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cgal/Ridges_3/include/CGAL/Ridges.h

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#ifndef _RIDGE_3_H_
#define _RIDGE_3_H_
#include <utility>
#include <list>
#include <map>
#include <boost/property_map.hpp>
#include <CGAL/basic.h>
#include <CGAL/Min_sphere_d.h>
#include <CGAL/Optimisation_d_traits_3.h>
//note : one has to orient monge normals according to mesh normals to
//define min/max curv
CGAL_BEGIN_NAMESPACE
enum Ridge_type {NONE=0, BLUE_RIDGE, RED_RIDGE, CREST,
BLUE_ELLIPTIC_RIDGE, BLUE_HYPERBOLIC_RIDGE, BLUE_CREST,
RED_ELLIPTIC_RIDGE, RED_HYPERBOLIC_RIDGE, RED_CREST};
//---------------------------------------------------------------------------
//Ridge_line : a connected sequence of edges of a Poly crossed by a
//ridge (with a barycentric coordinate to compute the crossing point),
//with type and weigths.
//--------------------------------------------------------------------------
template < class Poly > class Ridge_line
{
public:
typedef typename Poly::Traits::FT FT;
typedef typename Poly::Traits::Vector_3 Vector_3;
typedef typename Poly::Traits::Point_3 Point_3;
typedef typename Poly::Halfedge_handle Halfedge_handle;
typedef std::pair< Halfedge_handle, FT> ridge_he;
protected:
//one of BLUE_ELLIPTIC_RIDGE, BLUE_HYPERBOLIC_RIDGE, BLUE_CREST,
//RED_ELLIPTIC_RIDGE, RED_HYPERBOLIC_RIDGE or RED_CREST
Ridge_type m_line_type;
std::list<ridge_he> m_line;
FT m_strength;
FT m_sharpness;
public:
const 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_he>* line() const { return &m_line;}
std::list<ridge_he>* line() { return &m_line;}
//constructor
Ridge_line();
/* The output is :
line_type, strength, sharpness, list of points of the polyline.
*/
void dump_4ogl(std::ostream& out_stream) ;
void dump_verbose(std::ostream& out_stream) const ;
};
//--------------------------------------------------------------------------
// IMPLEMENTATION OF Ridge_line members
//--------------------------------------------------------------------------
//constructor
template < class Poly >
Ridge_line<Poly>::
Ridge_line() : m_strength(0.), m_sharpness(0.) {}
template < class Poly >
void Ridge_line<Poly>::
dump_4ogl(std::ostream& out_stream)
{
out_stream << line_type() << " "
<< strength() << " "
<< sharpness() << " ";
typename std::list<ridge_he >::iterator
iter = line()->begin(),
ite = line()->end();
for (;iter!=ite;iter++){
//he: p->q, r is the crossing point
Point_3 p = iter->first->opposite()->vertex()->point(),
q = iter->first->vertex()->point();
Vector_3 r = (p-CGAL::ORIGIN)*iter->second +
(q-CGAL::ORIGIN)*(1-iter->second);
out_stream << " " << r ;
}
out_stream << std::endl;
}
//verbose output
template < class Poly >
void Ridge_line<Poly>::
dump_verbose(std::ostream& out_stream) const
{
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_he>::const_iterator
iter = line()->begin(),
ite = line()->end();
for (;iter!=ite;iter++){
//he: p->q, r is the crossing point
Point_3 p = iter->first->opposite()->vertex()->point(),
q = iter->first->vertex()->point();
Vector_3 r = (p-CGAL::ORIGIN)*iter->second +
(q-CGAL::ORIGIN)*(1-iter->second);
out_stream << r << std::endl;
}
}
template <class Poly>
std::ostream&
operator<<(std::ostream& out_stream, const Ridge_line<Poly>& ridge_line)
{
ridge_line.dump_verbose(out_stream);
return out_stream;
}
//---------------------------------------------------------------------------
//Differential_quantities
//--------------------------------------------------------------------------
template < class Vertex2FTPropertyMap, class Vertex2VectorPropertyMap>
class Differential_quantities {
public :
Vertex2FTPropertyMap vertex2k1_pm, vertex2k2_pm,
vertex2b0_pm, vertex2b3_pm,
vertex2P1_pm, vertex2P2_pm;
Vertex2VectorPropertyMap vertex2d1_pm, vertex2d2_pm;
};
//---------------------------------------------------------------------------
//Ridge_approximation
//--------------------------------------------------------------------------
template < class Poly, class OutputIt, class Vertex2FTPropertyMap, class Vertex2VectorPropertyMap >
class Ridge_approximation
{
public:
typedef typename Poly::Traits::FT FT;
typedef typename Poly::Traits::Vector_3 Vector_3;
typedef typename Poly::Vertex_handle Vertex_handle;
typedef typename Poly::Halfedge_handle Halfedge_handle;
typedef typename Poly::Facet_handle Facet_handle;
typedef typename Poly::Facet_iterator Facet_iterator;
typedef std::pair< Halfedge_handle, FT> ridge_he;
typedef Ridge_line<Poly> Ridge_line;
//are ridges tagged as elliptic or hyperbolic using 3rd or 4th order
//differential quantitities?
