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dust3d/thirdparty/cgal/CGAL-4.13/include/CGAL/Ridges.h

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// Copyright (c) 2007 INRIA Sophia-Antipolis (France), INRIA Lorraine LORIA.
// 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 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.
//
// $URL$
// $Id$
// SPDX-License-Identifier: GPL-3.0+
//
// Author(s) : Marc Pouget and Frédéric Cazals
#ifndef CGAL_RIDGE_3_H_
#define CGAL_RIDGE_3_H_
#include <CGAL/license/Ridges_3.h>
#include <utility>
#include <list>
#include <map>
#include <CGAL/basic.h>
#include <CGAL/barycenter.h>
#include <CGAL/boost/graph/properties.h>
#include <CGAL/assertions.h>
#include <boost/type_traits/is_same.hpp>
#include <boost/foreach.hpp>
#include <CGAL/Bbox_3.h>
namespace CGAL {
enum Ridge_interrogation_type {MAX_RIDGE, MIN_RIDGE, CREST_RIDGE};
enum Ridge_type {NO_RIDGE=0,
MAX_ELLIPTIC_RIDGE, MAX_HYPERBOLIC_RIDGE, MAX_CREST_RIDGE,
MIN_ELLIPTIC_RIDGE, MIN_HYPERBOLIC_RIDGE, MIN_CREST_RIDGE};
//are ridges tagged as elliptic or hyperbolic using 3rd or 4th order
//differential quantitities?
//with Ridge_order_3 P1 and P2 are not used and the sharpness is not defined.
enum Ridge_order {Ridge_order_3 = 3, Ridge_order_4 = 4};
//---------------------------------------------------------------------------
//Ridge_line : a connected sequence of edges of a
//TriangularPolyhedralSurface crossed by a
//ridge (with a barycentric coordinate to compute the crossing point),
//with a Ridge_type and weights : strength and sharpness. Note
//sharpness is only available (more precisely only meaningful)
//if the Ridge_approximation has
//been computed with the Ridge_order Ridge_order_4.
//(else, if it is computed with Ridge_order_3 it keeps its initial
//value 0)
//--------------------------------------------------------------------------
template < class TriangleMesh > class Ridge_line
{
typedef typename boost::property_map<TriangleMesh,CGAL::vertex_point_t>::type VPM;
typedef typename boost::property_traits<VPM>::value_type Point_3;
typedef typename Kernel_traits<Point_3>::Kernel Kernel;
public:
typedef typename Kernel::FT FT;
typedef typename boost::graph_traits<TriangleMesh>::halfedge_descriptor halfedge_descriptor;
typedef std::pair< halfedge_descriptor, FT> Ridge_halfedge;
typedef Ridge_halfedge ridge_halfhedge; //kept for backward compatibility
Ridge_type line_type() const {return m_line_type;}
Ridge_type& line_type() {return m_line_type;}
const FT strength() const {return m_strength;}
FT& strength() {return m_strength;}
const FT sharpness() const {return m_sharpness;}
FT& sharpness() {return m_sharpness;}
const std::list<Ridge_halfedge>* line() const { return &m_line;}
std::list<Ridge_halfedge>* line() { return &m_line;}
//constructor
Ridge_line(const TriangleMesh& P);
/* The output is : line_type, strength, sharpness, list of points of
the polyline. An insert operator << is also available.
*/
template <class VertexPointMap>
void dump_4ogl(std::ostream& out_stream, VertexPointMap vpm) const ;
template <class VertexPointMap>
void dump_verbose(std::ostream& out_stream, VertexPointMap vpm) const ;
protected:
const TriangleMesh& P;
//one of MAX_ELLIPTIC_RIDGE, MAX_HYPERBOLIC_RIDGE, MAX_CREST_RIDGE,
//MIN_ELLIPTIC_RIDGE, MIN_HYPERBOLIC_RIDGE or MIN_CREST_RIDGE
Ridge_type m_line_type;
std::list<Ridge_halfedge> m_line;
FT m_strength;// = integral of ppal curvature along the line
FT m_sharpness;// = (integral of second derivative of curvature
// along the line) multiplied by the squared of
// the size of the model
// (which is the radius of the smallest enclosing
// ball)
};
//--------------------------------------------------------------------------
// IMPLEMENTATION OF Ridge_line members
//--------------------------------------------------------------------------
//constructor
template < class TriangleMesh >
Ridge_line<TriangleMesh>::
Ridge_line(const TriangleMesh& P)
: P(P), m_strength(0.), m_sharpness(0.)
