;
using Dt::finite_edges_begin;
using Dt::finite_edges_end;
using Dt::finite_vertices_begin;
using Dt::finite_vertices_end;
using Dt::finite_cells_begin;
using Dt::finite_cells_end;
using Dt::VERTEX;
using Dt::EDGE;
using Dt::FACET;
using Dt::CELL;
using Dt::OUTSIDE_CONVEX_HULL;
using Dt::OUTSIDE_AFFINE_HULL;
using Dt::vertex_triple_index;
using Dt::is_infinite;
using Dt::is_Gabriel;
using Dt::incident_cells;
using Dt::incident_vertices;
using Dt::incident_facets;
using Dt::locate;
enum Classification_type {EXTERIOR,
SINGULAR,
REGULAR,
INTERIOR};
enum Mode {GENERAL, REGULARIZED};
typedef CGAL::Alpha_status< NT > Alpha_status;
typedef Compact_container<Alpha_status> Alpha_status_container;
typedef typename Alpha_status_container::const_iterator
Alpha_status_const_iterator;
typedef typename Alpha_status_container::iterator
Alpha_status_iterator;
typedef std::vector< NT > Alpha_spectrum;
typedef std::multimap< NT, Cell_handle > Alpha_cell_map;
typedef std::multimap< NT, Facet> Alpha_facet_map;
typedef std::multimap< NT, Edge > Alpha_edge_map;
typedef std::multimap< NT, Vertex_handle> Alpha_vertex_map;
typedef std::pair<Vertex_handle, Vertex_handle> Vertex_handle_pair;
typedef std::map<Vertex_handle_pair,Alpha_status_iterator> Edge_alpha_map;
typedef typename std::list< Vertex_handle >::iterator
Alpha_shape_vertices_iterator;
typedef typename std::list< Facet >::iterator
Alpha_shape_facets_iterator;
//test if a cell is exterior to the alphashape
class Exterior_cell_test{
const Alpha_shape_3 * _as;
public:
Exterior_cell_test() {}
Exterior_cell_test(const Alpha_shape_3 * as) {_as = as;}
bool operator() ( const Finite_cells_iterator& fci) const {
return _as->classify(fci) == EXTERIOR ;
}
};
typedef Filter_iterator< Finite_cells_iterator, Exterior_cell_test>
Alpha_shape_cells_iterator;
typedef typename Alpha_spectrum::const_iterator Alpha_iterator;
// An iterator that allow to traverse the sorted sequence of
// different alpha-values. The iterator is bidirectional and
// non-mutable. Its value-type is NT
private:
typedef Unique_hash_map<Cell_handle, bool > Marked_cell_set;
private:
NT _alpha;
NT _alpha_solid;
Mode _mode;
mutable bool use_vertex_cache;
mutable bool use_facet_cache;
// only finite facets and simplices are inserted into the maps
Alpha_cell_map alpha_cell_map;
Alpha_facet_map alpha_min_facet_map;
Alpha_edge_map alpha_min_edge_map;
Alpha_vertex_map alpha_min_vertex_map;
Alpha_spectrum alpha_spectrum;
Alpha_status_container alpha_status_container;
Edge_alpha_map edge_alpha_map;
//deprecated - for backward compatibility
mutable std::list< Vertex_handle > alpha_shape_vertices_list;
mutable std::list< Facet > alpha_shape_facets_list;
//------------------------- CONSTRUCTORS ------------------------------
public:
// Introduces an empty alpha-shape `A' for a
// alpha-value `alpha'.
Alpha_shape_3(NT alpha = 0,
Mode m = REGULARIZED)
: _alpha(alpha), _mode(m),
use_vertex_cache(false), use_facet_cache(false)
{}
Alpha_shape_3(Dt& dt, NT alpha = 0, Mode m = REGULARIZED)
:_alpha(alpha), _mode(m),
use_vertex_cache(false), use_facet_cache(false)
{
Dt::swap(dt);
if (dimension() == 3) initialize_alpha();
}
// Introduces an alpha-shape `A' for the alpha-value
// `alpha' that is initialized with the points in the range
// from first to last
template < class InputIterator >
Alpha_shape_3(const InputIterator& first,
const InputIterator& last,
const NT& alpha = 0,
Mode m = REGULARIZED)
: _alpha(alpha), _mode(m),
use_vertex_cache(false), use_facet_cache(false)
{
Dt::insert(first, last);
if (dimension() == 3) initialize_alpha();
}
public:
//----------------------- OPERATIONS ---------------------------------
template < class InputIterator >
std::ptrdiff_t make_alpha_shape(const InputIterator& first,
const InputIterator& last)
{
clear();
size_type n = Dt::insert(first, last);
if (dimension() == 3){
initialize_alpha();
}
return n;
}
// Introduces an alpha-shape `A'
// that is initialized with the points in the range
// from first to last
private :
//--------------------- INITIALIZATION OF PRIVATE MEMBERS -----------
// called with reinitialize=false on first initialization
// reinitialize=true when switching the mode.
void initialize_alpha_cell_map();
void initialize_alpha_facet_maps(bool reinitialize = false);
void initialize_alpha_edge_maps(bool reinitialize = false);
void initialize_alpha_vertex_maps(bool reinitialize = false);
void initialize_alpha_spectrum();
void initialize_alpha(bool reinitialize = false) {
if (reinitialize == false) initialize_alpha_cell_map();
initialize_alpha_facet_maps(reinitialize);
initialize_alpha_edge_maps(reinitialize);
initialize_alpha_vertex_maps(reinitialize);
initialize_alpha_spectrum();
}
private :
Vertex_handle_pair
make_vertex_handle_pair( Vertex_handle v1, Vertex_handle v2) const {
return v1 < v2 ? std::make_pair(v1,v2)
: std::make_pair(v2,v1);
}
// the version to be used with Tag_true is templated to avoid
// instanciation through explicit instantiation of the whole class
void set_alpha_min_of_vertices(Tag_false)
{
for( Finite_vertices_iterator vit = finite_vertices_begin();
vit != finite_vertices_end(); ++vit){
Alpha_status* as = vit->get_alpha_status();
as->set_is_Gabriel(true);
as->set_alpha_min(NT(0));
}
// insert a single vertex into the map because they all have the
// same alpha_min value
alpha_min_vertex_map.insert(typename Alpha_vertex_map::value_type
( NT(0), finite_vertices_begin()));
}
template <class Tag>
void set_alpha_min_of_vertices(Tag)
{
for( Finite_vertices_iterator vit = finite_vertices_begin();
vit != finite_vertices_end(); ++vit) {
if (is_Gabriel(vit)) {
Alpha_status* as = vit->get_alpha_status();
as->set_is_Gabriel(true);
as->set_alpha_min(squared_radius(vit));
alpha_min_vertex_map.insert(typename Alpha_vertex_map::value_type
(as->alpha_min(),vit));
}
}
return;
}
//---------------------------------------------------------------------
public:
void clear()
{
// clears the structure
alpha_status_container.clear();
Dt::clear();
alpha_cell_map.clear();
alpha_min_facet_map.clear();
alpha_min_edge_map.clear();
alpha_min_vertex_map.clear();
alpha_spectrum.clear();
alpha_shape_vertices_list.clear();
alpha_shape_facets_list.clear();
use_vertex_cache = false;
use_facet_cache = false;
}
//---------------------------------------------------------------------
public:
NT set_alpha(const NT& alpha)
// Sets the alpha-value to `alpha'. Precondition: `alpha' >= 0.