//tag_3 is not working or badly, to be removed or improved?
enum Tag_order {Tag_3 = 3, Tag_4 = 4};
public:
Ridge_approximation(Poly &P,
Vertex2FTPropertyMap vertex2k1_pm, Vertex2FTPropertyMap vertex2k2_pm,
Vertex2FTPropertyMap vertex2b0_pm, Vertex2FTPropertyMap vertex2b3_pm,
Vertex2FTPropertyMap vertex2P1_pm, Vertex2FTPropertyMap vertex2P2_pm,
Vertex2VectorPropertyMap vertex2d1_pm, Vertex2VectorPropertyMap vertex2d2_pm);
OutputIt compute_all_ridges(Poly &P, OutputIt it, Tag_order ord = Tag_3);
//Find BLUE_RIDGE, RED_RIDGE or CREST ridges
//iterate on P facets, find a non-visited, regular, 2Xing triangle,
//follow non-visited, regular, 2Xing triangles in both sens to create
//a Ridge line.
//Each time an edge is added the strength of the current line is updated
// + length(ridge segment in the facet)*|k|
void compute_ridges(Poly &P,
Ridge_type r_type,
OutputIt ridge_lines_it,
Tag_order ord = Tag_3);
// void compute_umbilics(Poly &P );//container, class for umbilics?
protected:
Poly* P;
FT model_size;//radius of the smallest enclosing sphere of the Poly
//used to make the sharpness scale independant and iso indep
//tag to visit faces
struct Facet_cmp{ //comparison is wrt facet addresses
bool operator()(Facet_handle a, Facet_handle b) const{
return &*a < &*b;
}
};
typedef std::map<Facet_handle, bool, Facet_cmp> Facet2bool_map_type;
Facet2bool_map_type is_visited_map;
//Property maps
Vertex2FTPropertyMap k1, k2, b0, b3, P1, P2;
Vertex2VectorPropertyMap d1, d2;
//is a facet crossed by a BLUE, RED or CREST ridge? if so, return
//the crossed edges and more precise type from BLUE_ELLIPTIC_RIDGE,
//BLUE_HYPERBOLIC_RIDGE, BLUE_CREST, RED_ELLIPTIC_RIDGE,
//RED_HYPERBOLIC_RIDGE, RED_CREST or NONE
Ridge_type facet_ridge_type(Facet_handle f,
Halfedge_handle& he1,
Halfedge_handle& he2,
Ridge_type r_type,
Tag_order ord = Tag_3);
//is an edge crossed by a BLUE/RED ridge? (color is BLUE_RIDGE or
//RED_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(Halfedge_handle he,
bool& is_crossed,
Ridge_type color);
//for the computation with tag_order = 3
//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 = BLUE_RIDGE, sign = 1 if BLUE_ELLIPTIC_RIDGE, -1 if
// BLUE_HYPERBOLIC_RIDGE
//
// for color = RED_RIDGE, sign = -1 if RED_ELLIPTIC_RIDGE, 1 if
// RED_HYPERBOLIC_RIDGE
int b_sign_pointing_to_ridge(Vertex_handle v1,
Vertex_handle v2,
Vertex_handle v3,
Vector_3 r1, Vector_3 r2,
Ridge_type color);
//a ridge line begins with a segment in a triangle
void init_ridge_line(Ridge_line* ridge_line,
Halfedge_handle h1, Halfedge_handle h2,
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
//weigths are updated