{}
template < class TriangleMesh >
template <class VertexPointMap>
void Ridge_line<TriangleMesh>::
dump_4ogl(std::ostream& out_stream,
VertexPointMap vpm) const
{
out_stream << line_type() << " "
<< strength() << " "
<< sharpness() << " ";
typedef typename boost::property_traits<VertexPointMap>::value_type Point_3;
typename std::list<Ridge_halfedge >::const_iterator
iter = line()->begin(),
ite = line()->end();
for (;iter!=ite;iter++){
//he: p->q, r is the crossing point
Point_3 p = get(vpm, target(opposite(iter->first,P),P)),
q = get(vpm,target(iter->first,P));
Point_3 r = CGAL::barycenter(p, iter->second, q);
out_stream << " " << r ;
}
out_stream << std::endl;
}
//verbose output
template < class TriangleMesh >
template <class VertexPointMap>
void Ridge_line<TriangleMesh>::
dump_verbose(std::ostream& out_stream, VertexPointMap vpm) const
{
typedef typename boost::property_traits<VertexPointMap>::value_type Point_3;
out_stream << "Line type is : " << line_type() << std::endl
<< "Strength is : " << strength() << std::endl
<< "Sharpness is : " << sharpness() << std::endl
<< "Polyline point coordinates are : " << std::endl;
typename std::list<Ridge_halfedge>::const_iterator
iter = line()->begin(),
ite = line()->end();
for (;iter!=ite;iter++){
//he: p->q, r is the crossing point
Point_3 p = get(vpm, target(opposite(iter->first,P),P)),
q = get(vpm,target(iter->first,P));
Point_3 r = CGAL::barycenter(p, iter->second, q);
out_stream << r << std::endl;
}
}
template <class TriangleMesh>
std::ostream&
operator<<(std::ostream& out_stream, const Ridge_line<TriangleMesh>& ridge_line)
{
ridge_line.dump_verbose(out_stream);
return out_stream;
}
//---------------------------------------------------------------------------
//Ridge_approximation
//--------------------------------------------------------------------------
template < class TriangleMesh,
class VertexFTMap,
class VertexVectorMap >
class Ridge_approximation
{
typedef typename boost::property_map<TriangleMesh,vertex_point_t>::const_type VPM;
typedef typename boost::property_traits<VPM>::value_type Point_3;
typedef typename Kernel_traits<Point_3>::Kernel Kernel;
public:
typedef typename Kernel::FT FT;
typedef typename Kernel::Vector_3 Vector_3;
typedef typename boost::graph_traits<TriangleMesh>::vertex_descriptor vertex_descriptor;
typedef typename boost::graph_traits<TriangleMesh>::halfedge_descriptor halfedge_descriptor;
typedef typename boost::graph_traits<TriangleMesh>::face_descriptor face_descriptor;
typedef typename boost::graph_traits<TriangleMesh>::face_iterator face_iterator;
//requirements for the templates TriangleMesh and VertexFTMap or VertexVectorMap
CGAL_static_assertion((boost::is_same<vertex_descriptor, typename VertexFTMap::key_type>::value));
CGAL_static_assertion((boost::is_same<vertex_descriptor, typename VertexVectorMap::key_type>::value));
CGAL_static_assertion((boost::is_same<FT, typename VertexFTMap::value_type>::value));
CGAL_static_assertion((boost::is_same<Vector_3, typename VertexVectorMap::value_type>::value));
typedef std::pair< halfedge_descriptor, FT> Ridge_halfedge;
typedef Ridge_halfedge Ridge_halfhedge; // kept for backward compatibility
typedef CGAL::Ridge_line<TriangleMesh> Ridge_line;
Ridge_approximation(const TriangleMesh &P,
const VertexFTMap& vertex2k1_pm,
const VertexFTMap& vertex2k2_pm,
const VertexFTMap& vertex2b0_pm,
const VertexFTMap& vertex2b3_pm,
const VertexVectorMap& vertex2d1_pm,
const VertexVectorMap& vertex2d2_pm,
const VertexFTMap& vertex2P1_pm,
const VertexFTMap& vertex2P2_pm);
template <class OutputIterator>
OutputIterator compute_max_ridges(OutputIterator it, Ridge_order ord = Ridge_order_3);
template <class OutputIterator>
OutputIterator compute_min_ridges(OutputIterator it, Ridge_order ord = Ridge_order_3);
template <class OutputIterator>
OutputIterator compute_crest_ridges(OutputIterator it, Ridge_order ord = Ridge_order_3);
//Find MAX_RIDGE, MIN_RIDGE or CREST_RIDGE ridges iterate on P facets,
//find a non-visited, regular (i.e. if there is a coherent
//orientation of ppal dir at the facet vertices), 2Xing triangle,
//follow non-visited, regular, 2Xing triangles in both sens to
//create a Ridge line. Each time an edge is added the strength and
//sharpness(if Ridge_order_4) are updated.
