mirror of https://github.com/CGAL/cgal
513 lines
17 KiB
C++
513 lines
17 KiB
C++
// Copyright (c) 1997
|
|
// Utrecht University (The Netherlands),
|
|
// ETH Zurich (Switzerland),
|
|
// INRIA Sophia-Antipolis (France),
|
|
// Max-Planck-Institute Saarbruecken (Germany),
|
|
// and Tel-Aviv University (Israel). 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 Lesser 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 software.
|
|
//
|
|
// 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) : Lutz Kettner <kettner@inf.ethz.ch>
|
|
// Pedro Machado Manhaes de Castro <pmmc@cin.ufpe.br>
|
|
// Alexandru Tifrea
|
|
// Maxime Gimeno
|
|
|
|
#ifndef CGAL_POINT_GENERATORS_3_H
|
|
#define CGAL_POINT_GENERATORS_3_H 1
|
|
#include <CGAL/generators.h>
|
|
#include <CGAL/point_generators_2.h>
|
|
#include <CGAL/number_type_basic.h>
|
|
#include <CGAL/internal/Generic_random_point_generator.h>
|
|
#include <CGAL/boost/graph/property_maps.h>
|
|
|
|
namespace CGAL {
|
|
|
|
template < class P, class Creator =
|
|
Creator_uniform_3<typename Kernel_traits<P>::Kernel::RT,P> >
|
|
class Random_points_in_sphere_3 : public Random_generator_base<P> {
|
|
void generate_point();
|
|
public:
|
|
typedef Random_points_in_sphere_3<P,Creator> This;
|
|
Random_points_in_sphere_3( double r = 1, Random& rnd = CGAL::get_default_random())
|
|
// g is an input iterator creating points of type `P' uniformly
|
|
// distributed in the open sphere with radius r, i.e. |`*g'| < r .
|
|
// Three random numbers are needed from `rnd' for each point
|
|
: Random_generator_base<P>( r, rnd) { generate_point(); }
|
|
This& operator++() {
|
|
generate_point();
|
|
return *this;
|
|
}
|
|
This operator++(int) {
|
|
This tmp = *this;
|
|
++(*this);
|
|
return tmp;
|
|
}
|
|
};
|
|
|
|
template < class P, class Creator >
|
|
void
|
|
Random_points_in_sphere_3<P,Creator>::
|
|
generate_point() {
|
|
// A strip between z and z+dz has an area independant of z
|
|
typedef typename Creator::argument_type T;
|
|
double alpha = this->_rnd.get_double() * 2.0 * CGAL_PI;
|
|
double z = 2 * this->_rnd.get_double() - 1.0;
|
|
double r = std::sqrt( 1 - z * z);
|
|
r *= std::pow( this->_rnd.get_double() , 1.0/3.0 );
|
|
Creator creator;
|
|
this->d_item = creator( T(this->d_range * r * std::cos(alpha)),
|
|
T(this->d_range * r * std::sin(alpha)),
|
|
T(this->d_range * z));
|
|
}
|
|
|
|
|
|
template < class P, class Creator =
|
|
Creator_uniform_3<typename Kernel_traits<P>::Kernel::RT,P> >
|
|
class Random_points_on_sphere_3 : public Random_generator_base<P> {
|
|
void generate_point();
|
|
public:
|
|
typedef Random_points_on_sphere_3<P,Creator> This;
|
|
Random_points_on_sphere_3( double r = 1, Random& rnd = CGAL::get_default_random())
|
|
// g is an input iterator creating points of type `P' uniformly
|
|
// distributed on the sphere with radius r, i.e. |`*g'| == r . A
|
|
// two random numbers are needed from `rnd' for each point.