// Returns the previous alpha
{
NT previous_alpha = _alpha;
_alpha = alpha;
use_vertex_cache = false;
use_facet_cache = false;
return previous_alpha;
}
const NT& get_alpha() const
// Returns the current alpha-value.
{
return _alpha;
}
const NT& get_nth_alpha(int n) const
// Returns the n-th alpha-value.
// n < size()
{
CGAL_triangulation_assertion( n > 0 &&
n <= static_cast<int>(alpha_spectrum.size()) );
return alpha_spectrum[n-1];
}
size_type number_of_alphas() const
// Returns the number of different alpha-values
{
return alpha_spectrum.size();
}
const Edge_alpha_map* get_edge_alpha_map() const
{
return &edge_alpha_map;
}
//---------------------------------------------------------------------
private:
// the dynamic version is not yet implemented
// desactivate the tetrahedralization member functions
void insert(const Point& /*p*/) {}
// Inserts point `p' in the alpha shape and returns the
// corresponding vertex of the underlying Delaunay tetrahedralization.
// If point `p' coincides with an already existing vertex, this
// vertex is returned and the alpha shape remains unchanged.
// Otherwise, the vertex is inserted in the underlying Delaunay
// tetrahedralization and the associated intervals are updated.
void remove(Vertex_handle /*v*/) {}
// Removes the vertex from the underlying Delaunay tetrahedralization.
// The created hole is retriangulated and the associated intervals
// are updated.
//---------------------------------------------------------------------
public:
Mode set_mode(Mode mode = REGULARIZED )
// Sets `A' to its general or regularized version. Returns the
// previous mode.
{
Mode previous_mode = _mode;
_mode = mode;
if (previous_mode != _mode) {
initialize_alpha(true);
use_vertex_cache = false;
use_facet_cache = false;
}
return previous_mode;
}
Mode get_mode() const
// Returns whether `A' is general or regularized.
{
return _mode;
}
//---------------------------------------------------------------------
private:
void update_alpha_shape_vertex_list() const;
void update_alpha_shape_facet_list() const;
//---------------------------------------------------------------------
public:
Alpha_shape_vertices_iterator alpha_shape_vertices_begin() const
{
if(!use_vertex_cache) update_alpha_shape_vertex_list();
return alpha_shape_vertices_list.begin();
}
Alpha_shape_vertices_iterator Alpha_shape_vertices_begin() const
{
return alpha_shape_vertices_begin();
}
//---------------------------------------------------------------------
Alpha_shape_vertices_iterator alpha_shape_vertices_end() const
{
return alpha_shape_vertices_list.end();
}
Alpha_shape_vertices_iterator Alpha_shape_vertices_end() const
{
return alpha_shape_vertices_end();
}
//---------------------------------------------------------------------
Alpha_shape_facets_iterator alpha_shape_facets_begin() const
{
if(! use_facet_cache) update_alpha_shape_facet_list();
return alpha_shape_facets_list.begin();
}
Alpha_shape_facets_iterator Alpha_shape_facets_begin() const
{
return alpha_shape_facets_begin();
}
//---------------------------------------------------------------------
Alpha_shape_facets_iterator alpha_shape_facets_end() const
{
return alpha_shape_facets_list.end();
}
Alpha_shape_facets_iterator Alpha_shape_facets_end() const
{
return alpha_shape_facets_end();
}
Alpha_shape_cells_iterator alpha_shape_cells_begin() const
{
return CGAL::filter_iterator(finite_cells_end(),
Exterior_cell_test(this),
finite_cells_begin());
}
Alpha_shape_cells_iterator alpha_shape_cells_end() const
{
return CGAL::filter_iterator(finite_cells_end(),
Exterior_cell_test(this));
}
public:
// Traversal of the alpha-Values
//
// The alpha shape class defines an iterator that allows to
// visit the sorted sequence of alpha-values. This iterator is
// non-mutable and bidirectional. Its value type is NT.
Alpha_iterator alpha_begin() const { return alpha_spectrum.begin(); }
Alpha_iterator alpha_end() const {return alpha_spectrum.end();}
Alpha_iterator alpha_find(const NT& alpha) const
// Returns an iterator pointing to an element with alpha-value
// `alpha', or the corresponding past-the-end iterator if such an
// element is not found.
{
return std::find(alpha_spectrum.begin(),
alpha_spectrum.end(),
alpha);
}
Alpha_iterator alpha_lower_bound(const NT& alpha) const
// Returns an iterator pointing to the first element with
// alpha-value not less than `alpha'.
{
return std::lower_bound(alpha_spectrum.begin(),
alpha_spectrum.end(),
alpha);
}
Alpha_iterator alpha_upper_bound(const NT& alpha) const
// Returns an iterator pointing to the first element with
// alpha-value greater than `alpha'.
{
return std::upper_bound(alpha_spectrum.begin(),
alpha_spectrum.end(),
alpha);
}
//--------------------- PREDICATES -----------------------------------
public:
void compute_edge_status( const Cell_handle& c,
int i,
int j,
Alpha_status& as) const;
Classification_type classify(const Alpha_status& as, const NT& alpha) const;
Classification_type classify(const Alpha_status* as, const NT& alpha) const;
Classification_type classify(const Alpha_status_const_iterator as,
const NT& alpha) const;
public:
Classification_type classify(const Point& p) const
{
return classify(p, get_alpha());
}
Classification_type classify(const Point& p,
const NT& alpha) const
// Classifies a point `p' with respect to `A'.
{
Locate_type type;
int i, j;
Cell_handle pCell = locate(p, type, i, j);
switch (type)
{
case VERTEX : return classify(pCell->vertex(i), alpha);
case EDGE : return classify(pCell, i, j, alpha);
case FACET : return classify(pCell, i, alpha);
case CELL : return classify(pCell, alpha);
case OUTSIDE_CONVEX_HULL : return EXTERIOR;
case OUTSIDE_AFFINE_HULL : return EXTERIOR;
default : return EXTERIOR;
};
}
//---------------------------------------------------------------------
Classification_type classify(const Cell_handle& s) const
// Classifies the cell `f' of the underlying Delaunay
// tetrahedralization with respect to `A'.
{
return classify(s, get_alpha());
}
Classification_type classify(const Cell_handle& s,
const NT& alpha) const
// Classifies the cell `f' of the underlying Delaunay
// tetrahedralization with respect to `A'.