template <class OutputIterator>
OutputIterator compute_ridges(Ridge_interrogation_type r_type,
OutputIterator ridge_lines_it,
Ridge_order ord = Ridge_order_3);
protected:
const TriangleMesh& P;
FT squared_model_size;//squared radius of the smallest enclosing sphere of the TriangleMesh
//used to make the sharpness scale independant and iso indep
Ridge_order tag_order;
typedef std::map<face_descriptor, bool> Facet2bool_map_type;
Facet2bool_map_type is_visited_map;
//Property maps
const VertexFTMap &k1, &k2, &b0, &b3, &P1, &P2;
const VertexVectorMap &d1, &d2;
VPM vpm;
//is a facet crossed by a BLUE, RED or CREST_RIDGE ridge? if so, return
//the crossed edges and more precise type from MAX_ELLIPTIC_RIDGE,
//MAX_HYPERBOLIC_RIDGE, MAX_CREST_RIDGE, MIN_ELLIPTIC_RIDGE,
//MIN_HYPERBOLIC_RIDGE, MIN_CREST_RIDGE or NO_RIDGE
Ridge_type facet_ridge_type(const face_descriptor f,
halfedge_descriptor& he1,
halfedge_descriptor& he2,
Ridge_interrogation_type r_type);
//is an edge crossed by a BLUE/RED ridge? (color is MAX_RIDGE or
//MIN_RIDGE ). As we only test edges of regular triangles, the ppal
//direction at endpoints d_p and d_q cannot be orthogonal. If both
//extremalities vanish, we consider no crossing occurs. If only one
//of them vanishes, we consider it as an positive infinitesimal and
//apply the general rule. The general rule is that for both
//non-vanishing extremalities, a crossing occurs if their sign
//differ; Assuming the accute rule to orient the ppal directions,
//there is a crossing iff d_p.d_q * b_p*b_q < 0
void xing_on_edge(const halfedge_descriptor he,
bool& is_crossed,
Ridge_interrogation_type color);
//given a ridge segment of a given color, in a triangle crossing he1
//(v_p1 -> v_q1) and he2 (v_p2 -> v_q2) return true if it is
//elliptic, false if it is hyperbolic.
bool tag_as_elliptic_hyperbolic(const Ridge_interrogation_type color,
const halfedge_descriptor he1,
const halfedge_descriptor he2);
//for the computation with tag_order == 3 only
//for a ridge segment [r1,r2] in a triangle (v1,v2,v3), let r = r2 -
//r1 and normalize, the projection of a point p on the line (r1,r2)
//is pp=r1+tr, with t=(p-r1)*r then the vector v starting at p is
//pointing to the ridge line (r1,r2) if (pp-p)*v >0. Return the sign
//of b, for a ppal direction pointing to the ridge segment,
//appearing at least at two vertices of the facet.
//
// for color = MAX_RIDGE, sign = 1 if MAX_ELLIPTIC_RIDGE, -1 if
// MAX_HYPERBOLIC_RIDGE
//
// for color = MIN_RIDGE, sign = -1 if MIN_ELLIPTIC_RIDGE, 1 if
// MIN_HYPERBOLIC_RIDGE
int b_sign_pointing_to_ridge(const vertex_descriptor v1,
const vertex_descriptor v2,
const vertex_descriptor v3,
const Vector_3 r1, const Vector_3 r2,
const Ridge_interrogation_type color);
//a ridge line begins with a segment in a triangle given by the 2 he
//crossed
void init_ridge_line(Ridge_line* ridge_line,
const halfedge_descriptor h1,
const halfedge_descriptor h2,
const Ridge_type r_type);
//When the line is extended with a he, the bary coord of the
//crossing point is computed, the pair (he,coord) is added and the
//weights are updated
void addback(Ridge_line* ridge_line,
const halfedge_descriptor he,
const Ridge_type r_type);
void addfront(Ridge_line* ridge_line,
const halfedge_descriptor he,
const Ridge_type r_type);
//compute the barycentric coordinate of the xing point (blue or red)
//for he: p->q (wrt the extremality values b0/3). coord is st
//xing_point = coord*p + (1-coord)*q
FT bary_coord(const halfedge_descriptor he,
const Ridge_type r_type);
};
// IMPLEMENTATION OF Ridge_approximation members
/////////////////////////////////////////////////////////////////////////////
//constructor
template < class TriangleMesh,
class VertexFTMap,
class VertexVectorMap >
Ridge_approximation< TriangleMesh, VertexFTMap , VertexVectorMap >::
Ridge_approximation(const TriangleMesh &p,
const VertexFTMap& vertex2k1_pm,
const VertexFTMap& vertex2k2_pm,
const VertexFTMap& vertex2b0_pm,
const VertexFTMap& vertex2b3_pm,
const VertexVectorMap& vertex2d1_pm,
const VertexVectorMap& vertex2d2_pm,
const VertexFTMap& vertex2P1_pm,
const VertexFTMap& vertex2P2_pm)
: P(p), k1(vertex2k1_pm), k2(vertex2k2_pm), b0(vertex2b0_pm), b3(vertex2b3_pm),
P1(vertex2P1_pm), P2(vertex2P2_pm), d1(vertex2d1_pm), d2(vertex2d2_pm),
vpm(get(CGAL::vertex_point,p))
{
//init the is_visited_map and check that the mesh is a triangular one.
