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// Copyright (c) 2001 Max-Planck-Institute Saarbruecken (Germany).
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org); you may redistribute it under
// the terms of the Q Public License version 1.0.
// See the file LICENSE.QPL distributed with CGAL.
//
// 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) : Susan Hert <hert@mpi-sb.mpg.de>
// : Amol Prakash <prakash@mpi-sb.mpg.de>
#ifndef CGAL_CONVEX_HULL_3_H
#define CGAL_CONVEX_HULL_3_H
#include <CGAL/basic.h>
#include <CGAL/Unique_hash_map.h>
#include <CGAL/algorithm.h>
#include <CGAL/convex_hull_2.h>
#include <CGAL/Polyhedron_incremental_builder_3.h>
#include <CGAL/Convex_hull_traits_3.h>
#include <CGAL/Convex_hull_2/ch_assertions.h>
#include <iostream>
#include <algorithm>
#include <utility>
#include <list>
#include <vector>
#include <boost/bind.hpp>
#ifndef CGAL_CH_NO_POSTCONDITIONS
#include <CGAL/convexity_check_3.h>
#endif // CGAL_CH_NO_POSTCONDITIONS
namespace CGAL {
template<class HDS, class ForwardIterator>
class Build_coplanar_poly : public Modifier_base<HDS> {
public:
Build_coplanar_poly(ForwardIterator i, ForwardIterator j)
{
start = i;
end = j;
}
void operator()( HDS& hds) {
Polyhedron_incremental_builder_3<HDS> B(hds,true);
ForwardIterator iter = start;
int count = 0;
while (iter != end)
{
count++;
iter++;
}
B.begin_surface(count, 1, 2*count);
iter = start;
while (iter != end)
{
B.add_vertex(*iter);
iter++;
}
iter = start;
B.begin_facet();
int p = 0;
while (p < count)
{
B.add_vertex_to_facet(p);
p++;
}
B.end_facet();
B.end_surface();
}
private:
ForwardIterator start;
ForwardIterator end;
};
template <class InputIterator, class Plane_3, class Polyhedron_3, class Traits>
void coplanar_3_hull(InputIterator first, InputIterator beyond,
Plane_3 plane, Polyhedron_3& P, const Traits& traits)
{
typedef typename Traits::R R;
typedef typename Traits::Point_3 Point_3;
typedef typename Traits::Vector_3 Vector_3;
typedef typename Traits::Max_coordinate_3 Max_coordinate_3;
typedef Polyhedron_3 Polyhedron;
std::list<Point_3> CH_2;
typedef typename std::list<Point_3>::iterator CH_2_iterator;
typedef typename Traits::Construct_orthogonal_vector_3
Construct_normal_vec;
Max_coordinate_3 max_coordinate = traits.max_coordinate_3_object();
Construct_normal_vec c_normal =
traits.construct_orthogonal_vector_3_object();
Vector_3 normal = c_normal(plane);
int max_coord = max_coordinate(normal);
switch (max_coord)
{
case 0:
{
convex_hull_points_2(first, beyond, std::back_inserter(CH_2),
Convex_hull_projective_yz_traits_2<Point_3>());
break;
}
case 1:
{
convex_hull_points_2(first, beyond, std::back_inserter(CH_2),
Convex_hull_projective_xz_traits_2<Point_3>());
break;
}
case 2:
{
convex_hull_points_2(first, beyond, std::back_inserter(CH_2),
Convex_hull_projective_xy_traits_2<Point_3>());
break;
}
default:
break;
}
typedef typename Polyhedron::Halfedge_data_structure HDS;
Build_coplanar_poly<HDS,CH_2_iterator> poly(CH_2.begin(),CH_2.end());
P.delegate(poly);
}
//
// visible is the set of facets visible from point and reachable from
// start_facet.
//
template <class Facet_handle, class Traits>
void
find_visible_set(const typename Traits::Point_3& point,
Facet_handle start_facet,
std::list<Facet_handle>& visible,
const Traits& traits)
{
typedef typename Facet_handle::value_type Facet;
typedef typename Facet::Halfedge_around_facet_circulator Halfedge_circ;
typedef typename Facet::Halfedge_handle Halfedge_handle;
typedef typename Traits::Plane_3 Plane_3;
typename Traits::Has_on_positive_side_3 has_on_positive_side =
traits.has_on_positive_side_3_object();
visible.clear();
typename std::list<Facet_handle>::iterator vis_it;
CGAL::Unique_hash_map<Facet_handle, bool> visited(false);
visible.push_back(start_facet);
visited[start_facet] = true;
Facet_handle current;
for (vis_it = visible.begin(); vis_it != visible.end(); vis_it++)
{
// check all the neighbors of the current facet to see if they have
// already been visited or not and if not whether they are visible
// or not.
