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cgal/Subdivision_method_3/include/CGAL/Subdivision_mask_3.h

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// ======================================================================
//
// Copyright (c) 2005-2006 by Le-Jeng Shiue. 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): Le-Jeng Shiue <Andy.Shiue@gmail.com>
// <1998-2005 SurfLab, CISE, University of Florida>
// <2005- RapidMind Inc.>
//
// ======================================================================
#ifndef _POLYHEDRON_SUBDIVISION_STENCILS_H_01292002
#define _POLYHEDRON_SUBDIVISION_STENCILS_H_01292002
#include <CGAL/basic.h>
#include <CGAL/circulator.h>
#include <CGAL/Vector_3.h>
CGAL_BEGIN_NAMESPACE
// ======================================================================
/// The stencil of the Primal-Quadrilateral-Quadrisection
template <class Poly>
class PQQ_stencil_3 {
public:
typedef Poly Polyhedron;
typedef typename Polyhedron::Vertex_handle Vertex_handle;
typedef typename Polyhedron::Halfedge_handle Halfedge_handle;
typedef typename Polyhedron::Facet_handle Facet_handle;
typedef typename Polyhedron::Traits Traits;
typedef typename Traits::Kernel Kernel;
typedef typename Kernel::FT FT;
typedef typename Kernel::Point_3 Point;
typedef typename Kernel::Vector_3 Vector;
public:
void facet_node(Facet_handle, Point&) {};
void edge_node(Halfedge_handle, Point&) {};
void vertex_node(Vertex_handle, Point&) {};
void border_node(Halfedge_handle, Point&, Point&) {};
};
// ======================================================================
/// Bi-linear geometry mask for PQQ, PTQ, and Sqrt(3) scheme
template <class Poly>
class Linear_mask_3 : public PQQ_stencil_3<Poly> {
public:
typedef Poly Polyhedron;
typedef typename Polyhedron::Vertex_handle Vertex_handle;
typedef typename Polyhedron::Halfedge_handle Halfedge_handle;
typedef typename Polyhedron::Facet_handle Facet_handle;
typedef typename Polyhedron::Halfedge_around_facet_circulator
Halfedge_around_facet_circulator;
typedef typename Polyhedron::Halfedge_around_vertex_circulator
Halfedge_around_vertex_circulator;
typedef typename Polyhedron::Traits Traits;
typedef typename Traits::Kernel Kernel;
typedef typename Kernel::FT FT;
typedef typename Kernel::Point_3 Point;
typedef typename Kernel::Vector_3 Vector;
public:
//
void facet_node(Facet_handle facet, Point& pt) {
Halfedge_around_facet_circulator hcir = facet->facet_begin();
int n = 0;
Point p(0,0,0);
do {
p = p + (hcir->vertex()->point() - ORIGIN);
++n;
} while (++hcir != facet->facet_begin());
pt = ORIGIN + (p - ORIGIN)/FT(n);
}
//
void edge_node(Halfedge_handle edge, Point& pt) {
Point p1 = edge->vertex()->point();
Point p2 = edge->opposite()->vertex()->point();
pt = Point((p1[0]+p2[0])/2, (p1[1]+p2[1])/2, (p1[2]+p2[2])/2);
}
//
void vertex_node(Vertex_handle vertex, Point& pt) {
pt = vertex->point();
}
//
void border_node(Halfedge_handle edge, Point& ept, Point& vpt){
edge_node(edge, ept);
}
};
// ======================================================================
/// The geometry mask of Catmull-Clark subdivision
template <class Poly>
class CatmullClark_mask_3 : public Linear_mask_3<Poly> {
public:
typedef Poly Polyhedron;
typedef typename Polyhedron::Vertex_handle Vertex_handle;
typedef typename Polyhedron::Halfedge_handle Halfedge_handle;
typedef typename Polyhedron::Facet_handle Facet_handle;
typedef typename Polyhedron::Halfedge_around_facet_circulator
Halfedge_around_facet_circulator;
typedef typename Polyhedron::Halfedge_around_vertex_circulator
Halfedge_around_vertex_circulator;
typedef typename Polyhedron::Traits Traits;
