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// computes the normal vector for facets, assuming they are triangles
// (or at least reasonably planar convex polygons), and the normal
// vector for vertices by accumulating the normal vectors of all
// incident facets. All normal vectors are normalized, which requires
// sqrt computations. Therefore we use the Simple_cartesian<double>
// kernel, which is also a natural choice in graphics. Note that the
// normals computed are therefore not exact.
#include <CGAL/Simple_cartesian.h>
#include <CGAL/Polyhedron_3.h>
#include <iostream>
#include <algorithm>
// Two functors to compute the normals: We assume the
// Simple_cartesian<double> Kernel here and use its global functions.
struct Facet_normal {
template <class Facet>
void operator()( Facet& f) {
typename Facet::Halfedge_handle h = f.halfedge();
typename Facet::Normal_3 normal = CGAL::cross_product(
h->next()->vertex()->point() - h->vertex()->point(),
h->next()->next()->vertex()->point() - h->next()->vertex()->point());
f.normal() = normal / std::sqrt( normal * normal);
}
};
struct Vertex_normal {
template <class Vertex>
void operator()( Vertex& v) {
typename Vertex::Normal_3 normal = CGAL::NULL_VECTOR;
typedef typename Vertex::Halfedge_around_vertex_const_circulator Circ;
Circ c = v.vertex_begin();
Circ d = c;
CGAL_For_all( c, d) {
if ( ! c->is_border())
normal = normal + c->facet()->normal();
}
v.normal() = normal / std::sqrt( normal * normal);
}
};
// A redefined items class for the Polyhedron_3 with a refined vertex
// class that contains a member for the normal vector and a refined
// facet with a normal vector instead of the plane equation (this is
// an alternative solution instead of using Polyhedron_traits_with_normals_3).
template <class Refs, class T, class P, class Norm>
class My_vertex : public CGAL::HalfedgeDS_vertex_base<Refs, T, P> {
Norm norm;
public:
My_vertex() {} // repeat mandatory constructors
My_vertex( const P& pt) : CGAL::HalfedgeDS_vertex_base<Refs, T, P>(pt) {}
typedef Norm Normal_3;
Normal_3& normal() { return norm; }
const Normal_3& normal() const { return norm; }
};
template <class Refs, class T, class Norm>
class My_facet : public CGAL::HalfedgeDS_face_base<Refs, T> {
Norm norm;
public:
// no constructors to repeat, since only default constructor mandatory
typedef Norm Normal_3;
Normal_3& normal() { return norm; }
const Normal_3& normal() const { return norm; }
};
struct My_items : public CGAL::Polyhedron_items_3 {
template <class Refs, class Traits>
struct Vertex_wrapper {
typedef typename Traits::Point_3 Point;
typedef typename Traits::Vector_3 Normal;
typedef My_vertex<Refs, CGAL::Tag_true, Point, Normal> Vertex;
};
template <class Refs, class Traits>
struct Face_wrapper {
typedef typename Traits::Vector_3 Normal;
typedef My_facet<Refs, CGAL::Tag_true, Normal> Face;
};
};
// Tie all types together and a small main function using it.
typedef CGAL::Simple_cartesian<double> Kernel;
typedef Kernel::Point_3 Point_3;
typedef CGAL::Polyhedron_3<Kernel, My_items> Polyhedron;
typedef Polyhedron::Vertex_iterator Vertex_iterator;
int main() {
Point_3 p( 1, 0, 0);
Point_3 q( 0, 1, 0);
Point_3 r( 0, 0, 1);
Point_3 s( 0, 0, 0);
Polyhedron P;
P.make_tetrahedron( p, q, r, s);
std::for_each( P.facets_begin(), P.facets_end(), Facet_normal());
std::for_each( P.vertices_begin(), P.vertices_end(), Vertex_normal());
CGAL::set_pretty_mode( std::cout);
for ( Vertex_iterator i = P.vertices_begin(); i != P.vertices_end(); ++i)
std::cout << i->normal() << std::endl;
return 0;
}
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