current = *vis_it;
Halfedge_circ hdl_init = (*current).facet_begin();
Halfedge_circ hdl_curr = hdl_init;
do
{
// the facet on the other side of the current halfedge
Facet_handle f = (*(*hdl_curr).opposite()).facet();
// if haven't already seen this facet
if ( !visited[f] )
{
visited[f] = true;
Plane_3 plane;
get_plane(plane,f);
if ( has_on_positive_side(plane, point) ) // is visible
{
visible.push_back(f);
}
}
hdl_curr++;
}
while (hdl_curr != hdl_init);
}
}
// using a third template parameter for the point instead of getting it from
// the traits class as it should be is required by M$VC6
template <class Facet_handle, class Traits, class Point>
Point
farthest_outside_point(Facet_handle f_handle, std::list<Point>& outside_set,
const Traits& traits)
{
typedef typename std::list<Point>::iterator Outside_set_iterator;
typename Traits::Plane_3 plane;
get_plane(plane, f_handle);
CGAL_ch_assertion(!outside_set.empty());
typename Traits::Less_signed_distance_to_plane_3 less_dist_to_plane =
traits.less_signed_distance_to_plane_3_object();
Outside_set_iterator farthest_it =
std::max_element(outside_set.begin(),
outside_set.end(),
boost::bind(less_dist_to_plane, plane, _1, _2));
return *farthest_it;
}
template <class Facet_handle>
void compute_plane_equation(Facet_handle f)
{
typedef typename Facet_handle::value_type Facet;
typedef typename Facet::Halfedge_handle Halfedge_handle;
typedef typename Facet::Plane_3 Plane_3;
Halfedge_handle h = (*f).halfedge();
(*f).plane() = Plane_3(h->opposite()->vertex()->point(),
h->vertex()->point(),
h->next()->vertex()->point());
}
template <class Plane, class Facet_handle>
void get_plane(Plane& plane, Facet_handle f)
{
typedef typename Facet_handle::value_type Facet;
typedef typename Facet::Halfedge_handle Halfedge_handle;
Halfedge_handle h = (*f).halfedge();
plane = Plane(h->opposite()->vertex()->point(),
h->vertex()->point(),
h->next()->vertex()->point());
}
// using a template for the Unique_hash_map is required by M$VC7
// using a template for the Point type instead of getting it from
// the traits class as it should be is required by M$VC6
template <class Facet_handle, class Traits, class UHM, class Point>
void
partition_outside_sets(const std::list<Facet_handle>& new_facets,
std::list<Point>& vis_outside_set,
UHM& outside_sets,
std::list<Facet_handle>& pending_facets,
const Traits& traits)
{
typedef typename Traits::Plane_3 Plane_3;
typename std::list<Facet_handle>::const_iterator f_list_it;
typename std::list<Point>::iterator point_it;
typename Traits::Has_on_positive_side_3 has_on_positive_side =
traits.has_on_positive_side_3_object();
// walk through all the new facets and check each unassigned outside point
// to see if it belongs to the outside set of this new facet.
for (f_list_it = new_facets.begin(); f_list_it != new_facets.end();
f_list_it++)
{
Plane_3 plane;
get_plane(plane, *f_list_it);
for (point_it = vis_outside_set.begin();
point_it != vis_outside_set.end();)
{
if ( has_on_positive_side(plane, *point_it) )
{
outside_sets[(*f_list_it)].push_back(*point_it);
point_it = vis_outside_set.erase(point_it);
}
else
point_it++;
}
}
// put all the new facets with non-empty outside sets in the pending facets
// list.