typedef typename Traits::Kernel Kernel;
typedef typename Kernel::FT FT;
typedef typename Kernel::Point_3 Point;
typedef typename Kernel::Vector_3 Vector;
public:
//
void edge_node(Halfedge_handle edge, Point& pt) {
Point p1 = edge->vertex()->point();
Point p2 = edge->opposite()->vertex()->point();
Point f1, f2;
facet_node(edge->facet(), f1);
facet_node(edge->opposite()->facet(), f2);
pt = Point((p1[0]+p2[0]+f1[0]+f2[0])/4,
(p1[1]+p2[1]+f1[1]+f2[1])/4,
(p1[2]+p2[2]+f1[2]+f2[2])/4 );
}
//
void vertex_node(Vertex_handle vertex, Point& pt) {
Halfedge_around_vertex_circulator vcir = vertex->vertex_begin();
int n = circulator_size(vcir);
FT Q[] = {0.0, 0.0, 0.0}, R[] = {0.0, 0.0, 0.0};
Point& S = vertex->point();
Point q;
for (int i = 0; i < n; i++, ++vcir) {
Point& p2 = vcir->opposite()->vertex()->point();
R[0] += (S[0]+p2[0])/2;
R[1] += (S[1]+p2[1])/2;
R[2] += (S[2]+p2[2])/2;
facet_node(vcir->facet(), q);
Q[0] += q[0];
Q[1] += q[1];
Q[2] += q[2];
}
R[0] /= n; R[1] /= n; R[2] /= n;
Q[0] /= n; Q[1] /= n; Q[2] /= n;
pt = Point((Q[0] + 2*R[0] + S[0]*(n-3))/n,
(Q[1] + 2*R[1] + S[1]*(n-3))/n,
(Q[2] + 2*R[2] + S[2]*(n-3))/n );
}
//
void border_node(Halfedge_handle edge, Point& ept, Point& vpt) {
Point& ep1 = edge->vertex()->point();
Point& ep2 = edge->opposite()->vertex()->point();
ept = Point((ep1[0]+ep2[0])/2, (ep1[1]+ep2[1])/2, (ep1[2]+ep2[2])/2);
Halfedge_around_vertex_circulator vcir = edge->vertex_begin();
Point& vp1 = vcir->opposite()->vertex()->point();
Point& vp0 = vcir->vertex()->point();
Point& vp_1 = (--vcir)->opposite()->vertex()->point();
vpt = Point((vp_1[0] + 6*vp0[0] + vp1[0])/8,
(vp_1[1] + 6*vp0[1] + vp1[1])/8,
(vp_1[2] + 6*vp0[2] + vp1[2])/8 );
}
};
// ======================================================================
/// The geometry mask of Loop subdivision
template <class Poly>
class Loop_mask_3 : public PQQ_stencil_3<Poly> {
public:
typedef Poly Polyhedron;
typedef typename Polyhedron::Vertex_handle Vertex_handle;
typedef typename Polyhedron::Halfedge_handle Halfedge_handle;
typedef typename Polyhedron::Facet_handle Facet_handle;
typedef typename Polyhedron::Halfedge_around_facet_circulator
Halfedge_around_facet_circulator;
typedef typename Polyhedron::Halfedge_around_vertex_circulator
Halfedge_around_vertex_circulator;
typedef typename Polyhedron::Traits Traits;
typedef typename Traits::Kernel Kernel;
typedef typename Kernel::FT FT;
typedef typename Kernel::Point_3 Point;
typedef typename Kernel::Vector_3 Vector;
public:
//
void edge_node(Halfedge_handle edge, Point& pt) {
Point& p1 = edge->vertex()->point();
Point& p2 = edge->opposite()->vertex()->point();
Point& f1 = edge->next()->vertex()->point();
Point& f2 = edge->opposite()->next()->vertex()->point();
pt = Point((3*(p1[0]+p2[0])+f1[0]+f2[0])/8,
(3*(p1[1]+p2[1])+f1[1]+f2[1])/8,
(3*(p1[2]+p2[2])+f1[2]+f2[2])/8 );
}
//
void vertex_node(Vertex_handle vertex, Point& pt) {
Halfedge_around_vertex_circulator vcir = vertex->vertex_begin();
size_t n = circulator_size(vcir);
FT R[] = {0.0, 0.0, 0.0};
Point& S = vertex->point();
for (size_t i = 0; i < n; i++, ++vcir) {
Point& p = vcir->opposite()->vertex()->point();
R[0] += p[0]; R[1] += p[1]; R[2] += p[2];
}
if (n == 6) {
pt = Point((10*S[0]+R[0])/16, (10*S[1]+R[1])/16, (10*S[2]+R[2])/16);
} else {
FT Cn = (FT) (5.0/8.0 - std::sqrt(3+2*std::cos(6.283/n))/64.0);
FT Sw = n*(1-Cn)/Cn;
FT W = n/Cn;
pt = Point((Sw*S[0]+R[0])/W, (Sw*S[1]+R[1])/W, (Sw*S[2]+R[2])/W);
}
}
//
//void facet_node(Facet_handle facet, Point& pt) {};
//
void border_node(Halfedge_handle edge, Point& ept, Point& vpt) {
Point& ep1 = edge->vertex()->point();
Point& ep2 = edge->opposite()->vertex()->point();