void addback(Ridge_line* ridge_line, Halfedge_handle he, Ridge_type r_type);
void addfront(Ridge_line* ridge_line, Halfedge_handle he, Ridge_type r_type);
//compute the barycentric coordinate of the xing point (blue or red)
//for he: p->q coord is st xing_point = coord*p + (1-coord)*q
FT bary_coord(Halfedge_handle he, Ridge_type r_type);
};
// IMPLEMENTATION OF Ridge_approximation members
/////////////////////////////////////////////////////////////////////////////
//contructor
template < class Poly, class OutputIt, class Vertex2FTPropertyMap, class Vertex2VectorPropertyMap >
Ridge_approximation<Poly, OutputIt, Vertex2FTPropertyMap, Vertex2VectorPropertyMap>::
Ridge_approximation(Poly &P,
Vertex2FTPropertyMap vertex2k1_pm, Vertex2FTPropertyMap vertex2k2_pm,
Vertex2FTPropertyMap vertex2b0_pm, Vertex2FTPropertyMap vertex2b3_pm,
Vertex2FTPropertyMap vertex2P1_pm, Vertex2FTPropertyMap vertex2P2_pm,
Vertex2VectorPropertyMap vertex2d1_pm, Vertex2VectorPropertyMap vertex2d2_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)
{
CGAL::Min_sphere_d<CGAL::Optimisation_d_traits_3<typename Poly::Traits> >
min_sphere(P.points_begin(), P.points_end());
model_size = min_sphere.squared_radius();
//maybe better to use CGAL::Min_sphere_of_spheres_d ?? but need to create spheres?
//init the is_visited_map
Facet_iterator itb = P.facets_begin(), ite = P.facets_end();
for(;itb!=ite;itb++) is_visited_map[itb] = false;
}
template < class Poly, class OutputIt, class Vertex2FTPropertyMap, class Vertex2VectorPropertyMap >
OutputIt Ridge_approximation<Poly, OutputIt, Vertex2FTPropertyMap, Vertex2VectorPropertyMap>::
compute_all_ridges(Poly &P, OutputIt it, Tag_order ord)
{
compute_ridges(P, BLUE_RIDGE, it, ord);
compute_ridges(P, RED_RIDGE, it, ord);
compute_ridges(P, CREST, it, ord);
return it;
}
template < class Poly, class OutputIt, class Vertex2FTPropertyMap, class Vertex2VectorPropertyMap >
void Ridge_approximation<Poly, OutputIt, Vertex2FTPropertyMap, Vertex2VectorPropertyMap>::
compute_ridges(Poly &P, Ridge_type r_type,
OutputIt ridge_lines_it, Tag_order ord)
{
//set all facets non visited
Facet_iterator itb = P.facets_begin(), ite = P.facets_end();
for(;itb!=ite;itb++) is_visited_map[itb] = false;
itb = P.facets_begin();
for(;itb!=ite;itb++)
{
Facet_handle f = itb;
if (is_visited_map.find(f)->second) continue;
is_visited_map.find(f)->second = true;
Halfedge_handle h1, h2, curhe1, curhe2, curhe;
//h1 h2 are the hedges crossed if any, r_type should be
//BLUE_RIDGE, RED_RIDGE or CREST ; cur_ridge_type should be
//BLUE_ELLIPTIC_RIDGE, BLUE_HYPERBOLIC_RIDGE, BLUE_CREST,
//RED_ELLIPTIC_RIDGE, RED_HYPERBOLIC_RIDGE, RED_CREST or NONE
Ridge_type cur_ridge_type = facet_ridge_type(f,h1,h2,r_type, ord);