// s->radius == alpha => f interior
{
if (is_infinite(s)) return EXTERIOR;
return (s->get_alpha() <= alpha) ? INTERIOR : EXTERIOR;
}
//---------------------------------------------------------------------
Classification_type classify(const Facet& f) const
{
return classify(f.first, f.second, get_alpha());
}
Classification_type classify(const Cell_handle& s, int i) const
{
return classify(s, i, get_alpha());
}
Classification_type classify(const Facet& f, const NT& alpha) const
{
return classify(f.first, f.second, alpha);
}
Classification_type classify(const Cell_handle& s,
int i,
const NT& alpha) const;
// Classifies the face `f' of the underlying Delaunay
// tetrahedralization with respect to `A'.
//---------------------------------------------------------------------
Classification_type classify(const Edge& e) const
{
return classify(e.first, e.second, e.third, get_alpha());
}
Classification_type classify(const Cell_handle& s,
int i,
int j) const
{
return classify(s, i, j, get_alpha());
}
Classification_type classify(const Edge& e,
const NT& alpha ) const
{
return classify(e.first, e.second, e.third, alpha);
}
Classification_type classify(const Cell_handle& s,
int i,
int j,
const NT& alpha) const;
// Classifies the edge `e' of the underlying Delaunay
// tetrahedralization with respect to `A'.
//---------------------------------------------------------------------
Classification_type classify(const Vertex_handle& v) const
{
return classify(v, get_alpha());
}
Classification_type classify(const Vertex_handle& v,
const NT& alpha) const;
// Classifies the vertex `v' of the underlying Delaunay
// tetrahedralization with respect to `A'.
//--------------------- NB COMPONENTS ---------------------------------
size_type
number_solid_components() const
{
return number_of_solid_components(get_alpha());
}
size_type
number_of_solid_components() const
{
return number_of_solid_components(get_alpha());
}
size_type
number_solid_components(const NT& alpha) const
{
return number_of_solid_components(alpha);
}
size_type
number_of_solid_components(const NT& alpha) const;
// Determine the number of connected solid components
// takes time O(#alpha_shape) amortized if STL_HASH_TABLES
// O(#alpha_shape log n) otherwise
private:
void traverse(Cell_handle pCell,
Marked_cell_set& marked_cell_set,
const NT alpha) const;
//----------------------------------------------------------------------
public:
Alpha_iterator find_optimal_alpha(size_type nb_components) const;
// find the minimum alpha that satisfies the properties
// (1) all data points are on the boundary of some 3d component
// or in its interior
// (2) the nb of solid components is equal or less than nb_component
NT find_alpha_solid() const;
// compute the minumum alpha such that all data points
// are either on the boundary or in the interior
// not necessarily connected
// starting point for searching
// takes O(#alpha_shape) time
//------------------- GEOMETRIC PRIMITIVES ----------------------------
private:
NT squared_radius(const Cell_handle& s) const
{
return Compute_squared_radius_3()(*this)(
this->point(s,0), this->point(s,1),
this->point(s,2), this->point(s,3));
}
NT squared_radius(const Cell_handle& s, const int& i) const
{
return Compute_squared_radius_3()(*this) (
this->point(s,vertex_triple_index(i,0)),
this->point(s,vertex_triple_index(i,1)),
this->point(s,vertex_triple_index(i,2)) );
}
NT squared_radius(const Facet& f) const {
return squared_radius(f.first, f.second);
}
NT squared_radius(const Cell_handle& s,
const int& i, const int& j) const
{
return Compute_squared_radius_3()(*this)(
this->point(s,i), this->point(s,j));
}
NT squared_radius(const Edge& e) const {
return squared_radius(e.first,e.second,e.third);
}
NT squared_radius(const Vertex_handle& v) const {
return Compute_squared_radius_3()(*this)(v->point());
}
//---------------------------------------------------------------------
private:
// prevent default copy constructor and default assigment
Alpha_shape_3(const Alpha_shape_3&);
void operator=(const Alpha_shape_3&);
//---------------------------------------------------------------------
public:
#ifdef CGAL_USE_GEOMVIEW
void show_alpha_shape_faces(Geomview_stream &gv) const;
#endif
// to Debug
void print_maps() const;
void print_alphas() const;
void print_alpha_status( const Alpha_status& as) const;
// To extract the alpha_shape faces for a given alpha value
template<class OutputIterator>
OutputIterator get_alpha_shape_cells(OutputIterator it,
Classification_type type,
const NT& alpha) const
{
Finite_cells_iterator cit = finite_cells_begin();
for( ; cit != finite_cells_end() ; ++cit){
if (classify(cit, alpha) == type) *it++ = Cell_handle(cit);
}
return it;
}
template<class OutputIterator>
OutputIterator get_alpha_shape_facets(OutputIterator it,
Classification_type type,
const NT& alpha) const
{
Finite_facets_iterator fit = finite_facets_begin();
for( ; fit != finite_facets_end() ; ++fit){
if (classify(*fit, alpha) == type) *it++ = *fit;
}
return it;
}
template<class OutputIterator>
OutputIterator get_alpha_shape_edges(OutputIterator it,
Classification_type type,
const NT& alpha) const
{
Finite_edges_iterator eit = finite_edges_begin();
for( ; eit != finite_edges_end() ; ++eit){
if (classify(*eit, alpha) == type) *it++ = *eit;
}
return it;
}
template<class OutputIterator>
OutputIterator get_alpha_shape_vertices(OutputIterator it,
Classification_type type,
const NT& alpha) const
{
Finite_vertices_iterator vit = finite_vertices_begin();
for( ; vit != finite_vertices_end() ; ++vit){
if (classify(vit, alpha) == type) *it++ = Vertex_handle(vit);
}
return it;
}
template<class OutputIterator>
OutputIterator get_alpha_shape_cells(OutputIterator it,
Classification_type type) const
{ return get_alpha_shape_cells(it, type, get_alpha());}
template<class OutputIterator>
OutputIterator get_alpha_shape_facets(OutputIterator it,
Classification_type type) const
{ return get_alpha_shape_facets(it, type, get_alpha());}
template<class OutputIterator>
OutputIterator get_alpha_shape_edges(OutputIterator it,
Classification_type type) const