for (f_list_it = new_facets.begin(); f_list_it != new_facets.end();
f_list_it++)
{
if (!outside_sets[*f_list_it].empty())
pending_facets.push_back(*f_list_it);
}
}
template <class Polyhedron_3, class Traits>
void
ch_quickhull_3_scan(
Polyhedron_3& P,
std::list<typename Polyhedron_3::Facet_handle>& pending_facets,
CGAL::Unique_hash_map<typename Polyhedron_3::Facet_handle,
std::list<typename Traits::Point_3> >& outside_sets,
const Traits& traits)
{
typedef Polyhedron_3 Polyhedron;
typedef typename Polyhedron::Halfedge_handle Halfedge_handle;
typedef typename Polyhedron::Halfedge_iterator Halfedge_iterator;
typedef typename Polyhedron::Facet_handle Facet_handle;
typedef typename Traits::Point_3 Point_3;
typedef std::list<Point_3> Outside_set;
typedef typename std::list<Point_3>::iterator Outside_set_iterator;
std::list<Facet_handle> visible_set;
typename std::list<Facet_handle>::iterator vis_set_it;
Outside_set vis_outside_set;
Halfedge_iterator hole_halfedge;
Halfedge_handle new_pt_halfedge;
while (!pending_facets.empty())
{
vis_outside_set.clear();
Facet_handle f_handle = pending_facets.back();
pending_facets.pop_back();
Point_3 farthest_pt =
farthest_outside_point(f_handle, outside_sets[f_handle], traits);
#ifdef CGAL_CH_3_WINDOW_DEBUG
window << CGAL::RED;
window << farthest_pt;
cout << "farthest point is in red" << endl;
char ch;
cin >> ch;
CGAL_ch_assertion(P.is_valid(true));
window.clear();
#endif
find_visible_set(farthest_pt, f_handle, visible_set, traits);
// for each visible facet
for (vis_set_it = visible_set.begin(); vis_set_it != visible_set.end();
vis_set_it++)
{
// add its outside set to the global outside set list
std::copy(outside_sets[*vis_set_it].begin(),
outside_sets[*vis_set_it].end(),
std::back_inserter(vis_outside_set));
// delete this visible facet
P.erase_facet((*(*vis_set_it)).halfedge());
outside_sets[*vis_set_it].clear();
}
#ifdef CGAL_CH_3_WINDOW_DEBUG
window << CGAL::RED;
window << farthest_pt;
window << CGAL::BLUE;
window << P;
cout << "farthest point is in red" << endl;
cout << "after erasing visibile facets";
cin >> ch;
#endif
for (hole_halfedge = P.halfedges_begin();
hole_halfedge != P.halfedges_end() && !(*hole_halfedge).is_border();
hole_halfedge++)
{}
CGAL_ch_assertion(hole_halfedge->is_border());
CGAL_ch_assertion(hole_halfedge->next()->is_border());
// add a new facet and vertex to the surface. This is the first
// new facet to be added.
new_pt_halfedge = P.add_vertex_and_facet_to_border(hole_halfedge,
(*hole_halfedge).next());
// associate the farthest point with the new vertex.
(*(*new_pt_halfedge).vertex()).point() = farthest_pt;
CGAL_ch_assertion( !new_pt_halfedge->is_border() );
CGAL_ch_assertion( new_pt_halfedge->opposite()->is_border() );
std::list<Facet_handle> new_facets;
new_facets.push_back(new_pt_halfedge->facet());
Halfedge_handle start_hole_halfedge = new_pt_halfedge->opposite()->prev();
CGAL_ch_assertion( start_hole_halfedge->is_border() );
CGAL_ch_assertion( start_hole_halfedge->vertex()->point() == farthest_pt);
// need to move to second next halfedge to get to a point where a
// triangular facet can be created
Halfedge_handle curr_halfedge = start_hole_halfedge->next()->next();
CGAL_ch_assertion( curr_halfedge->is_border() );
Halfedge_handle new_halfedge;
// now walk around all the border halfedges and add a facet incident to
// each one to connect it to the farthest point
while (curr_halfedge->next() != start_hole_halfedge)
{
new_halfedge =
P.add_facet_to_border(start_hole_halfedge, curr_halfedge);
CGAL_ch_assertion( !new_halfedge->is_border() );
CGAL_ch_assertion( new_halfedge->opposite()->is_border() );
new_facets.push_back(new_halfedge->facet());
// once the new facet is added curr->next() will be the next halfedge
// on this facet (i.e., not a border halfedge), so the next border
// halfedge will be the one after the opposite of the new halfedge
curr_halfedge = new_halfedge->opposite()->next();
CGAL_ch_assertion( curr_halfedge->is_border() );
}
// fill in the last triangular hole with a facet
new_halfedge = P.fill_hole(curr_halfedge);
new_facets.push_back(new_halfedge->facet());
#ifdef CGAL_CH_3_WINDOW_DEBUG
window << CGAL::BLUE;
window << P;
cout << "after filling hole" << endl;
char c;
cin >> c;
CGAL_ch_assertion(P.is_valid(true));
#endif
// now partition the set of outside set points among the new facets.