|
|
: Random_generator_base<P>( r, rnd) { generate_point(); }
|
|
This& operator++() {
|
|
generate_point();
|
|
return *this;
|
|
}
|
|
This operator++(int) {
|
|
This tmp = *this;
|
|
++(*this);
|
|
return tmp;
|
|
}
|
|
};
|
|
|
|
template < class P, class Creator >
|
|
void
|
|
Random_points_on_sphere_3<P,Creator>::
|
|
generate_point() {
|
|
// A strip between z and z+dz has an area independant of z
|
|
typedef typename Creator::argument_type T;
|
|
double alpha = this->_rnd.get_double() * 2.0 * CGAL_PI;
|
|
double z = 2 * this->_rnd.get_double() - 1.0;
|
|
double r = std::sqrt( 1 - z * z);
|
|
Creator creator;
|
|
this->d_item = creator( T(this->d_range * r * std::cos(alpha)),
|
|
T(this->d_range * r * std::sin(alpha)),
|
|
T(this->d_range * z));
|
|
}
|
|
|
|
|
|
template < class P, class Creator =
|
|
Creator_uniform_3<typename Kernel_traits<P>::Kernel::RT,P> >
|
|
class Random_points_in_cube_3 : public Random_generator_base<P>{
|
|
void generate_point();
|
|
public:
|
|
typedef Random_points_in_cube_3<P,Creator> This;
|
|
Random_points_in_cube_3( double a = 1, Random& rnd = CGAL::get_default_random())
|
|
: Random_generator_base<P>( a, rnd) { generate_point(); }
|
|
This& operator++() {
|
|
generate_point();
|
|
return *this;
|
|
}
|
|
This operator++(int) {
|
|
This tmp = *this;
|
|
++(*this);
|
|
return tmp;
|
|
}
|
|
};
|
|
|
|
template < class P, class Creator >
|
|
void
|
|
Random_points_in_cube_3<P,Creator>::
|
|
generate_point() {
|
|
typedef typename Creator::argument_type T;
|
|
Creator creator;
|
|
this->d_item =
|
|
creator( T(this->d_range * ( 2 * this->_rnd.get_double() - 1.0)),
|
|
T(this->d_range * ( 2 * this->_rnd.get_double() - 1.0)),
|
|
T(this->d_range * ( 2 * this->_rnd.get_double() - 1.0)));
|
|
}
|
|
|
|
|
|
template <class OutputIterator, class Creator>
|
|
OutputIterator
|
|
points_on_cube_grid_3( double a, std::size_t n,
|
|
OutputIterator o, Creator creator)
|
|
{
|
|
if (n == 0)
|
|
return o;
|
|
|
|
int m = int(std::ceil(
|
|
std::sqrt(std::sqrt(static_cast<double>(n)))));
|
|
|
|
while (m*m*m < int(n)) m++;
|
|
|
|
double base = -a; // Left and bottom boundary.
|
|
double step = 2*a/(m-1);
|
|
int j = 0;
|
|
int k = 0;
|
|
double px = base;
|
|
double py = base;
|
|
double pz = base;
|
|
*o++ = creator( px, py, pz);
|
|
for (std::size_t i = 1; i < n; i++) {
|
|
j++;
|
|
if ( j == m) {
|
|
k++;
|
|
if ( k == m) {
|
|
py = base;
|
|
px = base;
|
|
pz = pz + step;
|
|
k = 0;
|
|
}
|
|
else {
|
|
px = base;
|
|
py = py + step;
|
|
}
|
|
j = 0;
|
|
} else {
|
|
px = px + step;
|
|
}
|
|
*o++ = creator( px, py, pz);
|
|
}
|
|
return o;
|
|
}
|
|
|
|
template <class OutputIterator>
|
|
OutputIterator
|
|
points_on_cube_grid_3( double a, std::size_t n, OutputIterator o)
|
|
{
|
|
typedef std::iterator_traits<OutputIterator> ITraits;
|
|
typedef typename ITraits::value_type P;
|
|
return points_on_square_grid_3(a, n, o,
|
|
Creator_uniform_3<typename Kernel_traits<P>::Kernel::RT,P>());
|
|
}
|
|
|
|
template < class P, class Creator =
|
|
Creator_uniform_3<typename Kernel_traits<P>::Kernel::RT,P> >
|
|
class Random_points_in_triangle_3 : public Random_generator_base<P> {
|
|
P _p,_q,_r;
|
|
void generate_point();
|
|
public:
|
|
typedef P result_type;
|
|
typedef Random_points_in_triangle_3<P> This;
|
|
typedef typename Kernel_traits<P>::Kernel::Triangle_3 Triangle_3;
|
|
Random_points_in_triangle_3() {}
|
|
Random_points_in_triangle_3( const This& x,Random& rnd = get_default_random())