if ( cur_ridge_type == NONE ) continue;
//a ridge_line is begining and stored
Ridge_line* cur_ridge_line = new Ridge_line();
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 ( !(h1->is_border_edge()) )
{
f = h1->opposite()->facet();
curhe = h1;
while (cur_ridge_type == facet_ridge_type(f,curhe1,curhe2,
r_type, ord))
{
//follow the ridge from curhe
if (is_visited_map.find(f)->second) break;
is_visited_map.find(f)->second = true;
if (curhe->opposite() == curhe1) curhe = curhe2;
else curhe = curhe1;//curhe stays at the ridge extremity
addfront(cur_ridge_line, curhe, cur_ridge_type);
if ( !(curhe->is_border_edge()) ) f =
curhe->opposite()->facet();
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 BLUE_ELLIPTIC_RIDGE
// follows a BLUE_HYPERBOLIC_RIDGE
}
//next triangle adjacent to h2 (push_back)
if ( !(h2->is_border_edge()) )
{
f = h2->opposite()->facet();
curhe = h2;
while (cur_ridge_type ==
facet_ridge_type(f,curhe1,curhe2,r_type, ord))
{
//follow the ridge from curhe
if (is_visited_map.find(f)->second) break;
is_visited_map.find(f)->second = true;
if (curhe->opposite() == curhe1) curhe = curhe2;
else curhe = curhe1;
addback(cur_ridge_line, curhe, cur_ridge_type);
if ( !(curhe->is_border_edge()) ) f =
curhe->opposite()->facet();
else break;
}
}
}
}
template < class Poly, class OutputIt, class Vertex2FTPropertyMap, class Vertex2VectorPropertyMap >
Ridge_type Ridge_approximation<Poly, OutputIt, Vertex2FTPropertyMap, Vertex2VectorPropertyMap>::
facet_ridge_type(Facet_handle f, Halfedge_handle& he1, Halfedge_handle&
he2, Ridge_type r_type, Tag_order ord)
{
//polyhedral data
//we have v1--h1-->v2--h2-->v3--h3-->v1
Halfedge_handle h1 = f->halfedge(), h2, h3;
Vertex_handle v1, v2, v3;
v2 = h1->vertex();
h2 = h1->next();
v3 = h2->vertex();
h3 = h2->next();
v1 = h3->vertex();
//check for regular facet
//i.e. if there is a coherent orientation of ppal dir at the facet vertices
if ( d1[v1]*d1[v2] * d1[v1]*d1[v3] * d1[v2]*d1[v3] < 0 )
return NONE;
//determine potential crest color
//BLUE_CREST if |sum(k1)|>|sum(k2)| sum over facet vertices vi
//RED_CREST if |sum(k1)|<|sum(k2)|
Ridge_type crest_color = NONE;
if (r_type == CREST)
{
if ( CGAL::abs(k1[v1]+k1[v2]+k1[v3]) > CGAL::abs(k2[v1]+k2[v2]+k2[v3]) )
crest_color = BLUE_CREST;
if ( CGAL::abs(k1[v1]+k1[v2]+k1[v3]) < CGAL::abs(k2[v1]+k2[v2]+k2[v3]) )
crest_color = RED_CREST;
if ( CGAL::abs(k1[v1]+k1[v2]+k1[v3]) == CGAL::abs(k2[v1]+k2[v2]+k2[v3]) )
return NONE;
}
//compute Xing on the 3 edges
bool h1_is_crossed = false, h2_is_crossed = false, h3_is_crossed = false;
if ( r_type == BLUE_RIDGE || crest_color == BLUE_CREST )
{
xing_on_edge(h1, h1_is_crossed, BLUE_RIDGE);