partition_outside_sets(new_facets, vis_outside_set, outside_sets,
pending_facets, traits);
}
}
template <class Polyhedron_3, class Traits>
void non_coplanar_quickhull_3(std::list<typename Traits::Point_3>& points,
Polyhedron_3& P, const Traits& traits)
{
typedef Polyhedron_3 Polyhedron;
typedef typename Polyhedron::Facet_handle Facet_handle;
typedef typename Polyhedron::Facet_iterator Facet_iterator;
typedef typename Traits::Point_3 Point_3;
typedef typename Traits::Plane_3 Plane_3;
typedef CGAL::Unique_hash_map<Facet_handle, std::list<Point_3> >
Outside_set_map;
typedef typename std::list<Point_3>::iterator P3_iterator;
std::list<Facet_handle> pending_facets;
Facet_iterator f_it;
typename Traits::Has_on_positive_side_3 has_on_positive_side =
traits.has_on_positive_side_3_object();
Outside_set_map outside_sets;
// for each facet, look at each unassigned point and decide if it belongs
// to the outside set of this facet.
for (f_it = P.facets_begin(); f_it != P.facets_end(); f_it++)
{
Plane_3 plane;
get_plane(plane, f_it);
for (P3_iterator point_it = points.begin() ; point_it != points.end(); )
{
if ( has_on_positive_side(plane, *point_it) ){
outside_sets[f_it].push_back(*point_it);
point_it = points.erase(point_it);
} else {
++point_it;
}
}
}
// add all the facets with non-empty outside sets to the set of facets for
// further consideration
for (f_it = P.facets_begin(); f_it != P.facets_end(); f_it++)
if (!outside_sets[f_it].empty())
pending_facets.push_back(f_it);
ch_quickhull_3_scan(P, pending_facets, outside_sets, traits);
CGAL_ch_expensive_postcondition(all_points_inside(points.begin(),
points.end(),P,traits));
CGAL_ch_postcondition(is_strongly_convex_3(P, traits));
}
template <class InputIterator, class Polyhedron_3, class Traits>
void
ch_quickhull_polyhedron_3(std::list<typename Traits::Point_3>& points,
InputIterator point1_it, InputIterator point2_it,
InputIterator point3_it, Polyhedron_3& P,
const Traits& traits)
{
typedef typename Traits::Point_3 Point_3;
typedef typename Traits::Plane_3 Plane_3;
typedef typename std::list<Point_3>::iterator P3_iterator;
// found three points that are not collinear, so construct the plane defined
// by these points and then find a point that has maximum distance from this
// plane.
typename Traits::Construct_plane_3 construct_plane =
traits.construct_plane_3_object();
Plane_3 plane = construct_plane(*point3_it, *point2_it, *point1_it);
typedef typename Traits::Less_signed_distance_to_plane_3 Dist_compare;
Dist_compare compare_dist = traits.less_signed_distance_to_plane_3_object();
typename Traits::Coplanar_3 coplanar = traits.coplanar_3_object();
// find both min and max here since using signed distance. If all points
// are on the negative side of ths plane, the max element will be on the
// plane.
std::pair<P3_iterator, P3_iterator> min_max;
min_max = CGAL::min_max_element(points.begin(), points.end(),
boost::bind(compare_dist, plane, _1, _2),
boost::bind(compare_dist, plane, _1, _2));
P3_iterator max_it;
if (coplanar(*point1_it, *point2_it, *point3_it, *min_max.second))
{
max_it = min_max.first;
// want the orientation of the points defining the plane to be positive
// so have to reorder these points if all points were on negative side
// of plane
std::swap(*point1_it, *point3_it);
}
else
max_it = min_max.second;
#ifdef CGAL_CH_3_WINDOW_DEBUG
window << CGAL::GREEN;
window << *point1_it;
window << *point2_it;
window << *point3_it;
window << CGAL::RED;
window << *max_it;
char ch;
cin >> ch;
#endif
// if the maximum distance point is on the plane then all are coplanar
if (coplanar(*point1_it, *point2_it, *point3_it, *max_it)) {
coplanar_3_hull(points.begin(), points.end(), plane, P, traits);
} else {
P.make_tetrahedron(*point1_it, *point2_it, *point3_it, *max_it);
points.erase(point1_it);
points.erase(point2_it);
points.erase(point3_it);
points.erase(max_it);
if (!points.empty())
non_coplanar_quickhull_3(points, P, traits);
}
}
template <class InputIterator, class Traits>
void
convex_hull_3(InputIterator first, InputIterator beyond,
Object& ch_object, const Traits& traits)
{
typedef typename Traits::Point_3 Point_3;
typedef typename Traits::Plane_3 Plane_3;
typedef std::list<Point_3> Point_3_list;