face_iterator itb,ite;
boost::tie(itb,ite) = faces(P);
for(;itb!=ite;itb++) {
is_visited_map[*itb] = false;
}
CGAL_precondition( is_triangle_mesh(p) );
std::vector<Point_3> points;
BOOST_FOREACH(vertex_descriptor v, vertices(p)){
points.push_back(get(vpm,v));
}
Bbox_3 bb = bbox_3(points.begin(), points.end());
double width = bb.xmax() - bb.xmin();
double yw = bb.ymax() - bb.ymin();
width = (std::max)(width,yw);
double zw = bb.zmax() - bb.zmin();
width = (std::max)(width,zw);
squared_model_size = (width*width)/4.0 ;
tag_order = Ridge_order_3;
}
template < class TriangleMesh,
class VertexFTMap,
class VertexVectorMap >
template <class OutputIterator>
OutputIterator
Ridge_approximation< TriangleMesh, VertexFTMap , VertexVectorMap >::
compute_max_ridges(OutputIterator it, Ridge_order ord)
{
compute_ridges(MAX_RIDGE, it, ord);
return it;
}
template < class TriangleMesh,
class VertexFTMap,
class VertexVectorMap >
template <class OutputIterator>
OutputIterator
Ridge_approximation< TriangleMesh, VertexFTMap , VertexVectorMap >::
compute_min_ridges(OutputIterator it, Ridge_order ord)
{
compute_ridges(MIN_RIDGE, it, ord);
return it;
}
template < class TriangleMesh,
class VertexFTMap,
class VertexVectorMap >
template <class OutputIterator>
OutputIterator
Ridge_approximation< TriangleMesh, VertexFTMap , VertexVectorMap >::
compute_crest_ridges(OutputIterator it, Ridge_order ord)
{
compute_ridges(CREST_RIDGE, it, ord);
return it;
}
template < class TriangleMesh,
class VertexFTMap,
class VertexVectorMap >
template <class OutputIterator>
OutputIterator
Ridge_approximation< TriangleMesh, VertexFTMap , VertexVectorMap >::
compute_ridges(Ridge_interrogation_type r_type, OutputIterator ridge_lines_it, Ridge_order ord)
{
tag_order = ord;
//reinit the is_visited_map
face_iterator itb,ite;
boost::tie(itb,ite) = faces(P);
for(;itb!=ite;itb++) is_visited_map[*itb] = false;
boost::tie(itb,ite) = faces(P);
for(;itb!=ite;itb++)
{
face_descriptor f = *itb;
if (is_visited_map.find(f)->second) continue;
is_visited_map.find(f)->second = true;
halfedge_descriptor h1, h2, curhe1, curhe2, curhe;
//h1 h2 are the hedges crossed if any, r_type should be
//MAX_RIDGE, MIN_RIDGE or CREST_RIDGE ; cur_ridge_type should be
//MAX_ELLIPTIC_RIDGE, MAX_HYPERBOLIC_RIDGE, MAX_CREST_RIDGE,
//MIN_ELLIPTIC_RIDGE, MIN_HYPERBOLIC_RIDGE, MIN_CREST_RIDGE or NO_RIDGE
Ridge_type cur_ridge_type = facet_ridge_type(f,h1,h2,r_type);
if ( cur_ridge_type == NO_RIDGE ) continue;
//a ridge_line is begining and stored
Ridge_line* cur_ridge_line = new Ridge_line(P);
init_ridge_line(cur_ridge_line, h1, h2, cur_ridge_type);
*ridge_lines_it++ = cur_ridge_line;
//next triangle adjacent to h1 (push_front)
if ( ! is_border_edge(h1,P) )
{
f = face(opposite(h1,P),P);
curhe = h1;
while (cur_ridge_type == facet_ridge_type(f,curhe1,curhe2,r_type))
{
//follow the ridge from curhe
if (is_visited_map.find(f)->second) break;
is_visited_map.find(f)->second = true;
if (opposite(curhe,P) == curhe1) curhe = curhe2;
else curhe = curhe1;//curhe stays at the ridge extremity
addfront(cur_ridge_line, curhe, cur_ridge_type);
if ( ! is_border_edge(curhe,P) ) f = face(opposite(curhe,P),P);
else break;
}
//exit from the while if
//1. border or already visited (this is a ridge loop)
//2. not same type, then do not set visisted cause a MAX_ELLIPTIC_RIDGE
// follows a MAX_HYPERBOLIC_RIDGE
}
//next triangle adjacent to h2 (push_back)
if ( ! is_border_edge(h2,P) )
{
f = face(opposite(h2,P),P);
curhe = h2;
while (cur_ridge_type ==
facet_ridge_type(f,curhe1,curhe2,r_type))
{
//follow the ridge from curhe
if (is_visited_map.find(f)->second) break;
is_visited_map.find(f)->second = true;
if (opposite(curhe,P) == curhe1) curhe = curhe2;
else curhe = curhe1;
addback(cur_ridge_line, curhe, cur_ridge_type);
if ( ! is_border_edge(curhe,P) ) f = face(opposite(curhe,P),P);
else break;
}
}
}
return ridge_lines_it;
}
template < class TriangleMesh,
class VertexFTMap,
class VertexVectorMap >
Ridge_type
Ridge_approximation< TriangleMesh, VertexFTMap , VertexVectorMap >::