{ return get_alpha_shape_edges(it, type, get_alpha());}
template<class OutputIterator>
OutputIterator get_alpha_shape_vertices(OutputIterator it,
Classification_type type) const
{ return get_alpha_shape_vertices(it, type, get_alpha());}
template<class OutputIterator>
OutputIterator filtration(OutputIterator it) const
// scan the alpha_cell_map, alpha_min_facet_map, alpha_min_edge_map
// and alpha_min_vertex in GENERAL mode
// only alpha_cell_map in REGULARIZED mode
// and output all the faces in order of alpha value of their appearing
// in the alpha complexe
{
typename Alpha_cell_map::const_iterator cit ;
typename Alpha_facet_map::const_iterator fit ;
typename Alpha_edge_map::const_iterator eit ;
typename Alpha_vertex_map::const_iterator vit;
if (get_mode() == GENERAL) {
cit = alpha_cell_map.begin();
fit = alpha_min_facet_map.begin();
eit = alpha_min_edge_map.begin();
vit = alpha_min_vertex_map.begin();
}
else { //mode==REGULARIZED do not scan maps of Gabriel elements
cit = alpha_cell_map.begin();
fit = alpha_min_facet_map.end();
eit = alpha_min_edge_map.end();
vit = alpha_min_vertex_map.end();
}
// sets to avoid multiple output of the same face
// as a regular subfaces of different faces
std::set<Facet> facet_set;
std::set<Vertex_handle_pair> edge_set;
std::set<Vertex_handle> vertex_set;
NT alpha_current = 0;
while (cit != alpha_cell_map.end()) {
if ( vit != alpha_min_vertex_map.end()
&& (eit == alpha_min_edge_map.end() || (vit->first <= eit->first))
&& (fit == alpha_min_facet_map.end()|| (vit->first <= fit->first))
&& (cit == alpha_cell_map.end() || (vit->first <= cit->first)))
{
//advance on vit
filtration_set_management(vit, alpha_current,
facet_set, edge_set, vertex_set);
filtration_output(vit->first, vit->second, it);
vit++;
}
if ( eit != alpha_min_edge_map.end()
&& ( fit == alpha_min_facet_map.end() || (eit->first <= fit->first) )
&& ( cit == alpha_cell_map.end() || (eit->first <= cit->first) )
&& ( vit == alpha_min_vertex_map.end()|| (vit->first > eit->first) )
) { //advance on eit
filtration_set_management(eit, alpha_current,
facet_set, edge_set, vertex_set);
filtration_output(eit->first, eit->second, it, vertex_set);
eit++;
}
if ( fit != alpha_min_facet_map.end()
&& (cit == alpha_cell_map.end() || (fit->first <= cit->first))
&& (eit == alpha_min_edge_map.end() || (eit->first > fit->first))
&& (vit == alpha_min_vertex_map.end()|| (vit->first > fit->first))
) { //advance on fit
filtration_set_management(fit, alpha_current,
facet_set, edge_set, vertex_set);
filtration_output(fit->first, fit->second, it,
edge_set, vertex_set);
fit++;
}
if ( cit != alpha_cell_map.end()
&& (fit == alpha_min_facet_map.end() || (fit->first > cit->first) )
&& (eit == alpha_min_edge_map.end() || (eit->first > cit->first) )
&& (vit == alpha_min_vertex_map.end()|| (vit->first > cit->first) )
) { //advance on cit
filtration_set_management(cit, alpha_current,
facet_set, edge_set, vertex_set);
filtration_output(cit->first, cit->second, it,
facet_set, edge_set, vertex_set);
cit++;
}
}
return it;
}
private:
template<class Alpha_face_iterator>
void
filtration_set_management ( Alpha_face_iterator afit,
NT& alpha_current,
std::set<Facet>& facet_set,
std::set<Vertex_handle_pair>& edge_set,
std::set<Vertex_handle>& vertex_set) const
{
if (afit->first != alpha_current) { //new alpha_value
alpha_current = afit->first;
facet_set.clear();
edge_set.clear();
vertex_set.clear();
}
return;
}
template<class OutputIterator>
OutputIterator
filtration_output( const NT & /*alpha*/,
Vertex_handle vh,
OutputIterator it,
Tag_true) const
{
it++ = make_object(vh);
//std::cerr << "filtration " << alpha << " \t VERTEX " << std::endl;
return it;
}
template<class OutputIterator>
OutputIterator
filtration_output( const NT& /*alpha*/,
Vertex_handle vh,
OutputIterator it,
Tag_false) const
{
// when Delaunay, the alpha_min_vertex_map contains a single vertex
// because all vertices are Gabriel with the same alpha_min=0
// this affects only the GENERAL mode
if (get_mode() == GENERAL){
Finite_vertices_iterator vit=finite_vertices_begin();
for( ; vit != finite_vertices_end(); vit++) {
it++ = make_object( Vertex_handle(vit));
}
}
else {
it++ = make_object(vh);
}
//std::cerr << "filtration " << alpha << " \t VERTEX " << std::endl;
return it;
}
template<class OutputIterator>
OutputIterator
filtration_output( const NT& alpha,
Vertex_handle vh,
OutputIterator it) const
{
return filtration_output(alpha, vh, it, Weighted_tag());
}
template<class OutputIterator>
OutputIterator
filtration_output( const NT& alpha,
Edge e,
OutputIterator it,
std::set<Vertex_handle>& vertex_set) const
{
Vertex_handle vh[] = {e.first->vertex(e.second),
e.first->vertex(e.third)};
for(int i=0; i<2; i++) {
Alpha_status* as = vh[i]->get_alpha_status();
if ( (get_mode()== REGULARIZED || !as->is_Gabriel())
&& as->alpha_mid() == alpha
&& vertex_set.find(vh[i]) == vertex_set.end() ) {
filtration_output( alpha, vh[i], it);
vertex_set.insert(vh[i]);
}
}
it++ = make_object(e);
//std::cerr << "filtration " << alpha << " \t EDGE " << std::endl;
return it;
}
template<class OutputIterator>
OutputIterator
filtration_output( const NT& alpha,
Facet f,
OutputIterator it,
std::set<Vertex_handle_pair>& edge_set,
std::set<Vertex_handle>& vertex_set ) const
{
Cell_handle c = f.first;
int facet_index = f.second;
for(int k=0; k<3; k++) {
int i = vertex_triple_index(facet_index, k );
int j = vertex_triple_index(facet_index, this->ccw(k));
Alpha_status as;
Vertex_handle_pair
vhp = make_vertex_handle_pair(c->vertex(i),c->vertex(j));
if (get_mode() == GENERAL) {
as = *(edge_alpha_map.find(vhp)->second);
}
else{ //no edge map in REGULARIZED mode - classify on the fly
compute_edge_status( c, i, j, as);
}
if ( (get_mode()== REGULARIZED || !as.is_Gabriel())
&& as.alpha_mid() == alpha
&& edge_set.find(vhp)== edge_set.end() ) {
filtration_output( alpha, make_triple(c,i,j), it, vertex_set);
edge_set.insert(vhp);
}
}
it++ = make_object(f);
//std::cerr << "filtration " << alpha << " \t FACET " << std::endl;
return it;
}
template<class OutputIterator>
OutputIterator
filtration_output( const NT& alpha,
Cell_handle c,
OutputIterator it,