typedef typename Point_3_list::iterator P3_iterator;
typedef std::pair<P3_iterator,P3_iterator> P3_iterator_pair;
if (first == beyond) // No point
return;
Point_3_list points(first, beyond);
unsigned int size = points.size();
if ( size == 1 ) // 1 point
{
ch_object = make_object(*points.begin());
return;
}
else if ( size == 2 ) // 2 points
{
typedef typename Traits::Segment_3 Segment_3;
typename Traits::Construct_segment_3 construct_segment =
traits.construct_segment_3_object();
Segment_3 seg = construct_segment(*points.begin(), *(++points.begin()));
ch_object = make_object(seg);
return;
}
else if ( size == 3 ) // 3 points
{
typedef typename Traits::Triangle_3 Triangle_3;
typename Traits::Construct_triangle_3 construct_triangle =
traits.construct_triangle_3_object();
Triangle_3 tri = construct_triangle(*(points.begin()),
*(++points.begin()),
*(--points.end()));
ch_object = make_object(tri);
return;
}
// at least 4 points
typename Traits::Collinear_3 collinear = traits.collinear_3_object();
P3_iterator point1_it = points.begin();
P3_iterator point2_it = points.begin();
point2_it++;
P3_iterator point3_it = points.end();
point3_it--;
// find three that are not collinear
while (point2_it != points.end() &&
collinear(*point1_it,*point2_it,*point3_it))
point2_it++;
// all are collinear, so the answer is a segment
if (point2_it == points.end())
{
typedef typename Traits::Less_distance_to_point_3 Less_dist;
Less_dist less_dist = traits.less_distance_to_point_3_object();
P3_iterator_pair endpoints =
min_max_element(points.begin(), points.end(),
boost::bind(less_dist, *points.begin(), _1, _2),
boost::bind(less_dist, *points.begin(), _1, _2));
typename Traits::Construct_segment_3 construct_segment =
traits.construct_segment_3_object();
typedef typename Traits::Segment_3 Segment_3;
Segment_3 seg = construct_segment(*endpoints.first, *endpoints.second);
ch_object = make_object(seg);
return;
}
typename Traits::Polyhedron_3 P;
// result will be a polyhedron
ch_quickhull_polyhedron_3(points, point1_it, point2_it, point3_it,
P, traits);
ch_object = make_object(P);
}
template <class InputIterator>
void convex_hull_3(InputIterator first, InputIterator beyond,
Object& ch_object)
{
typedef typename std::iterator_traits<InputIterator>::value_type Point_3;
typedef typename Kernel_traits<Point_3>::Kernel K;
convex_hull_3(first, beyond, ch_object, Convex_hull_traits_3<K>());
}
template <class InputIterator, class Polyhedron_3, class Traits>
void convex_hull_3(InputIterator first, InputIterator beyond,
Polyhedron_3& polyhedron, const Traits& traits)
{
typedef typename Traits::Point_3 Point_3;
typedef typename Traits::Plane_3 Plane_3;
typedef std::list<Point_3> Point_3_list;
typedef typename Point_3_list::iterator P3_iterator;
Point_3_list points(first, beyond);
CGAL_ch_precondition(points.size() > 3);
// at least 4 points
typename Traits::Collinear_3 collinear = traits.collinear_3_object();
typename Traits::Equal_3 equal = traits.equal_3_object();
P3_iterator point1_it = points.begin();
P3_iterator point2_it = points.begin();
point2_it++;
// find three that are not collinear
while (point2_it != points.end() && equal(*point1_it,*point2_it))
++point2_it;
CGAL_ch_precondition_msg(point2_it != points.end(),
"All points are equal; cannot construct polyhedron.");
P3_iterator point3_it = point2_it;
++point3_it;
CGAL_ch_precondition_msg(point3_it != points.end(),
"Only two points with different coordinates; cannot construct polyhedron.");
while (point3_it != points.end() && collinear(*point1_it,*point2_it,*point3_it))
++point3_it;
CGAL_ch_precondition_msg(point3_it != points.end(),
"All points are collinear; cannot construct polyhedron.");
polyhedron.clear();
// result will be a polyhedron
ch_quickhull_polyhedron_3(points, point1_it, point2_it, point3_it,
polyhedron, traits);
}
template <class InputIterator, class Polyhedron_3>
void convex_hull_3(InputIterator first, InputIterator beyond,
Polyhedron_3& polyhedron)
{
typedef typename std::iterator_traits<InputIterator>::value_type Point_3;
typedef typename Kernel_traits<Point_3>::Kernel K;
convex_hull_3(first, beyond, polyhedron, Convex_hull_traits_3<K>());
}
} // namespace CGAL
#endif // CGAL_CONVEX_HULL_3_H
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