facet_ridge_type(const face_descriptor f, halfedge_descriptor& he1, halfedge_descriptor&
he2, Ridge_interrogation_type r_type)
{
//polyhedral data
//we have v1--h1-->v2--h2-->v3--h3-->v1
const halfedge_descriptor h1 = halfedge(f,P);
const vertex_descriptor v2 = target(h1,P);
const halfedge_descriptor h2 = next(h1,P);
const vertex_descriptor v3 = target(h2,P);
const halfedge_descriptor h3 = next(h2,P);
const vertex_descriptor v1 = target(h3,P);
//check for regular facet
//i.e. if there is a coherent orientation of ppal dir at the facet vertices
if ( get(d1,v1)*get(d1,v2) * get(d1,v1)*get(d1,v3) * get(d1,v2)*get(d1,v3) < 0 )
return NO_RIDGE;
//determine potential crest color
//MAX_CREST_RIDGE if |sum(k1)|>|sum(k2)| sum over facet vertices vi
//MIN_CREST_RIDGE if |sum(k1)|<|sum(k2)|
Ridge_type crest_color = NO_RIDGE;
if (r_type == CREST_RIDGE)
{
if ( CGAL::abs(get(k1,v1)+get(k1,v2)+get(k1,v3)) > CGAL::abs(get(k2, v1)+get(k2,v2)+get(k2,v3)) )
crest_color = MAX_CREST_RIDGE;
if ( CGAL::abs(get(k1,v1)+get(k1,v2)+get(k1,v3)) < CGAL::abs(get(k2,v1)+get(k2,v2)+get(k2,v3)) )
crest_color = MIN_CREST_RIDGE;
if ( CGAL::abs(get(k1,v1)+get(k1,v2)+get(k1,v3)) == CGAL::abs(get(k2,v1)+get(k2,v2)+get(k2,v3)) )
return NO_RIDGE;
}
//compute Xing on the 3 edges
bool h1_is_crossed = false, h2_is_crossed = false, h3_is_crossed = false;
if ( r_type == MAX_RIDGE || crest_color == MAX_CREST_RIDGE )
{
xing_on_edge(h1, h1_is_crossed, MAX_RIDGE);
xing_on_edge(h2, h2_is_crossed, MAX_RIDGE);
xing_on_edge(h3, h3_is_crossed, MAX_RIDGE);
}
if ( r_type == MIN_RIDGE || crest_color == MIN_CREST_RIDGE )
{
xing_on_edge(h1, h1_is_crossed, MIN_RIDGE);
xing_on_edge(h2, h2_is_crossed, MIN_RIDGE);
xing_on_edge(h3, h3_is_crossed, MIN_RIDGE);
}
//there are either 0 or 2 crossed edges
if ( !h1_is_crossed && !h2_is_crossed && !h3_is_crossed )
return NO_RIDGE;
if (h1_is_crossed && h2_is_crossed && !h3_is_crossed)
{
he1 = h1;
he2 = h2;
}
if (h1_is_crossed && !h2_is_crossed && h3_is_crossed)
{
he1 = h1;
he2 = h3;
}
if (!h1_is_crossed && h2_is_crossed && h3_is_crossed)
{
he1 = h2;
he2 = h3;
}
//check there is no other case (just one edge crossed)
CGAL_postcondition ( !( (h1_is_crossed && !h2_is_crossed && !h3_is_crossed)
|| (!h1_is_crossed && h2_is_crossed && !h3_is_crossed)
|| (!h1_is_crossed && !h2_is_crossed && h3_is_crossed)) );
//There is a ridge segment in the triangle, determine its type elliptic/hyperbolic
bool is_elliptic;
if ( r_type == MAX_RIDGE || crest_color == MAX_CREST_RIDGE )
is_elliptic = tag_as_elliptic_hyperbolic(MAX_RIDGE, he1, he2);
else is_elliptic = tag_as_elliptic_hyperbolic(MIN_RIDGE, he1, he2);
if (r_type == MAX_RIDGE)
{if (is_elliptic) return MAX_ELLIPTIC_RIDGE;
else return MAX_HYPERBOLIC_RIDGE; }
if (crest_color == MAX_CREST_RIDGE && is_elliptic) return MAX_CREST_RIDGE;
if (r_type == MIN_RIDGE)
{if (is_elliptic) return MIN_ELLIPTIC_RIDGE;
else return MIN_HYPERBOLIC_RIDGE; }
if (crest_color == MIN_CREST_RIDGE && is_elliptic) return MIN_CREST_RIDGE;
return NO_RIDGE;
}
template < class TriangleMesh,
class VertexFTMap,
class VertexVectorMap >
void
Ridge_approximation< TriangleMesh, VertexFTMap , VertexVectorMap >::
xing_on_edge(const halfedge_descriptor he, bool& is_crossed, Ridge_interrogation_type color)
{
is_crossed = false;
FT sign = 0;
FT b_p, b_q; // extremalities at p and q for he: p->q
Vector_3 d_p = get(d1,target(opposite(he,P),P)),
d_q = get(d1,target(he,P)); //ppal dir
if ( color == MAX_RIDGE ) {
b_p = get(b0,target(opposite(he,P),P));
b_q = get(b0,target(he,P));
}
else {
b_p = get(b3,target(opposite(he,P),P));
b_q = get(b3,target(he,P));
}
if ( b_p == 0 && b_q == 0 ) return;
if ( b_p == 0 && b_q !=0 ) sign = d_p*d_q * b_q;
if ( b_p != 0 && b_q ==0 ) sign = d_p*d_q * b_p;
if ( b_p != 0 && b_q !=0 ) sign = d_p*d_q * b_p * b_q;
if ( sign < 0 ) is_crossed = true;
}
template < class TriangleMesh,
class VertexFTMap,
class VertexVectorMap >
bool
Ridge_approximation< TriangleMesh, VertexFTMap , VertexVectorMap >::
tag_as_elliptic_hyperbolic(const Ridge_interrogation_type color,