std::set<Facet>& facet_set,
std::set<Vertex_handle_pair>& edge_set,
std::set<Vertex_handle>& vertex_set) const
{
for(int i=0; i<4; i++) {
Alpha_status_iterator as = c->get_facet_status(i);
Facet f = std::make_pair(c,i);
if ((get_mode()== REGULARIZED || !as->is_Gabriel())
&& as->alpha_mid() == alpha
&& facet_set.find(f) == facet_set.end()
&& facet_set.find(std::make_pair(c->neighbor(i),
this->mirror_index(c, i)))
== facet_set.end()) {
filtration_output( alpha, f, it, edge_set, vertex_set);
facet_set.insert(f);
}
}
it++ = make_object(c);
//std::cerr << "filtration " << alpha << " \t CELL " << std::endl;
return it;
}
};
//---------------------------------------------------------------------
//--------------------- MEMBER FUNCTIONS-------------------------------
//---------------------------------------------------------------------
//--------------------- INITIALIZATION OF PRIVATE MEMBERS -------------
template <class Dt,class EACT>
void
Alpha_shape_3<Dt,EACT>::initialize_alpha_cell_map()
{
Finite_cells_iterator cell_it, done = finite_cells_end();
NT alpha ;
for( cell_it = finite_cells_begin(); cell_it != done; ++cell_it) {
alpha = squared_radius(cell_it);
alpha_cell_map.insert(typename Alpha_cell_map::value_type(alpha, cell_it));
// cross references
cell_it->set_alpha(alpha);
}
return;
}
//---------------------------------------------------------------------
template <class Dt,class EACT>
void
Alpha_shape_3<Dt,EACT>::initialize_alpha_facet_maps(bool reinitialize)
{
Finite_facets_iterator fit;
Cell_handle pCell, pNeighbor ;
int i, iNeigh;
Alpha_status_iterator as;
if (!reinitialize) {
NT alpha_max, alpha_mid;
for( fit = finite_facets_begin();
fit != finite_facets_end(); ++fit) {
as = alpha_status_container.insert(Alpha_status());
pCell = fit->first;
i = fit->second;
pNeighbor = pCell->neighbor(i);
iNeigh = pNeighbor->index(pCell);
// not on the convex hull
if(!is_infinite(pCell) && !is_infinite(pNeighbor)) {
NT alpha_Cell = pCell->get_alpha();
NT alpha_Neighbor = pNeighbor->get_alpha();
if ( alpha_Cell < alpha_Neighbor) {
alpha_mid = alpha_Cell;
alpha_max = alpha_Neighbor;
}
else {
alpha_mid = alpha_Neighbor;
alpha_max = alpha_Cell;
}
as->set_is_on_chull(false);
as->set_alpha_mid(alpha_mid);
as->set_alpha_max(alpha_max);
// alpha_mid_facet_map.insert(typename
// Alpha_facet_map::value_type(alpha_mid, *fit));
}
else { // on the convex hull
alpha_mid = !is_infinite(pCell) ? pCell->get_alpha()
: pNeighbor->get_alpha();
as->set_alpha_mid(alpha_mid);
as->set_is_on_chull(true);
}
//cross links
pCell->set_facet_status(i, as);
pNeighbor->set_facet_status(iNeigh,as);
}
}
// initialize alpha_min if mode GENERAL
if(get_mode() == GENERAL && alpha_min_facet_map.empty()) {
//already done if !alpha_min_facet_map.empty()
NT alpha_min;
for( fit = finite_facets_begin();
fit != finite_facets_end(); ++fit) {
as = fit->first->get_facet_status(fit->second);
if (is_Gabriel(*fit)) {
as->set_is_Gabriel(true);
alpha_min = squared_radius(*fit);
as->set_alpha_min(alpha_min);
alpha_min_facet_map.insert(typename
Alpha_facet_map::value_type(alpha_min, *fit));
}
else as->set_is_Gabriel(false);
}
}
return;
}
template <class Dt,class EACT>
void
Alpha_shape_3<Dt,EACT>::initialize_alpha_edge_maps(bool )
{
// alpha_status for edges, edge_alpha_map
// and alpha_mid_edge and alpha_min_edge
// are initialized only in GENERAL mode
if(get_mode() == REGULARIZED) {return;} //no_edge_map in REGULARIZED mode
if ( !edge_alpha_map.empty()) return; // already done
Finite_edges_iterator eit;
Alpha_status_iterator as;
for (eit = finite_edges_begin();
eit != finite_edges_end(); ++eit) {
as = alpha_status_container.insert(Alpha_status());
compute_edge_status(eit->first, eit->second, eit->third, *as);
if ( as->is_Gabriel()) {
alpha_min_edge_map.insert(typename
Alpha_edge_map::value_type(as->alpha_min(),
*eit));
}
//cross links
Vertex_handle_pair
vhp = make_vertex_handle_pair( eit->first->vertex(eit->second),
eit->first->vertex(eit->third));
edge_alpha_map.insert(std::make_pair(vhp, as));
}
return;
}
template <class Dt,class EACT>
void
Alpha_shape_3<Dt,EACT>::initialize_alpha_vertex_maps(bool reinitialize)
{
//for a vertex
// alpha_max = max of alpha values of incident cells
// alpha_mid = min of alpha values of incident cells in REGULAR mode
// = min of alpha values of incidents faces in GENERAL mode
// alpha_min = -squared_radius of weighted point,
// if the vertex is Gabriel set only in GENERAL mode
NT alpha, alpha_mid;
Finite_vertices_iterator vit;
if (reinitialize == false) _alpha_solid = alpha_cell_map.begin()->first;
for( vit = finite_vertices_begin();
vit != finite_vertices_end(); ++vit) {
Alpha_status* as = vit->get_alpha_status();
if (reinitialize == false) {
// set is_on_chull, compute alpha_max
// and alpha_mid (version REGULAR)
// compute _alpha_solid (max of alpha_mid of vertices in REGULAR mode)
as->set_is_on_chull(false);
std::list<Cell_handle> incidents;
incident_cells(static_cast<Vertex_handle>(vit),
back_inserter(incidents));
typename std::list<Cell_handle>::iterator chit=incidents.begin();
if (is_infinite(*chit)) as->set_is_on_chull(true);
while (is_infinite(*chit)) ++chit; //skip infinte cells
alpha = (*chit)->get_alpha();
as->set_alpha_mid(alpha);
as->set_alpha_max(alpha);
++chit;
for( ; chit != incidents.end(); ++chit) {
if (is_infinite(*chit)) as->set_is_on_chull(true);
else {
alpha = (*chit)->get_alpha();
if (alpha < as->alpha_mid()) as->set_alpha_mid(alpha);
if (alpha > as->alpha_max()) as->set_alpha_max(alpha);
}
}
if (as->alpha_mid() > _alpha_solid) _alpha_solid = as->alpha_mid();
}
if (get_mode() == GENERAL) { //reset alpha_mid, set alph_min
std::list<Vertex_handle> incidentv;
incident_vertices(static_cast<Vertex_handle>(vit),
back_inserter(incidentv));
typename std::list<Vertex_handle>::iterator vvit=incidentv.begin();
for( ; vvit != incidentv.end(); ++vvit) {
if (!is_infinite(*vvit)) {
Vertex_handle_pair vhp = make_vertex_handle_pair( *vvit, vit);
Alpha_status_iterator asedge = edge_alpha_map[vhp];
alpha_mid = asedge->is_Gabriel() ? asedge->alpha_min()
: asedge->alpha_mid();
if ( alpha_mid < as->alpha_mid()) as->set_alpha_mid(alpha_mid);