|
|
: Random_generator_base<P>( 1, rnd ),_p(x._p),_q(x._q),_r(x._r) {
|
|
generate_point();
|
|
}
|
|
Random_points_in_triangle_3( const P& p, const P& q, const P& r, Random& rnd = get_default_random())
|
|
: Random_generator_base<P>( 1, rnd ),_p(p),_q(q),_r(r) {
|
|
generate_point();
|
|
}
|
|
Random_points_in_triangle_3( const Triangle_3& triangle,Random& rnd = get_default_random())
|
|
: Random_generator_base<P>( 1,
|
|
rnd),_p(triangle[0]),_q(triangle[1]),_r(triangle[2]) {
|
|
generate_point();
|
|
}
|
|
This& operator++() {
|
|
generate_point();
|
|
return *this;
|
|
}
|
|
This operator++(int) {
|
|
This tmp = *this;
|
|
++(*this);
|
|
return tmp;
|
|
}
|
|
};
|
|
|
|
|
|
template<class P, class Creator >
|
|
void Random_points_in_triangle_3<P, Creator>::generate_point() {
|
|
typedef typename Creator::argument_type T;
|
|
Creator creator;
|
|
double a1 = this->_rnd.get_double(0,1);
|
|
double a2 = this->_rnd.get_double(0,1);
|
|
if(a1>a2) std::swap(a1,a2);
|
|
double b1 = a1;
|
|
double b2 = a2-a1;
|
|
double b3 = 1.0-a2;
|
|
T ret[3];
|
|
for(int i = 0; i < 3; ++i) {
|
|
ret[i] = T(to_double(_p[i])*b1+to_double(_q[i])*b2+to_double(_r[i])*b3);
|
|
}
|
|
this->d_item = creator(ret[0],ret[1],ret[2]);
|
|
}
|
|
|
|
template < class P, class Creator =
|
|
Creator_uniform_3<typename Kernel_traits<P>::Kernel::RT,P> >
|
|
class Random_points_in_tetrahedron_3 : public Random_generator_base<P> {
|
|
P _p,_q,_r,_s;
|
|
void generate_point();
|
|
public:
|
|
typedef P result_type;
|
|
typedef Random_points_in_tetrahedron_3<P> This;
|
|
typedef typename Kernel_traits<P>::Kernel::Tetrahedron_3 Tetrahedron_3;
|
|
Random_points_in_tetrahedron_3() {}
|
|
Random_points_in_tetrahedron_3( const This& x,Random& rnd = get_default_random())
|
|
: Random_generator_base<P>( 1, rnd ),_p(x._p),_q(x._q),_r(x._r),_s(x._s) {
|
|
generate_point();
|
|
}
|
|
Random_points_in_tetrahedron_3( const P& p, const P& q, const P& r, const P& s,Random& rnd = get_default_random())
|
|
: Random_generator_base<P>( 1, rnd ),_p(p),_q(q),_r(r),_s(s) {
|
|
generate_point();
|
|
}
|
|
Random_points_in_tetrahedron_3( const Tetrahedron_3& tetrahedron,Random& rnd = get_default_random())
|
|
: Random_generator_base<P>( 1, rnd),_p(tetrahedron[0]),_q(tetrahedron[1]),_r(tetrahedron[2]),_s(tetrahedron[3]) {
|
|
generate_point();
|
|
}
|
|
This& operator++() {
|
|
generate_point();
|
|
return *this;
|
|
}
|
|
This operator++(int) {
|
|
This tmp = *this;
|
|
++(*this);
|
|
return tmp;
|
|
}
|
|
};
|
|
|
|
template<class P, class Creator >
|
|
void Random_points_in_tetrahedron_3<P, Creator>::generate_point() {
|
|
typedef typename Creator::argument_type T;
|
|
Creator creator;
|
|
double a[3];
|
|
for(int i = 0; i < 3; ++i) {
|
|
a[i]=this->_rnd.get_double(0,1);
|
|
}
|
|
std::sort(a,a+3);
|
|
double b[4];
|
|
b[0]=a[0];
|
|
b[1]=a[1]-a[0];
|
|
b[2]=a[2]-a[1];
|
|
b[3]=1.0-a[2];
|
|
T ret[3];
|
|
for(int i = 0; i < 3; ++i) {
|
|
ret[i] = T(to_double(_p[i])*b[0]+to_double(_q[i])*b[1]+to_double(_r[i])*b[2]+to_double(_s[i])*b[3]);
|
|
}
|
|
this->d_item = creator(ret[0],ret[1],ret[2]);
|
|
}
|
|
|
|
|
|
|
|
template <class TriangleMesh, class VertexPointMap = typename boost::property_map<TriangleMesh,
|
|
CGAL::vertex_point_t>::type>
|
|
class Random_points_on_triangle_mesh_3 : public Generic_random_point_generator<
|
|
typename boost::graph_traits <TriangleMesh>::face_descriptor ,
|
|
CGAL::Property_map_to_unary_function<CGAL::Triangle_from_face_descriptor_map<