xing_on_edge(h2, h2_is_crossed, BLUE_RIDGE);
xing_on_edge(h3, h3_is_crossed, BLUE_RIDGE);
}
if ( r_type == RED_RIDGE || crest_color == RED_CREST )
{
xing_on_edge(h1, h1_is_crossed, RED_RIDGE);
xing_on_edge(h2, h2_is_crossed, RED_RIDGE);
xing_on_edge(h3, h3_is_crossed, RED_RIDGE);
}
//there are either 0 or 2 crossed edges
if ( !h1_is_crossed && !h2_is_crossed && !h3_is_crossed )
return NONE;
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 on edge crossed)
assert ( !( (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
Vertex_handle v_p1 = he1->opposite()->vertex(), v_q1 = he1->vertex(),
v_p2 = he2->opposite()->vertex(), v_q2 = he2->vertex(); // he1: p1->q1
if ( r_type == BLUE_RIDGE || crest_color == BLUE_CREST ) {
FT coord1 = CGAL::abs(b0[v_q1]) / ( CGAL::abs(b0[v_p1]) +
CGAL::abs(b0[v_q1]) ),
coord2 = CGAL::abs(b0[v_q2]) / ( CGAL::abs(b0[v_p2]) +
CGAL::abs(b0[v_q2]) );
if ( ord == Tag_3 ) {
Vector_3 r1 = (v_p1->point()-ORIGIN)*coord1 +
(v_q1->point()-ORIGIN)*(1-coord1),
r2 = (v_p2->point()-ORIGIN)*coord2 +
(v_q2->point()-ORIGIN)*(1-coord2);
int b_sign = b_sign_pointing_to_ridge(v1, v2, v3, r1, r2, BLUE_RIDGE);
if (r_type == CREST) {if (b_sign == 1) return BLUE_CREST;
else return NONE;}
if (b_sign == 1) return BLUE_ELLIPTIC_RIDGE;
else return BLUE_HYPERBOLIC_RIDGE;
}
else {//ord == Tag_4, check the sign of the meanvalue of the signs
// of P1 at the two crossing points
FT sign_P1 = P1[v_p1]*coord1 + P1[v_q1]*(1-coord1)
+ P1[v_p2]*coord2 + P1[v_q2]*(1-coord2);
if (r_type == CREST) {if ( sign_P1 < 0 ) return BLUE_CREST; else return NONE;}
if ( sign_P1 < 0 ) return BLUE_ELLIPTIC_RIDGE; else return BLUE_HYPERBOLIC_RIDGE;
}
}
if ( r_type == RED_RIDGE || crest_color == RED_CREST ) {
FT coord1 = CGAL::abs(b3[v_q1]) / ( CGAL::abs(b3[v_p1]) +
CGAL::abs(b3[v_q1]) ),
coord2 = CGAL::abs(b3[v_q2]) / ( CGAL::abs(b3[v_p2]) +
CGAL::abs(b3[v_q2]) );
if ( ord == Tag_3 ) {
Vector_3 r1 = (v_p1->point()-ORIGIN)*coord1 +
(v_q1->point()-ORIGIN)*(1-coord1),
r2 = (v_p2->point()-ORIGIN)*coord2 +
(v_q2->point()-ORIGIN)*(1-coord2);
int b_sign = b_sign_pointing_to_ridge(v1, v2, v3, r1, r2, RED_RIDGE);
if (r_type == CREST) {if (b_sign == -1) return RED_CREST; else return NONE;}
if (b_sign == -1) return RED_ELLIPTIC_RIDGE; else return RED_HYPERBOLIC_RIDGE;
}
else {//ord == Tag_4, check the sign of the meanvalue of the signs
// of P2 at the two crossing points
FT sign_P2 = P2[v_p1]*coord1 + P2[v_q1]*(1-coord1)
+ P2[v_p2]*coord2 + P2[v_q2]*(1-coord2);
if (r_type == CREST) {if ( sign_P2 < 0 ) return RED_CREST; else return NONE;}
if ( sign_P2 < 0 ) return RED_ELLIPTIC_RIDGE; else return RED_HYPERBOLIC_RIDGE;
}
}
assert(0);//should return before!