ept = Point((ep1[0]+ep2[0])/2, (ep1[1]+ep2[1])/2, (ep1[2]+ep2[2])/2);
Halfedge_around_vertex_circulator vcir = edge->vertex_begin();
Point& vp1 = vcir->opposite()->vertex()->point();
Point& vp0 = vcir->vertex()->point();
Point& vp_1 = (--vcir)->opposite()->vertex()->point();
vpt = Point((vp_1[0] + 6*vp0[0] + vp1[0])/8,
(vp_1[1] + 6*vp0[1] + vp1[1])/8,
(vp_1[2] + 6*vp0[2] + vp1[2])/8 );
}
};
//==========================================================================
/// The setncil of the Dual-Quadrilateral-Quadrisection
template <class Poly>
class DQQ_stencil_3 {
public:
typedef Poly Polyhedron;
typedef typename Polyhedron::Halfedge_handle Halfedge_handle;
typedef typename Polyhedron::Traits Traits;
typedef typename Traits::Kernel Kernel;
typedef typename Kernel::FT FT;
typedef typename Kernel::Point_3 Point;
typedef typename Kernel::Vector_3 Vector;
public:
//
void corner_node(Halfedge_handle edge, Point& pt) {};
};
// ======================================================================
/// The geometry mask of Doo-Sabin subdivision
template <class Poly>
class DooSabin_mask_3 : public DQQ_stencil_3<Poly> {
public:
typedef Poly Polyhedron;
typedef typename Polyhedron::Halfedge_handle Halfedge_handle;
typedef typename Polyhedron::Halfedge_around_facet_circulator
Halfedge_around_facet_circulator;
typedef typename Polyhedron::Traits Traits;
typedef typename Traits::Kernel Kernel;
typedef typename Kernel::FT FT;
typedef typename Kernel::Point_3 Point;
typedef typename Kernel::Vector_3 Vector;
public:
//
void corner_node(Halfedge_handle he, Point& pt) {
size_t n = CGAL::circulator_size(he->facet()->facet_begin());
Vector cv(0,0,0);
if (n == 4) {
cv = cv + (he->vertex()->point()-CGAL::ORIGIN)*9;
cv = cv + (he->next()->vertex()->point()-CGAL::ORIGIN)*3;
cv = cv + (he->next()->next()->vertex()->point()-CGAL::ORIGIN);
cv = cv + (he->prev()->vertex()->point()-CGAL::ORIGIN)*3;
cv = cv/16;
} else {
FT a;
for (size_t k = 0; k < n; ++k, he = he->next()) {
if (k == 0) a = (FT) ((5.0/n) + 1);
else a = (FT) (3+2*std::cos(2*k*3.141593/n))/n;
cv = cv + (he->vertex()->point()-CGAL::ORIGIN)*a;
}
cv = cv/4;
}
pt = CGAL::ORIGIN + cv;
}
};
// ======================================================================
// The geometry mask of Sqrt(3) subdivision
template <class Poly>
class Sqrt3_mask_3 : public Linear_mask_3<Poly> {
public:
typedef Poly Polyhedron;
typedef typename Polyhedron::Traits Traits;
typedef typename Traits::Kernel Kernel;
typedef typename Polyhedron::Vertex_handle Vertex_handle;
typedef typename Polyhedron::Halfedge_handle Halfedge_handle;
typedef typename Polyhedron::Facet_handle Facet_handle;
typedef typename Polyhedron::Halfedge_around_facet_circulator
Halfedge_around_facet_circulator;
typedef typename Polyhedron::Halfedge_around_vertex_circulator
Halfedge_around_vertex_circulator;
typedef typename Kernel::FT FT;
typedef typename Kernel::Point_3 Point;
typedef typename Kernel::Vector_3 Vector;
public:
//
//void edge_node(Halfedge_handle edge, Point& pt) {}
//
void vertex_node(Vertex_handle vertex, Point& pt) {
Halfedge_around_vertex_circulator vcir = vertex->vertex_begin();
size_t n = circulator_size(vcir);
const double pi = 3.1415926;
FT a = (FT) ((4.0-2.0*cos(2.0*pi/n))/9.0);
Vector cv = ((FT)(1.0-a)) * (vertex->point() - CGAL::ORIGIN);
for (size_t i = 1; i <= n; ++i, --vcir) {
cv = cv + (a/n)*(vcir->opposite()->vertex()->point()-CGAL::ORIGIN);
}
pt = CGAL::ORIGIN + cv;
}
//
// TODO
//void border_node(Halfedge_handle edge, Point& ept, Point& vpt) {}
};
CGAL_END_NAMESPACE
#endif //_POLYHEDRON_SUBDIVISION_STENCILS_H_01292002
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