mirror of https://github.com/CGAL/cgal
move predicates and constructions in Kernel packages
This commit is contained in:
Andreas Fabri
Jane Tournois
parent
ea6e48e1e4
commit
95027822f5
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@ -30,7 +30,6 @@
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#include <CGAL/predicates/kernel_ftC3.h>
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#include <CGAL/predicates/kernel_ftC3.h>
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#include <CGAL/constructions/kernel_ftC2.h>
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#include <CGAL/constructions/kernel_ftC2.h>
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#include <CGAL/constructions/kernel_ftC3.h>
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#include <CGAL/constructions/kernel_ftC3.h>
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#include <CGAL/predicates/Regular_triangulation_ftC3.h>
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#include <CGAL/Cartesian/solve_3.h>
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#include <CGAL/Cartesian/solve_3.h>
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namespace CGAL {
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namespace CGAL {
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@ -20,7 +20,7 @@
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// $Id$
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// $Id$
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//
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//
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//
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//
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// Author(s) : Herve Bronnimann
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// Author(s) : Herve Bronnimann, Mariette Yvinec
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#ifndef CGAL_CONSTRUCTIONS_KERNEL_FTC3_H
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#ifndef CGAL_CONSTRUCTIONS_KERNEL_FTC3_H
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#define CGAL_CONSTRUCTIONS_KERNEL_FTC3_H
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#define CGAL_CONSTRUCTIONS_KERNEL_FTC3_H
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@ -403,6 +403,520 @@ squared_areaC3(const FT &px, const FT &py, const FT &pz,
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return (CGAL_NTS square(vx) + CGAL_NTS square(vy) + CGAL_NTS square(vz))/4;
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return (CGAL_NTS square(vx) + CGAL_NTS square(vy) + CGAL_NTS square(vz))/4;
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}
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}
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template <class FT>
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void
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determinants_for_weighted_circumcenterC3(
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const FT &px, const FT &py, const FT &pz, const FT &pw,
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const FT &qx, const FT &qy, const FT &qz, const FT &qw,
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const FT &rx, const FT &ry, const FT &rz, const FT &rw,
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const FT &sx, const FT &sy, const FT &sz, const FT &sw,
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FT &num_x, FT &num_y, FT &num_z, FT& den)
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{
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// translate origin to p
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// and compute determinants for weighted_circumcenter and
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// circumradius
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FT qpx = qx-px;
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FT qpy = qy-py;
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FT qpz = qz-pz;
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FT qp2 = CGAL_NTS square(qpx) + CGAL_NTS square(qpy) +
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CGAL_NTS square(qpz) - qw + pw;
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FT rpx = rx-px;
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FT rpy = ry-py;
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FT rpz = rz-pz;
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FT rp2 = CGAL_NTS square(rpx) + CGAL_NTS square(rpy) +
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CGAL_NTS square(rpz) - rw + pw;
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FT spx = sx-px;
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FT spy = sy-py;
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FT spz = sz-pz;
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FT sp2 = CGAL_NTS square(spx) + CGAL_NTS square(spy) +
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CGAL_NTS square(spz) - sw + pw;
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num_x = determinant(qpy,qpz,qp2,
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rpy,rpz,rp2,
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spy,spz,sp2);
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num_y = determinant(qpx,qpz,qp2,
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rpx,rpz,rp2,
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spx,spz,sp2);
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num_z = determinant(qpx,qpy,qp2,
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rpx,rpy,rp2,
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spx,spy,sp2);
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den = determinant(qpx,qpy,qpz,
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rpx,rpy,rpz,
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spx,spy,spz);
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}
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template <class FT>
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void
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determinants_for_circumcenterC3(
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const FT &px, const FT &py, const FT &pz,
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const FT &qx, const FT &qy, const FT &qz,
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const FT &rx, const FT &ry, const FT &rz,
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const FT &sx, const FT &sy, const FT &sz,
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FT &num_x, FT &num_y, FT &num_z, FT& den)
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{
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// translate origin to p
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// and compute determinants for weighted_circumcenter and
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// circumradius
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FT qpx = qx-px;
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FT qpy = qy-py;
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FT qpz = qz-pz;
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FT qp2 = CGAL_NTS square(qpx) + CGAL_NTS square(qpy) +
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CGAL_NTS square(qpz);
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FT rpx = rx-px;
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FT rpy = ry-py;
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FT rpz = rz-pz;
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FT rp2 = CGAL_NTS square(rpx) + CGAL_NTS square(rpy) +
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CGAL_NTS square(rpz);
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FT spx = sx-px;
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FT spy = sy-py;
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FT spz = sz-pz;
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FT sp2 = CGAL_NTS square(spx) + CGAL_NTS square(spy) +
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CGAL_NTS square(spz);
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num_x = determinant(qpy,qpz,qp2,