const halfedge_descriptor he1,
const halfedge_descriptor he2)
{
const vertex_descriptor v_p1 = target(opposite(he1,P),P), v_q1 = target(he1,P),
v_p2 = target(opposite(he2,P),P), v_q2 = target(he2,P); // hei: pi->qi
FT coord1, coord2;
if (color == MAX_RIDGE)
{
coord1 = CGAL::abs(get(b0,v_q1)) / ( CGAL::abs(get(b0,v_p1)) + CGAL::abs(get(b0,v_q1)) );
coord2 = CGAL::abs(get(b0,v_q2)) / ( CGAL::abs(get(b0,v_p2)) + CGAL::abs(get(b0,v_q2)) );
}
else
{
coord1 = CGAL::abs(get(b3,v_q1)) / ( CGAL::abs(get(b3,v_p1)) + CGAL::abs(get(b3,v_q1)) );
coord2 = CGAL::abs(get(b3,v_q2)) / ( CGAL::abs(get(b3,v_p2)) + CGAL::abs(get(b3,v_q2)) );
}
if ( tag_order == Ridge_order_3 ) {
Vector_3 r1 = CGAL::barycenter(get(vpm, v_p1), coord1, get(vpm, v_q1)) - ORIGIN,
r2 = CGAL::barycenter(get(vpm,v_p2), coord2, get(vpm,v_q2)) - ORIGIN;
//identify the 3 different vertices v_p1, v_q1 and v3 = v_p2 or v_q2
vertex_descriptor v3;
if (v_p2 == v_p1 || v_p2 == v_q1) v3 = v_q2;
else v3 = v_p2;
int b_sign = b_sign_pointing_to_ridge(v_p1, v_q1, v3, r1, r2, color);
if (color == MAX_RIDGE)
if (b_sign == 1) return true;
else return false;
else if (b_sign == -1) return true;
else return false;
}
else {//tag_order == Ridge_order_4, check the sign of the meanvalue of the signs
// of Pi at the two crossing points
FT sign_P;
if (color == MAX_RIDGE)
sign_P = get(P1,v_p1)*coord1 + get(P1,v_q1)*(1-coord1)
+ get(P1,v_p2)*coord2 + get(P1,v_q2)*(1-coord2);
else sign_P = get(P2,v_p1)*coord1 + get(P2,v_q1)*(1-coord1)
+ get(P2,v_p2)*coord2 + get(P2,v_q2)*(1-coord2);
if ( sign_P < 0 ) return true; else return false;
}
}
template < class TriangleMesh,
class VertexFTMap,
class VertexVectorMap >
int Ridge_approximation< TriangleMesh, VertexFTMap , VertexVectorMap >::
b_sign_pointing_to_ridge(const vertex_descriptor v1,
const vertex_descriptor v2,
const vertex_descriptor v3,
const Vector_3 r1, const Vector_3 r2,
const Ridge_interrogation_type color)
{
Vector_3 r = r2 - r1, dv1, dv2, dv3;
FT bv1, bv2, bv3;
if ( color == MAX_RIDGE ) {
bv1 = get(b0,v1);
bv2 = get(b0,v2);
bv3 = get(b0,v3);
dv1 = get(d1,v1);
dv2 = get(d1,v2);
dv3 = get(d1,v3);
}
else {
bv1 = get(b3,v1);
bv2 = get(b3,v2);
bv3 = get(b3,v3);
dv1 = get(d2,v1);
dv2 = get(d2,v2);
dv3 = get(d2,v3);
}
if ( r != CGAL::NULL_VECTOR ) r = r/CGAL::sqrt(r*r);
FT sign1, sign2, sign3;
sign1 = bv1*(r1 - (get(vpm, v1)-ORIGIN) + (((get(vpm, v1)-ORIGIN)-r1)*r)*r )*dv1;
sign2 = bv2*(r1 - (get(vpm, v2)-ORIGIN) + (((get(vpm, v2)-ORIGIN)-r1)*r)*r )*dv2;
sign3 = bv3*(r1 - (get(vpm, v3)-ORIGIN) + (((get(vpm, v3)-ORIGIN)-r1)*r)*r )*dv3;
int compt = 0;
if ( sign1 > 0 ) compt++; else if (sign1 < 0) compt--;
if ( sign2 > 0 ) compt++; else if (sign2 < 0) compt--;
if ( sign3 > 0 ) compt++; else if (sign3 < 0) compt--;
if (compt > 0) return 1; else return -1;
}
template < class TriangleMesh,
class VertexFTMap,
class VertexVectorMap >
void Ridge_approximation< TriangleMesh, VertexFTMap , VertexVectorMap >::
init_ridge_line(Ridge_line* ridge_line,
const halfedge_descriptor h1,
const halfedge_descriptor h2,
const Ridge_type r_type)
{
ridge_line->line_type() = r_type;
ridge_line->line()->push_back(Ridge_halfedge(h1, bary_coord(h1,r_type)));
addback(ridge_line, h2, r_type);
}
template < class TriangleMesh,
class VertexFTMap,
class VertexVectorMap >
void Ridge_approximation< TriangleMesh, VertexFTMap , VertexVectorMap >::
addback(Ridge_line* ridge_line, const halfedge_descriptor he,
const Ridge_type r_type)
{
halfedge_descriptor he_cur = ( --(ridge_line->line()->end()) )->first;
FT coord_cur = ( --(ridge_line->line()->end()) )->second;//bary_coord(he_cur);
FT coord = bary_coord(he,r_type);
vertex_descriptor v_p = target(opposite(he,P),P), v_q = target(he,P),
v_p_cur = target(opposite(he_cur,P),P), v_q_cur = target(he_cur,P); // he: p->q
Vector_3 segment = CGAL::barycenter(get(vpm, v_p), coord, get(vpm, v_q)) -
CGAL::barycenter(get(vpm, v_p_cur), coord_cur, get(vpm, v_q_cur));
FT k1x, k2x; //abs value of the ppal curvatures at the Xing point on he.