}
}
}
if (get_mode()== REGULARIZED && reinitialize == true) {
// reset alpha_mid
std::list<Cell_handle> incidents;
incident_cells(static_cast<Vertex_handle>(vit),
back_inserter(incidents));
typename std::list<Cell_handle>::iterator chit=incidents.begin();
while (is_infinite(*chit)) ++chit; //skip infinte cells
alpha = (*chit)->get_alpha();
as->set_alpha_mid(alpha);
for( ; chit != incidents.end(); ++chit) {
if (is_infinite(*chit)) as->set_is_on_chull(true);
else {
alpha = (*chit)->get_alpha();
if (alpha < as->alpha_mid()) as->set_alpha_mid(alpha);
}
}
}
}
// set alpha_min in case GENERAL
if (get_mode() == GENERAL && alpha_min_vertex_map.empty()) {
set_alpha_min_of_vertices(Weighted_tag());
}
return;
}
//---------------------------------------------------------------------
template <class Dt,class EACT>
void
Alpha_shape_3<Dt,EACT>::initialize_alpha_spectrum()
// merges the alpha values of alpha_cell_map
// and alpha_min_facet_map alpha_min_edge_map alpha_min_vertex in GENERAL mode
// only alpha_cell_map in REGULARIZED mode
{
typename Alpha_cell_map::iterator cit ;
typename Alpha_facet_map::iterator fit ;
typename Alpha_edge_map::iterator eit ;
typename Alpha_vertex_map::iterator vit;
alpha_spectrum.clear();
if (get_mode() == GENERAL) {
cit = alpha_cell_map.begin();
fit = alpha_min_facet_map.begin();
eit = alpha_min_edge_map.begin();
vit = alpha_min_vertex_map.begin();
alpha_spectrum.reserve(alpha_cell_map.size() +
alpha_min_facet_map.size() +
alpha_min_edge_map.size() +
alpha_min_vertex_map.size());
}
else {
alpha_spectrum.reserve(alpha_cell_map.size());
cit = alpha_cell_map.begin();
fit = alpha_min_facet_map.end();
eit = alpha_min_edge_map.end();
vit = alpha_min_vertex_map.end();
}
while (cit != alpha_cell_map.end() ||
fit != alpha_min_facet_map.end() ||
eit != alpha_min_edge_map.end() ) {
if ( cit != alpha_cell_map.end()
&& ( fit == alpha_min_facet_map.end() || !(fit->first < cit->first) )
&& ( eit == alpha_min_edge_map.end() || !(eit->first < cit->first) )
&& ( vit == alpha_min_vertex_map.end() || !(vit->first < cit->first) )
) { //advance on cit
if (alpha_spectrum.empty() || alpha_spectrum.back() < cit->first){
alpha_spectrum.push_back(cit->first);
}
cit++;
}
if ( fit != alpha_min_facet_map.end()
&& ( cit == alpha_cell_map.end() || !(cit->first < fit->first) )
&& ( eit == alpha_min_edge_map.end() || !(eit->first < fit->first) )
&& ( vit == alpha_min_vertex_map.end() || !(vit->first < fit->first) )
) { //advance on fit
if (alpha_spectrum.empty() || alpha_spectrum.back() < fit->first){
alpha_spectrum.push_back(fit->first);
}
fit++;
}
if ( eit != alpha_min_edge_map.end()
&& ( fit == alpha_min_facet_map.end() || !(fit->first < eit->first) )
&& ( cit == alpha_cell_map.end() || !(cit->first < eit->first) )
&& ( vit == alpha_min_vertex_map.end() || !(vit->first < eit->first) )
) { //advance on eit
if (alpha_spectrum.empty() || alpha_spectrum.back() < eit->first) {
alpha_spectrum.push_back(eit->first);
}
eit++;
}
if ( vit != alpha_min_vertex_map.end()
&& ( fit == alpha_min_facet_map.end() || !(fit->first < vit->first) )
&& ( cit == alpha_cell_map.end() || !(cit->first < vit->first) )
&& ( eit == alpha_min_edge_map.end() || !(eit->first < vit->first) )
) { //advance on vit
if (alpha_spectrum.empty() || alpha_spectrum.back() < vit->first) {
alpha_spectrum.push_back(vit->first);
}
vit++;
}
}
}
//---------------------------------------------------------------------
#if 0
// Obviously not ready yet
template <class Dt,class EACT>
std::istream& operator>>(std::istream& is, const Alpha_shape_3<Dt,EACT>& A)
// Reads a alpha shape from stream `is' and assigns it to
// Unknown creationvariable. Precondition: The extract operator must
// be defined for `Point'.
{}
#endif
//---------------------------------------------------------------------
template <class Dt,class EACT>
std::ostream& operator<<(std::ostream& os, const Alpha_shape_3<Dt,EACT>& A)
// Inserts the alpha shape into the stream `os' as an indexed face set.
// Precondition: The insert operator must be defined for `Point'
{
typedef Alpha_shape_3<Dt,EACT> AS;
typedef typename AS::size_type size_type;
typedef typename AS::Vertex_handle Vertex_handle;
typedef typename AS::Cell_handle Cell_handle;
typedef typename AS::Alpha_shape_vertices_iterator
Alpha_shape_vertices_iterator;
typedef typename AS::Alpha_shape_facets_iterator
Alpha_shape_facets_iterator;
Unique_hash_map< Vertex_handle, size_type > V;
size_type number_of_vertices = 0;
Alpha_shape_vertices_iterator vit;
for( vit = A.alpha_shape_vertices_begin();
vit != A.alpha_shape_vertices_end();
++vit) {
V[*vit] = number_of_vertices++;
os << (*vit)->point() << std::endl;
}
Cell_handle c;
int i;
Alpha_shape_facets_iterator fit;
for( fit = A.alpha_shape_facets_begin();
fit != A.alpha_shape_facets_end();
++fit) {
c = fit->first;
i = fit->second;
// the following ensures that regular facets are output
// in ccw order
if (A.classify(*fit) == AS::REGULAR && (A.classify(c) == AS::INTERIOR)){
c = c->neighbor(i);
i = c->index(fit->first);
}
int i0 = Triangulation_utils_3::vertex_triple_index(i,0);
int i1 = Triangulation_utils_3::vertex_triple_index(i,1);
int i2 = Triangulation_utils_3::vertex_triple_index(i,2);
os << V[c->vertex(i0)] << ' '
<< V[c->vertex(i1)] << ' '
<< V[c->vertex(i2)] << std::endl;
}
return os;
}
//---------------------------------------------------------------------
template <class Dt,class EACT>
void
Alpha_shape_3<Dt,EACT>::update_alpha_shape_vertex_list() const
{
alpha_shape_vertices_list.clear();
use_vertex_cache = true;
std::back_insert_iterator<std::list< Vertex_handle > >
it = back_inserter(alpha_shape_vertices_list);
get_alpha_shape_vertices(it, REGULAR);
if (get_mode()==GENERAL) get_alpha_shape_vertices(it, SINGULAR);
return;
}
//---------------------------------------------------------------------
template <class Dt,class EACT>
void
Alpha_shape_3<Dt,EACT>::update_alpha_shape_facet_list() const
{
alpha_shape_facets_list.clear();
use_facet_cache = true;
// Writes the faces of the alpha shape `A' for the current 'alpha'-value
// to the container where 'out' refers to.