|
|
TriangleMesh, VertexPointMap > >,
|
|
Random_points_in_triangle_3<typename boost::property_traits<VertexPointMap>::value_type> ,
|
|
typename boost::property_traits<VertexPointMap>::value_type> {
|
|
public:
|
|
typedef typename boost::property_traits<VertexPointMap>::value_type P;
|
|
typedef Generic_random_point_generator<
|
|
typename boost::graph_traits <TriangleMesh>::face_descriptor ,
|
|
CGAL::Property_map_to_unary_function<typename CGAL::Triangle_from_face_descriptor_map<
|
|
TriangleMesh,typename boost::property_map<TriangleMesh,
|
|
CGAL::vertex_point_t>::type> >,
|
|
Random_points_in_triangle_3<P> , P> Base;
|
|
typedef typename CGAL::Triangle_from_face_descriptor_map<
|
|
TriangleMesh,VertexPointMap> Pmap;
|
|
typedef typename CGAL::Triangle_from_face_descriptor_map<
|
|
TriangleMesh,VertexPointMap> Object_from_id_map;
|
|
typedef Random_points_in_triangle_3<P> Generator_on_object;
|
|
typedef typename boost::graph_traits<TriangleMesh>::face_descriptor Id;
|
|
typedef P result_type;
|
|
typedef Random_points_on_triangle_mesh_3< TriangleMesh> This;
|
|
|
|
|
|
Random_points_on_triangle_mesh_3( TriangleMesh& mesh,Random& rnd = default_random)
|
|
: Base( faces(mesh),
|
|
CGAL::Property_map_to_unary_function<Pmap>(&mesh),
|
|
typename Kernel_traits<P>::Kernel::Compute_area_3(),
|
|
rnd )
|
|
{
|
|
}
|
|
This& operator++() {
|
|
Base::generate_point();
|
|
return *this;
|
|
}
|
|
This operator++(int) {
|
|
This tmp = *this;
|
|
++(*this);
|
|
return tmp;
|
|
}
|
|
double mesh_area() const
|
|
{
|
|
this->sum_of_weights();
|
|
}
|
|
};
|
|
|
|
namespace internal
|
|
{
|
|
|
|
template<class T>
|
|
class Triangle_from_face_C3t3
|
|
{
|
|
typedef typename T::Triangle Triangle;
|
|
typedef typename T::Point Point;
|
|
typedef std::pair<typename T::Cell_handle, int> Face;
|
|
public:
|
|
typedef Triangle result_type;
|
|
|
|
Triangle_from_face_C3t3()
|
|
{}
|
|
Triangle operator()(Face face)const
|
|
{
|
|
typename T::Cell_handle cell = face.first;
|
|
int index = face.second;
|
|
const Point& pa = cell->vertex((index+1)&3)->point();
|
|
const Point& pb = cell->vertex((index+2)&3)->point();
|
|
const Point& pc = cell->vertex((index+3)&3)->point();
|
|
return Triangle(pa, pb, pc);
|
|
}
|
|
};
|
|
|
|
template<class T>
|
|
class Tetrahedron_from_cell_C3t3
|
|
{
|
|
typedef typename T::Cell_handle Cell;
|
|
typedef typename T::Point Point;
|
|
typedef typename Kernel_traits<Point>::Kernel::Tetrahedron_3 Tetrahedron;
|
|
public:
|
|
typedef Tetrahedron result_type;
|
|
|
|
Tetrahedron_from_cell_C3t3()
|
|
{}
|
|
Tetrahedron operator()(Cell cell)const
|
|
{
|
|
Point p0 = cell->vertex(0)->point();
|
|
Point p1 = cell->vertex(1)->point();
|
|
Point p2 = cell->vertex(2)->point();
|
|
Point p3 = cell->vertex(3)->point();
|
|
return Tetrahedron(p0,p1,p2,p3);
|
|
}
|
|
};
|
|
}//end namespace internal
|
|
|
|
template <class C3t3>
|
|
class Random_points_on_tetrahedral_mesh_boundary : public Generic_random_point_generator<
|
|
std::pair<typename C3t3::Triangulation::Cell_handle, int>,
|
|
internal::Triangle_from_face_C3t3<typename C3t3::Triangulation>,
|
|
Random_points_in_triangle_3<typename C3t3::Point> , typename C3t3::Point> {
|
|
public:
|
|
typedef Generic_random_point_generator<
|
|
std::pair<typename C3t3::Triangulation::Cell_handle, int>,
|
|
internal::Triangle_from_face_C3t3<typename C3t3::Triangulation>,
|
|
Random_points_in_triangle_3<typename C3t3::Point> , typename C3t3::Point> Base;