}
template < class Poly, class OutputIt, class Vertex2FTPropertyMap, class Vertex2VectorPropertyMap >
void Ridge_approximation<Poly, OutputIt, Vertex2FTPropertyMap, Vertex2VectorPropertyMap>::
xing_on_edge(Halfedge_handle he, bool& is_crossed, Ridge_type color)
{
is_crossed = false;
FT sign;
FT b_p, b_q; // extremalities at p and q for he: p->q
Vector_3 d_p = d1[he->opposite()->vertex()],
d_q = d1[he->vertex()]; //ppal dir
if ( color == BLUE_RIDGE ) {
b_p = b0[he->opposite()->vertex()];
b_q = b0[he->vertex()];
}
else {
b_p = b3[he->opposite()->vertex()];
b_q = b3[he->vertex()];
}
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 Poly, class OutputIt, class Vertex2FTPropertyMap, class Vertex2VectorPropertyMap >
int Ridge_approximation<Poly, OutputIt, Vertex2FTPropertyMap, Vertex2VectorPropertyMap>::
b_sign_pointing_to_ridge(Vertex_handle v1, Vertex_handle v2, Vertex_handle v3,
Vector_3 r1, Vector_3 r2, Ridge_type color)
{
Vector_3 r = r2 - r1, dv1, dv2, dv3;
FT bv1, bv2, bv3;
if ( color == BLUE_RIDGE ) {
bv1 = b0[v1];
bv2 = b0[v2];
bv3 = b0[v3];
dv1 = d1[v1];
dv2 = d1[v2];
dv3 = d1[v3];
}
else {
bv1 = b3[v1];
bv2 = b3[v2];
bv3 = b3[v3];
dv1 = d2[v1];
dv2 = d2[v2];
dv3 = d2[v3];
}
if ( r != CGAL::NULL_VECTOR ) r = r/CGAL::sqrt(r*r);
FT sign1, sign2, sign3;
sign1 = (r1 - (v1->point()-ORIGIN) + (((v1->point()-ORIGIN)-r1)*r)*r )*dv1;
sign2 = (r1 - (v2->point()-ORIGIN) + (((v2->point()-ORIGIN)-r1)*r)*r )*dv2;
sign3 = (r1 - (v3->point()-ORIGIN) + (((v3->point()-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 Poly, class OutputIt, class Vertex2FTPropertyMap, class Vertex2VectorPropertyMap >
void Ridge_approximation<Poly, OutputIt, Vertex2FTPropertyMap, Vertex2VectorPropertyMap>::
init_ridge_line(Ridge_line* ridge_line,
Halfedge_handle h1, Halfedge_handle h2,
Ridge_type r_type)
{
ridge_line->line_type() = r_type;
ridge_line->line()->push_back(ridge_he(h1, bary_coord(h1,r_type)));
addback(ridge_line, h2, r_type);
}
template < class Poly, class OutputIt, class Vertex2FTPropertyMap, class Vertex2VectorPropertyMap >
void Ridge_approximation<Poly, OutputIt, Vertex2FTPropertyMap, Vertex2VectorPropertyMap>::
addback(Ridge_line* ridge_line, Halfedge_handle he, Ridge_type r_type)
{
Halfedge_handle 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_handle v_p = he->opposite()->vertex(), v_q = he->vertex(),
v_p_cur = he_cur->opposite()->vertex(), v_q_cur = he->vertex(); // he: p->q
Vector_3 segment = (v_p->point()-ORIGIN)*coord + (v_q->point()-ORIGIN)*(1-coord) -
((v_p_cur->point()-ORIGIN)*coord_cur + (v_q_cur->point()-ORIGIN)*(1-coord_cur));
FT k1x, k2x; //abs value of the ppal curvatures at the Xing point on he.