FT k_second = 0; // abs value of the second derivative of the curvature
// along the line of curvature
k1x = CGAL::abs(get(k1,v_p)) * coord + CGAL::abs(get(k1,v_q)) * (1-coord) ;
k2x = CGAL::abs(get(k2,v_p)) * coord + CGAL::abs(get(k2,v_q)) * (1-coord) ;
if ( (ridge_line->line_type() == MAX_ELLIPTIC_RIDGE)
|| (ridge_line->line_type() == MAX_HYPERBOLIC_RIDGE)
|| (ridge_line->line_type() == MAX_CREST_RIDGE) ) {
ridge_line->strength() += k1x * CGAL::sqrt(segment * segment);
if (tag_order == Ridge_order_4) {
if (k1x != k2x)
k_second =CGAL::abs(( CGAL::abs(get(P1,v_p)) * coord + CGAL::abs(get(P1,v_q)) * (1-coord) )/(k1x-k2x));
ridge_line->sharpness() += k_second * CGAL::sqrt(segment * segment) * squared_model_size; }
}
if ( (ridge_line->line_type() == MIN_ELLIPTIC_RIDGE)
|| (ridge_line->line_type() == MIN_HYPERBOLIC_RIDGE)
|| (ridge_line->line_type() == MIN_CREST_RIDGE) ) {
ridge_line->strength() += k2x * CGAL::sqrt(segment * segment);
if (tag_order == Ridge_order_4) {
if (k1x != k2x)
k_second =CGAL::abs(( CGAL::abs(get(P2,v_p)) * coord + CGAL::abs(get(P2,v_q)) * (1-coord) )/(k1x-k2x));
ridge_line->sharpness() += k_second * CGAL::sqrt(segment * segment) * squared_model_size; }
}
ridge_line->line()->push_back( Ridge_halfedge(he, coord));
}
template < class TriangleMesh,
class VertexFTMap,
class VertexVectorMap >
void Ridge_approximation< TriangleMesh, VertexFTMap , VertexVectorMap >::
addfront(Ridge_line* ridge_line,
const halfedge_descriptor he,
const Ridge_type r_type)
{
halfedge_descriptor he_cur = ( ridge_line->line()->begin() )->first;
FT coord_cur = ( ridge_line->line()->begin() )->second;
FT coord = bary_coord(he,r_type);
vertex_descriptor v_p = target(opposite(he,P),P), v_q = target(he,P),
v_p_cur = target(opposite(he_cur,P),P), v_q_cur = target(he_cur,P); // he: p->q
Vector_3 segment = CGAL::barycenter(get(vpm, v_p), coord, get(vpm, v_q)) -
CGAL::barycenter(get(vpm, v_p_cur), coord_cur, get(vpm, v_q_cur));
FT k1x, k2x; //abs value of the ppal curvatures at the Xing point on he.