|
|
typedef std::pair<typename C3t3::Triangulation::Cell_handle, int> Id;
|
|
typedef typename C3t3::Point result_type;
|
|
typedef Random_points_on_tetrahedral_mesh_boundary<C3t3> This;
|
|
|
|
|
|
Random_points_on_tetrahedral_mesh_boundary( C3t3& c3t3,Random& rnd = default_random)
|
|
: Base( make_range( c3t3.facets_in_complex_begin(),
|
|
c3t3.facets_in_complex_end()),
|
|
internal::Triangle_from_face_C3t3<typename C3t3::Triangulation>(),
|
|
typename Kernel_traits<typename C3t3::Point>::Kernel::Compute_area_3(),
|
|
rnd )
|
|
{
|
|
}
|
|
This& operator++() {
|
|
Base::generate_point();
|
|
return *this;
|
|
}
|
|
This operator++(int) {
|
|
This tmp = *this;
|
|
++(*this);
|
|
return tmp;
|
|
}
|
|
};
|
|
|
|
template <class C3t3>
|
|
class Random_points_in_tetrahedral_mesh_3 : public Generic_random_point_generator<
|
|
typename C3t3::Triangulation::Cell_handle,
|
|
internal::Tetrahedron_from_cell_C3t3<typename C3t3::Triangulation>,
|
|
Random_points_in_tetrahedron_3<typename C3t3::Point> , typename C3t3::Point> {
|
|
public:
|
|
typedef Generic_random_point_generator<
|
|
typename C3t3::Triangulation::Cell_handle,
|
|
internal::Tetrahedron_from_cell_C3t3<typename C3t3::Triangulation>,
|
|
Random_points_in_tetrahedron_3<typename C3t3::Point> , typename C3t3::Point> Base;
|
|
typedef typename C3t3::Triangulation::Cell_handle Id;
|
|
typedef typename C3t3::Point result_type;
|
|
typedef Random_points_in_tetrahedral_mesh_3<C3t3> This;
|
|
|
|
|
|
Random_points_in_tetrahedral_mesh_3( C3t3& c3t3,Random& rnd = default_random)
|
|
: Base( CGAL::make_prevent_deref_range(c3t3.cells_in_complex_begin(),
|
|
c3t3.cells_in_complex_end()),
|
|
internal::Tetrahedron_from_cell_C3t3<typename C3t3::Triangulation>(),
|
|
typename Kernel_traits<typename C3t3::Point>::Kernel::Compute_volume_3(),
|
|
rnd )
|
|
{
|
|
}
|
|
This& operator++() {
|
|
Base::generate_point();
|
|
return *this;
|
|
}
|
|
This operator++(int) {
|
|
This tmp = *this;
|
|
++(*this);
|
|
return tmp;
|
|
}
|
|
};
|
|
|
|
|
|
template <class Point_3>
|
|
class Random_points_on_triangles_3 : public Generic_random_point_generator<
|
|
const typename Kernel_traits<Point_3>::Kernel::Triangle_3*,
|
|
internal::Deref<const typename Kernel_traits<Point_3>::Kernel::Triangle_3*>,
|
|
Random_points_in_triangle_3<Point_3> ,Point_3> {
|
|
public:
|
|
typedef typename Kernel_traits<Point_3>::Kernel::Triangle_3 Triangle_3;
|
|
typedef Generic_random_point_generator<
|
|
const typename Kernel_traits<Point_3>::Kernel::Triangle_3*,
|
|
internal::Deref<const Triangle_3*>,
|
|
Random_points_in_triangle_3<Point_3> ,Point_3> Base;
|
|
typedef const Triangle_3* Id;
|
|
typedef Point_3 result_type;
|
|
typedef Random_points_on_triangles_3<Point_3> This;
|
|
|
|
template<typename TriangleRange>
|
|
Random_points_on_triangles_3( const TriangleRange& triangles, Random& rnd = default_random)
|
|
: Base(make_range( boost::make_transform_iterator(triangles.begin(), internal::Address_of<Triangle_3>()),
|
|
boost::make_transform_iterator(triangles.end(), internal::Address_of<Triangle_3>()) ),
|
|
internal::Deref<const Triangle_3*>(),
|
|
typename Kernel_traits<Point_3>::Kernel::Compute_area_3()
|
|
,rnd )
|
|
{
|
|
}
|
|
This& operator++() {
|
|
Base::generate_point();
|
|
return *this;
|
|
}
|
|
This operator++(int) {
|
|
This tmp = *this;
|
|
++(*this);
|
|
return tmp;
|
|
}
|
|
};
|
|
|
|
} //namespace CGAL
|
|
|
|
|
|
#endif // CGAL_POINT_GENERATORS_3_H //
|
|
// EOF //
|