std::back_insert_iterator<std::list< Facet> >
it = back_inserter(alpha_shape_facets_list);
get_alpha_shape_facets(it, REGULAR);
if (get_mode()==GENERAL) get_alpha_shape_facets(it, SINGULAR);
return;
}
//---------------------------------------------------------------------
template <class Dt,class EACT>
typename Alpha_shape_3<Dt,EACT>::Classification_type
Alpha_shape_3<Dt,EACT>::classify(const Alpha_status& as,
const NT& alpha) const
{
//tetrahedra with circumradius=alpha are considered inside
if ( !as.is_on_chull() && alpha >= as.alpha_max()) return INTERIOR;
else if ( alpha >= as.alpha_mid()) return REGULAR;
else if ( get_mode() == GENERAL &&
as.is_Gabriel() &&
alpha >= as.alpha_min()) return SINGULAR;
else return EXTERIOR;
}
template <class Dt,class EACT>
typename Alpha_shape_3<Dt,EACT>::Classification_type
Alpha_shape_3<Dt,EACT>::classify(const Alpha_status* as,
const NT& alpha) const
{
//tetrahedra with circumradius=alpha are considered inside
if ( !as->is_on_chull() && alpha >= as->alpha_max()) return INTERIOR;
else if ( alpha >= as->alpha_mid()) return REGULAR;
else if ( get_mode() == GENERAL &&
as->is_Gabriel() &&
alpha >= as->alpha_min()) return SINGULAR;
else return EXTERIOR;
}
template <class Dt,class EACT>
typename Alpha_shape_3<Dt,EACT>::Classification_type
Alpha_shape_3<Dt,EACT>::classify(Alpha_status_const_iterator as,
const NT& alpha) const
{
return classify(&(*as), alpha);
}
template <class Dt,class EACT>
typename Alpha_shape_3<Dt,EACT>::Classification_type
Alpha_shape_3<Dt,EACT>::classify(const Cell_handle& s,
int i,
const NT& alpha) const
// Classifies the face `f' of the underlying Delaunay
// tetrahedralization with respect to `A'.
{
if (is_infinite(s,i)) return EXTERIOR;
Alpha_status_iterator as = s->get_facet_status(i);
return classify(as, alpha);
}
template <class Dt,class EACT>
typename Alpha_shape_3<Dt,EACT>::Classification_type
Alpha_shape_3<Dt,EACT>::classify(const Cell_handle& c,
int i,
int j,
const NT& alpha) const
// Classifies the edge `e' of the underlying Delaunay
// tetrahedralization with respect to `A'.
{
if (is_infinite(c, i, j)) return EXTERIOR;
if (get_mode() == GENERAL) {
Alpha_status_iterator asit;
Vertex_handle_pair
vhp=make_vertex_handle_pair(c->vertex(i),c->vertex(j));
asit = edge_alpha_map.find(vhp)->second;
return classify(asit,alpha);
}
//no edge map in REGULARIZED mode - classify on the fly
Alpha_status as;
compute_edge_status( c, i, j, as);
return classify(as, alpha);
}
template <class Dt,class EACT>
void
Alpha_shape_3<Dt,EACT>::
compute_edge_status( const Cell_handle& c,
int i,
int j,
Alpha_status& as) const
{
Facet_circulator fcirc, done;
Alpha_status_iterator asf;
NT alpha;
as.set_is_on_chull(false);
Cell_circulator ccirc, last;
ccirc = incident_cells(c,i,j);
last=ccirc;
while (is_infinite(ccirc) ) ++ccirc; //skip infinite incident cells
alpha = (*ccirc).get_alpha();
as.set_alpha_mid(alpha); // initialise as.alpha_mid to alpha value of an incident cell
as.set_alpha_max(alpha); // same for as.alpha_max
while (++ccirc != last)
{
if (!is_infinite(ccirc)) {
alpha = (*ccirc).get_alpha();
if (alpha < as.alpha_mid())
as.set_alpha_mid(alpha);
if ( ! as.is_on_chull()) {
if( as.alpha_max() < alpha)
as.set_alpha_max( alpha );
}
}
}
fcirc = incident_facets(c,i,j);
done = fcirc;
do {
if (!is_infinite(*fcirc)) {
asf = (*fcirc).first->get_facet_status((*fcirc).second);
if (get_mode() == GENERAL && asf->is_Gabriel()){
alpha = asf->alpha_min();
if (alpha < as.alpha_mid()) as.set_alpha_mid(alpha);
}
if (asf->is_on_chull())
as.set_is_on_chull(true);
}
} while (++fcirc != done);
// initialize alphamin
if ( get_mode() == GENERAL){
if (is_Gabriel(c,i,j)) {
alpha = squared_radius(c,i,j);
as.set_is_Gabriel(true);
as.set_alpha_min(alpha);
}
else as.set_is_Gabriel(false);
}
}
//---------------------------------------------------------------------
template <class Dt,class EACT>
typename Alpha_shape_3<Dt,EACT>::Classification_type
Alpha_shape_3<Dt,EACT>::classify(const Vertex_handle& v,
const NT& alpha) const
// Classifies the vertex `v' of the underlying Delaunay
// tetrahedralization with respect to `A'.