FT k_second; // abs value of the second derivative of the curvature
// along the line of curvature
k1x = CGAL::abs(k1[v_p]) * coord + CGAL::abs(k1[v_q]) * (1-coord) ;
k2x = CGAL::abs(k2[v_p]) * coord + CGAL::abs(k2[v_q]) * (1-coord) ;
if ( (ridge_line->line_type() == BLUE_ELLIPTIC_RIDGE)
|| (ridge_line->line_type() == BLUE_HYPERBOLIC_RIDGE)
|| (ridge_line->line_type() == BLUE_CREST) ) {
ridge_line->strength() += k1x * CGAL::sqrt(segment * segment);
k_second =CGAL::abs(( CGAL::abs(P1[v_p]) * coord + CGAL::abs(P1[v_q]) * (1-coord) )/(k1x-k2x));
ridge_line->sharpness() += k_second * CGAL::sqrt(segment * segment) * model_size;
}
if ( (ridge_line->line_type() == RED_ELLIPTIC_RIDGE)
|| (ridge_line->line_type() == RED_HYPERBOLIC_RIDGE)
|| (ridge_line->line_type() == RED_CREST) ) {
ridge_line->strength() += k2x * CGAL::sqrt(segment * segment);
k_second =CGAL::abs(( CGAL::abs(P2[v_p]) * coord + CGAL::abs(P2[v_q]) * (1-coord) )/(k1x-k2x));
ridge_line->sharpness() += k_second * CGAL::sqrt(segment * segment) * model_size;
}
ridge_line->line()->push_back( ridge_he(he, coord));
}
template < class Poly, class OutputIt, class Vertex2FTPropertyMap, class Vertex2VectorPropertyMap >
void Ridge_approximation<Poly, OutputIt, Vertex2FTPropertyMap, Vertex2VectorPropertyMap>::
addfront(Ridge_line* ridge_line, Halfedge_handle he, Ridge_type r_type)
{
Halfedge_handle he_cur = ( ridge_line->line()->begin() )->first;
FT coord_cur = ( ridge_line->line()->begin() )->second;
FT coord = bary_coord(he,r_type);
Vertex_handle v_p = he->opposite()->vertex(), v_q = he->vertex(),
v_p_cur = he_cur->opposite()->vertex(), v_q_cur = he->vertex(); // he: p->q
Vector_3 segment = (v_p->point()-ORIGIN)*coord + (v_q->point()-ORIGIN)*(1-coord) -
((v_p_cur->point()-ORIGIN)*coord_cur + (v_q_cur->point()-ORIGIN)*(1-coord_cur));
FT k1x, k2x; //abs value of the ppal curvatures at the Xing point on he.
FT k_second; // abs value of the second derivative of the curvature
// along the line of curvature
k1x = CGAL::abs(k1[v_p]) * coord + CGAL::abs(k1[v_q]) * (1-coord) ;
k2x = CGAL::abs(k2[v_p]) * coord + CGAL::abs(k2[v_q]) * (1-coord) ;
if ( (ridge_line->line_type() == BLUE_ELLIPTIC_RIDGE)
|| (ridge_line->line_type() == BLUE_HYPERBOLIC_RIDGE)
|| (ridge_line->line_type() == BLUE_CREST) ) {
ridge_line->strength() += k1x * CGAL::sqrt(segment * segment);
k_second =CGAL::abs(( CGAL::abs(P1[v_p]) * coord + CGAL::abs(P1[v_q]) * (1-coord) )/(k1x-k2x));
ridge_line->sharpness() += k_second * CGAL::sqrt(segment * segment) * model_size;
}
if ( (ridge_line->line_type() == RED_ELLIPTIC_RIDGE)
|| (ridge_line->line_type() == RED_HYPERBOLIC_RIDGE)
|| (ridge_line->line_type() == RED_CREST) ) {
ridge_line->strength() += k2x * CGAL::sqrt(segment * segment);
k_second =CGAL::abs(( CGAL::abs(P2[v_p]) * coord + CGAL::abs(P2[v_q]) * (1-coord) )/(k1x-k2x));
ridge_line->sharpness() += k_second * CGAL::sqrt(segment * segment) * model_size;
}
ridge_line->line()->push_front( ridge_he(he, coord));
}
template < class Poly, class OutputIt, class Vertex2FTPropertyMap, class Vertex2VectorPropertyMap >
typename Poly::Traits::FT Ridge_approximation<Poly, OutputIt, Vertex2FTPropertyMap, Vertex2VectorPropertyMap>::
bary_coord(Halfedge_handle he, Ridge_type r_type)
{
FT b_p, b_q; // extremalities at p and q for he: p->q
if ( (r_type == BLUE_ELLIPTIC_RIDGE)
|| (r_type == BLUE_HYPERBOLIC_RIDGE)
|| (r_type == BLUE_CREST) ) {
b_p = b0[he->opposite()->vertex()];
b_q = b0[he->vertex()];
}
if ( (r_type == RED_ELLIPTIC_RIDGE)
|| (r_type == RED_HYPERBOLIC_RIDGE)
|| (r_type == RED_CREST) ) {
b_p = b3[he->opposite()->vertex()];
b_q = b3[he->vertex()];
}
return CGAL::abs(b_q) / ( CGAL::abs(b_q) + CGAL::abs(b_p) );
}
CGAL_END_NAMESPACE
#endif
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