FT k_second = 0.; // abs value of the second derivative of the curvature
// along the line of curvature
k1x = CGAL::abs(get(k1,v_p)) * coord + CGAL::abs(get(k1,v_q)) * (1-coord) ;
k2x = CGAL::abs(get(k2,v_p)) * coord + CGAL::abs(get(k2,v_q)) * (1-coord) ;
if ( (ridge_line->line_type() == MAX_ELLIPTIC_RIDGE)
|| (ridge_line->line_type() == MAX_HYPERBOLIC_RIDGE)
|| (ridge_line->line_type() == MAX_CREST_RIDGE) ) {
ridge_line->strength() += k1x * CGAL::sqrt(segment * segment);
if (tag_order == Ridge_order_4) {
if (k1x != k2x)
k_second =CGAL::abs(( CGAL::abs(get(P1,v_p)) * coord + CGAL::abs(get(P1,v_q)) * (1-coord) )/(k1x-k2x));
ridge_line->sharpness() += k_second * CGAL::sqrt(segment * segment) * squared_model_size; }
}
if ( (ridge_line->line_type() == MIN_ELLIPTIC_RIDGE)
|| (ridge_line->line_type() == MIN_HYPERBOLIC_RIDGE)
|| (ridge_line->line_type() == MIN_CREST_RIDGE) ) {
ridge_line->strength() += k2x * CGAL::sqrt(segment * segment);
if (tag_order == Ridge_order_4) {
if (k1x != k2x)
k_second =CGAL::abs(( CGAL::abs(get(P2,v_p)) * coord + CGAL::abs(get(P2,v_q)) * (1-coord) )/(k1x-k2x));
ridge_line->sharpness() += k_second * CGAL::sqrt(segment * segment) * squared_model_size; }
}
ridge_line->line()->push_front( Ridge_halfedge(he, coord));
}
template < class TriangleMesh,
class VertexFTMap,
class VertexVectorMap >
typename Ridge_approximation< TriangleMesh, VertexFTMap , VertexVectorMap>::FT
Ridge_approximation< TriangleMesh, VertexFTMap , VertexVectorMap>::
bary_coord(const halfedge_descriptor he, const Ridge_type r_type)
{
FT b_p = 0., b_q = 0.; // extremalities at p and q for he: p->q
if ( (r_type == MAX_ELLIPTIC_RIDGE)
|| (r_type == MAX_HYPERBOLIC_RIDGE)
|| (r_type == MAX_CREST_RIDGE) ) {
b_p = get(b0,target(opposite(he,P),P));
b_q = get(b0,target(he,P));
}
if ( (r_type == MIN_ELLIPTIC_RIDGE)
|| (r_type == MIN_HYPERBOLIC_RIDGE)
|| (r_type == MIN_CREST_RIDGE) ) {
b_p = get(b3,target(opposite(he,P),P));
b_q = get(b3,target(he,P));
}
//denominator cannot be 0 since there is no crossing when both extremalities are 0
return CGAL::abs(b_q) / ( CGAL::abs(b_q) + CGAL::abs(b_p) );
}
//---------------------------------------------------------------------------
//Global functions
//--------------------------------------------------------------------------
template < class TriangleMesh,
class VertexFTMap,
class VertexVectorMap,
class OutputIterator>
OutputIterator compute_max_ridges(const TriangleMesh &P,
const VertexFTMap& vertex2k1_pm,
const VertexFTMap& vertex2k2_pm,
const VertexFTMap& vertex2b0_pm,
const VertexFTMap& vertex2b3_pm,
const VertexVectorMap& vertex2d1_pm,
const VertexVectorMap& vertex2d2_pm,
const VertexFTMap& vertex2P1_pm,
const VertexFTMap& vertex2P2_pm,
OutputIterator it,
Ridge_order order = Ridge_order_3)
{
typedef Ridge_approximation < TriangleMesh,
VertexFTMap, VertexVectorMap > Ridge_approximation;
Ridge_approximation ridge_approximation(P,
vertex2k1_pm, vertex2k2_pm,
vertex2b0_pm, vertex2b3_pm,
vertex2d1_pm, vertex2d2_pm,
vertex2P1_pm, vertex2P2_pm );
return ridge_approximation.compute_max_ridges(it, order);
}
template < class TriangleMesh,
class VertexFTMap,
class VertexVectorMap,
class OutputIterator>
OutputIterator compute_min_ridges(const TriangleMesh &P,
const VertexFTMap& vertex2k1_pm,
const VertexFTMap& vertex2k2_pm,
const VertexFTMap& vertex2b0_pm,
const VertexFTMap& vertex2b3_pm,
const VertexVectorMap& vertex2d1_pm,
const VertexVectorMap& vertex2d2_pm,
const VertexFTMap& vertex2P1_pm,
const VertexFTMap& vertex2P2_pm,
OutputIterator it,
Ridge_order order = Ridge_order_3)
{
typedef Ridge_approximation < TriangleMesh,
VertexFTMap, VertexVectorMap > Ridge_approximation;
Ridge_approximation ridge_approximation(P,
vertex2k1_pm, vertex2k2_pm,
vertex2b0_pm, vertex2b3_pm,
vertex2d1_pm, vertex2d2_pm,
vertex2P1_pm, vertex2P2_pm );
return ridge_approximation.compute_min_ridges(it, order);
}
template < class TriangleMesh,
class VertexFTMap,
class VertexVectorMap,
class OutputIterator>
OutputIterator compute_crest_ridges(const TriangleMesh &P,
const VertexFTMap& vertex2k1_pm,
const VertexFTMap& vertex2k2_pm,
const VertexFTMap& vertex2b0_pm,
const VertexFTMap& vertex2b3_pm,
const VertexVectorMap& vertex2d1_pm,
const VertexVectorMap& vertex2d2_pm,
const VertexFTMap& vertex2P1_pm,
const VertexFTMap& vertex2P2_pm,
OutputIterator it,
Ridge_order order = Ridge_order_3)
{
typedef Ridge_approximation < TriangleMesh,
VertexFTMap, VertexVectorMap > Ridge_approximation;
Ridge_approximation ridge_approximation(P,
vertex2k1_pm, vertex2k2_pm,
vertex2b0_pm, vertex2b3_pm,
vertex2d1_pm, vertex2d2_pm,
vertex2P1_pm, vertex2P2_pm );
return ridge_approximation.compute_crest_ridges(it, order);
}
} //namespace CGAL
#endif
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