{
if (is_infinite(v)) return EXTERIOR;
Alpha_status* as = v->get_alpha_status();
return classify(as, alpha);
}
//--------------------- NB COMPONENTS ---------------------------------
template <class Dt,class EACT>
typename Alpha_shape_3<Dt,EACT>::size_type
Alpha_shape_3<Dt,EACT>::number_of_solid_components(const NT& alpha) const
// Determine the number of connected solid components
// takes time O(#alpha_shape) amortized if STL_HASH_TABLES
// O(#alpha_shape log n) otherwise
{
typedef typename Marked_cell_set::Data Data;
Marked_cell_set marked_cell_set(false);
Finite_cells_iterator cell_it, done = finite_cells_end();
size_type nb_solid_components = 0;
// only finite simplices
for( cell_it = finite_cells_begin(); cell_it != done; ++cell_it)
{
Cell_handle pCell = cell_it;
CGAL_triangulation_assertion(pCell != NULL);
if (classify(pCell, alpha) == INTERIOR){
Data& data = marked_cell_set[pCell];
if(data == false) {
// we traverse only interior simplices
data = true;
traverse(pCell, marked_cell_set, alpha);
nb_solid_components++;
}
}
}
return nb_solid_components;
}
template <class Dt,class EACT>
void Alpha_shape_3<Dt,EACT>::traverse(Cell_handle pCell,
Marked_cell_set& marked_cell_set,
const NT alpha) const
{
typedef typename Marked_cell_set::Data Data;
std::list<Cell_handle> cells;
cells.push_back(pCell);
Cell_handle pNeighbor;
while(! cells.empty()){
pCell = cells.back();
cells.pop_back();
for (int i=0; i<=3; i++)
{
pNeighbor = pCell->neighbor(i);
CGAL_triangulation_assertion(pNeighbor != NULL);
if (classify(pNeighbor, alpha) == INTERIOR){
Data& data = marked_cell_set[pNeighbor];
if(data == false){
data = true;
cells.push_back(pNeighbor);
}
}
}
}
}
//----------------------------------------------------------------------
template <class Dt,class EACT>
typename Alpha_shape_3<Dt,EACT>::Alpha_iterator
Alpha_shape_3<Dt,EACT>::find_optimal_alpha(size_type nb_components) const
// find the minimum alpha that satisfies the properties
// (1) nb_components solid components <= nb_components
// (2) all data points on the boundary or in its interior
{
NT alpha = find_alpha_solid();
// from this alpha on the alpha_solid satisfies property (2)
Alpha_iterator first = alpha_lower_bound(alpha);
if (number_of_solid_components(alpha) == nb_components)
{
// if ((first+1) < alpha_end())
// return (first+1);
// else
return first;
}
// do binary search on the alpha values
// number_of_solid_components() is a monotone function
// if we start with find_alpha_solid
Alpha_iterator last = alpha_end();
Alpha_iterator middle;
std::ptrdiff_t len = last - first - 1;
std::ptrdiff_t half;
while (len > 0)
{
half = len / 2;
middle = first + half;
/* //#ifdef DEBUG */
/* std::cerr << "first : " << *first */
/* << " last : " */
/* << ((first+len != last) ? *(first+len) : *(last-1)) */
/* << " mid : " << *middle */
/* << " nb comps : " << number_of_solid_components(*middle) */
/* << std::endl; */
/* //#endif // DEBUG */
if (number_of_solid_components(*middle) > nb_components)
{
first = middle + 1;
len = len - half -1;
}
else // number_of_solid_components(*middle) <= nb_components
{
len = half;
}
}
/* std::cerr << "a la fin " << std::endl */
/* << "first : " << *first */
/* << " nb comps : " << number_of_solid_components(*first) */
/* << std::endl; */
/* if ((first+1) < alpha_end()) */
/* std::cerr << "first+1 " << *(first+1) */
/* << " nb comps : " << number_of_solid_components(*(first+1)) */
/* << std::endl; */
/* std::cerr << std::endl; */
if (number_of_solid_components(*first) <= nb_components ) return first;
else return first+1;
}
//----------------------------------------------------------------------
template <class Dt,class EACT>
typename Alpha_shape_3<Dt,EACT>::NT
Alpha_shape_3<Dt,EACT>::find_alpha_solid() const
// compute the minumum alpha such that all data points
// are either on the boundary or in the interior
// not necessarily connected
{
return _alpha_solid;
}
// TO DEBUG
template <class Dt,class EACT>
void
Alpha_shape_3<Dt,EACT>::print_maps() const
{
typename Alpha_cell_map::const_iterator cit ;
typename Alpha_facet_map::const_iterator fit ;
typename Alpha_edge_map::const_iterator eit ;
typename Alpha_vertex_map::const_iterator vit;
std::cerr << "size of cell map " << alpha_cell_map.size()
<< std::endl;
std::cerr << "size of facet map " << alpha_min_facet_map.size() <<
std::endl;
std::cerr << "size of edge map " << alpha_min_edge_map.size() <<
std::endl;
std::cerr << "size of vertex map " << alpha_min_vertex_map.size() <<
std::endl;
std::cerr << std::endl;
std::cerr << "alpha_cell_map " << std::endl;
for(cit = alpha_cell_map.begin();
cit != alpha_cell_map.end(); ++cit) {
std::cerr << cit->first << std::endl;
}
std::cerr << std::endl;
std::cerr << "alpha_min_facet_map " << std::endl;
for(fit = alpha_min_facet_map.begin();
fit != alpha_min_facet_map.end(); ++fit) {
std::cerr << fit->first << std::endl;
}
std::cerr << std::endl;
std::cerr << "alpha_min_edge_map " << std::endl;
for(eit = alpha_min_edge_map.begin();
eit != alpha_min_edge_map.end(); ++eit) {
std::cerr << eit->first << std::endl;
}
std::cerr << std::endl;
std::cerr << "alpha_min_vertex_map " << std::endl;
for(vit = alpha_min_vertex_map.begin();
vit != alpha_min_vertex_map.end(); ++vit) {
std::cerr << vit->first << std::endl;
}
std::cerr << std::endl;
}
template <class Dt,class EACT>
void
Alpha_shape_3<Dt,EACT>::print_alphas() const
{
std::cerr << std::endl;
std::cerr << " alpha values of facets" << std::endl;
for(Finite_facets_iterator fit = finite_facets_begin();
fit != finite_facets_end();
++fit) {
Alpha_status_iterator as = fit->first->get_facet_status(fit->second);
print_alpha_status(*as);
}
std::cerr << std::endl;
std::cerr << " alpha values of edges " << std::endl;
if (get_mode() == GENERAL) {
for(Finite_edges_iterator eit = finite_edges_begin();
eit != finite_edges_end();
++eit) {
Vertex_handle_pair
vhp = make_vertex_handle_pair(eit->first->vertex(eit->second),
eit->first->vertex(eit->third));
Alpha_status_iterator as = edge_alpha_map.find(vhp)->second;
print_alpha_status(*as);
}
}
std::cerr << std::endl;
std::cerr << " alpha values of vertices " << std::endl;
for(Finite_vertices_iterator vit = finite_vertices_begin();
vit != finite_vertices_end();
++vit) {
Alpha_status* as = vit->get_alpha_status();
print_alpha_status(*as);
}
}
template <class Dt,class EACT>
void
Alpha_shape_3<Dt,EACT>::print_alpha_status(const Alpha_status& as) const
{
if ( get_mode() == GENERAL && as.is_Gabriel())
std::cerr << as.alpha_min() ;
else std::cerr << "--- " ;
std::cerr << "\t";
std::cerr << as.alpha_mid() << "\t";
if(as.is_on_chull()) std::cerr << "--- ";
else std::cerr << as.alpha_max();
std::cerr << std::endl;
}
} //namespace CGAL
#ifdef CGAL_USE_GEOMVIEW
#include <CGAL/IO/alpha_shape_geomview_ostream_3.h>
#endif
#endif //CGAL_ALPHA_SHAPE_3_H
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