// Copyright (c) 2011 CNRS and LIRIS' Establishments (France).
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org)
//
// $URL: https://github.com/CGAL/cgal/blob/v5.2/Linear_cell_complex/include/CGAL/Linear_cell_complex_operations.h $
// $Id: Linear_cell_complex_operations.h 0779373 2020-03-26T13:31:46+01:00 Sébastien Loriot
// SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial
//
// Author(s) : Guillaume Damiand <guillaume.damiand@liris.cnrs.fr>
//
#ifndef CGAL_LINEAR_CELL_COMPLEX_OPERATIONS_H
#define CGAL_LINEAR_CELL_COMPLEX_OPERATIONS_H 1
#include <CGAL/Cell_iterators.h>
#include <CGAL/Cell_const_iterators.h>
#include <CGAL/Origin.h>
namespace CGAL {
/** @file Linear_cell_complex_operations.h
* Basic operators on a linear cell complex.
*/
namespace internal {
template <class Point, class Vector>
void newell_single_step_3_for_lcc(const Point& p, const Point& q, Vector& n)
{
// Compute normal of the face by using Newell's method: for each edge PQ
// Nx += (Py - Qy) * (Pz + Qz);
// Ny += (Pz - Qz) * (Px + Qx);
// Nz += (Px - Qx) * (Py + Qy);
n = Vector(n.x()+((p.y()-q.y())*(p.z()+q.z())),
n.y()+((p.z()-q.z())*(p.x()+q.x())),
n.z()+((p.x()-q.x())*(p.y()+q.y())));
// Dot product formula
/*n=Vector(n.x()+((p.y()*q.z())-(p.z()*q.y())),
n.y()+((p.x()*q.z())-(p.z()*q.x())),
n.z()+((p.x()*q.y())-(p.y()*q.x())));*/
}
} // End namespace internal
/** Compute the normal of the given facet.
* @param amap the used linear cell complex.
* @param adart a dart incident to the facet.
* @return the normal of the facet.
*/
template <class LCC>
typename LCC::Vector compute_normal_of_cell_2
(const LCC& amap, typename LCC::Dart_const_handle adart)
{
typedef typename LCC::Point Point;
typedef typename LCC::Vector Vector;
typename LCC::Dart_const_handle start=adart;
Vector normal(CGAL::NULL_VECTOR);
// We go to the beginning of the face (first dart)
while ( amap.is_previous_exist(start) && amap.previous(start)!=adart )
start = amap.previous(start);
// Now we advance to process each edge
unsigned int nb = 0;
const Point* curr = &amap.point(start);
adart=start;
do
{
if (amap.other_extremity(adart)==LCC::null_handle)
adart=start; // To leave the loop, because we know that adart has no next dart
else
{
const Point* next = &amap.point(amap.other_extremity(adart));
internal::newell_single_step_3_for_lcc(*curr, *next, normal);
++nb;
curr = next;
if (amap.is_next_exist(adart) && amap.next(adart)!=start)
adart=amap.next(adart);
else
adart=start;
}
}
while(adart!=start);
assert(nb>0);
return (typename LCC::Traits::Construct_scaled_vector()(normal, 1.0/nb));
// return normal / std::sqrt(normal * normal);
}
/** Compute the normal of the given vertex.
* @param amap the used linear cell complex.
* @param adart a dart incident to the vertex.
* @return the normal of the vertex.
*/
template <class LCC>
typename LCC::Vector compute_normal_of_cell_0
(const LCC& amap, typename LCC::Dart_const_handle adart)
{
typedef typename LCC::Vector Vector;
Vector normal(CGAL::NULL_VECTOR);
unsigned int nb = 0;
for ( typename LCC::template One_dart_per_incident_cell_range<2,0>::
const_iterator it(amap, adart); it.cont(); ++it )
{
normal = typename LCC::Traits::Construct_sum_of_vectors()
(normal, CGAL::compute_normal_of_cell_2(amap,it));
++nb;
}
if ( nb<2 ) return normal;
return (typename LCC::Traits::Construct_scaled_vector()(normal, 1.0/nb));
}
// Compute the barycenter of a given i-cell
// General case, 1<i<=dimension
template<class LCC, unsigned int i, unsigned int dim=LCC::dimension>
struct Barycenter_functor
{
static typename LCC::Point run(const LCC& amap,
typename LCC::Dart_const_handle adart)
{
CGAL_static_assertion(0<i && i<=LCC::dimension);
CGAL_assertion(adart != LCC::null_handle);
typename LCC::Vector vec
(typename LCC::Traits::Construct_vector()(CGAL::ORIGIN,
amap.point(adart)));
unsigned int nb = 1;
typename LCC::template One_dart_per_incident_cell_range<0, i, i>::
const_iterator it(amap, adart);
for ( ++it; it.cont(); ++it)
{
vec = typename LCC::Traits::Construct_sum_of_vectors()
(vec, typename LCC::Traits::Construct_vector()(CGAL::ORIGIN,
amap.point(it) ));
++nb;
}
return typename LCC::Traits::Construct_translated_point()
(CGAL::ORIGIN, typename LCC::Traits::Construct_scaled_vector()
(vec, 1.0/nb));
}
};
// Compute the barycenter of a given 1-cell
template<class LCC, unsigned int dim>
struct Barycenter_functor<LCC, 1, dim>
{
static typename LCC::Point run(const LCC& amap,
typename LCC::Dart_const_handle adart)
{
CGAL_static_assertion(1<=LCC::dimension);
CGAL_assertion(adart != LCC::null_handle);
typename LCC::Dart_const_handle d2=amap.other_extremity(adart);
if (d2==amap.null_handle) return amap.point(adart);
return typename LCC::Traits::Construct_midpoint()
(amap.point(adart),
amap.point(d2));
}
};
// Compute the barycenter of a given 2-cell
template<class LCC, unsigned int dim>
struct Barycenter_functor<LCC, 2, dim>
{
static typename LCC::Point run(const LCC& amap,
typename LCC::Dart_const_handle adart)
{
CGAL_static_assertion(2<=LCC::dimension);
CGAL_assertion(adart != LCC::null_handle);
// We go to the beginning of the face (first dart, case of open face)
typename LCC::Dart_const_handle start=adart;
while ( amap.is_previous_exist(start) && amap.previous(start)!=adart )
start = amap.previous(start);
typename LCC::Vector vec
(typename LCC::Traits::Construct_vector()(CGAL::ORIGIN,
amap.point(start)));
if ((!amap.is_previous_exist(adart) && !amap.is_next_exist(adart)) ||
amap.next(adart)==adart)
return typename LCC::Traits::Construct_translated_point()
(CGAL::ORIGIN, vec); // case of face with only one edge
unsigned int nb = 1;
// Now we advance to process each edge
adart=amap.next(start); // Because the first vertex was already sum up
do
{
vec = typename LCC::Traits::Construct_sum_of_vectors()
(vec, typename LCC::Traits::Construct_vector()(CGAL::ORIGIN,
amap.point(adart)));
++nb;
if (amap.is_next_exist(adart) && amap.next(adart)!=start)
adart=amap.next(adart);
else
adart=start;
}
while(adart!=start);
assert(nb>1);
return typename LCC::Traits::Construct_translated_point()
(CGAL::ORIGIN, typename LCC::Traits::Construct_scaled_vector()
(vec, 1.0/nb));
}
};
} // namespace CGAL
#endif // CGAL_LINEAR_CELL_COMPLEX_OPERATIONS_H //
// EOF //