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rpy,rpz,rp2,
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spy,spz,sp2);
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num_y = determinant(qpx,qpz,qp2,
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rpx,rpz,rp2,
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spx,spz,sp2);
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num_z = determinant(qpx,qpy,qp2,
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rpx,rpy,rp2,
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spx,spy,sp2);
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den = determinant(qpx,qpy,qpz,
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rpx,rpy,rpz,
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spx,spy,spz);
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}
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template < class FT>
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void
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weighted_circumcenterC3(
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const FT &px, const FT &py, const FT &pz, const FT &pw,
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const FT &qx, const FT &qy, const FT &qz, const FT &qw,
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const FT &rx, const FT &ry, const FT &rz, const FT &rw,
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const FT &sx, const FT &sy, const FT &sz, const FT &sw,
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FT &x, FT &y, FT &z)
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{
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// this function compute the weighted circumcenter point only
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// Translate p to origin and compute determinants
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FT num_x, num_y, num_z, den;
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determinants_for_weighted_circumcenterC3(px, py, pz, pw,
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qx, qy, qz, qw,
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rx, ry, rz, rw,
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sx, sy, sz, sw,
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num_x, num_y, num_z,den);
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CGAL_assertion( ! CGAL_NTS is_zero(den) );
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FT inv = FT(1)/(FT(2) * den);
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x = px + num_x*inv;
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y = py - num_y*inv;
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z = pz + num_z*inv;
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}
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template < class FT>
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void
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weighted_circumcenterC3(
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const FT &px, const FT &py, const FT &pz, const FT &pw,
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const FT &qx, const FT &qy, const FT &qz, const FT &qw,
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const FT &rx, const FT &ry, const FT &rz, const FT &rw,
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const FT &sx, const FT &sy, const FT &sz, const FT &sw,
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FT &x, FT &y, FT &z, FT &w)
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{
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// this function compute the weighted circumcenter point
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// and the squared weighted circumradius
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// Translate p to origin and compute determinants
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FT num_x, num_y, num_z, den;
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determinants_for_weighted_circumcenterC3(px, py, pz, pw,
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qx, qy, qz, qw,
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rx, ry, rz, rw,
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sx, sy, sz, sw,
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num_x, num_y, num_z, den);
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CGAL_assertion( ! CGAL_NTS is_zero(den) );
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FT inv = FT(1)/(FT(2) * den);
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x = px + num_x*inv;
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y = py - num_y*inv;
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z = pz + num_z*inv;
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w = (CGAL_NTS square(num_x)+CGAL_NTS square(num_y)+CGAL_NTS square(num_z))
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*CGAL_NTS square(inv) - pw;
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}
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template< class FT >
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FT
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squared_radius_orthogonal_sphereC3(
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const FT &px, const FT &py, const FT &pz, const FT &pw,
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const FT &qx, const FT &qy, const FT &qz, const FT &qw,
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const FT &rx, const FT &ry, const FT &rz, const FT &rw,
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const FT &sx, const FT &sy, const FT &sz, const FT &sw)
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{
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// this function compute the squared weighted circumradius only
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// Translate p to origin and compute determinants
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FT num_x, num_y, num_z, den;
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determinants_for_weighted_circumcenterC3(px, py, pz, pw,
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qx, qy, qz, qw,
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rx, ry, rz, rw,
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sx, sy, sz, sw,
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num_x, num_y, num_z,den);
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CGAL_assertion( ! CGAL_NTS is_zero(den) );
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FT inv = FT(1)/(FT(2) * den);
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return
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(CGAL_NTS square(num_x)+CGAL_NTS square(num_y)+CGAL_NTS square(num_z))
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*CGAL_NTS square(inv) - pw;
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}
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template <class FT>
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void
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determinants_for_weighted_circumcenterC3(
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const FT &px, const FT &py, const FT &pz, const FT &pw,
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const FT &qx, const FT &qy, const FT &qz, const FT &qw,
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const FT &rx, const FT &ry, const FT &rz, const FT &rw,
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FT &num_x, FT &num_y, FT &num_z, FT &den)
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{
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// translate origin to p
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// and compute determinants for weighted_circumcenter and
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// circumradius
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// Translate s to origin to simplify the expression.
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FT qpx = qx-px;
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FT qpy = qy-py;
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FT qpz = qz-pz;
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FT qp2 = CGAL_NTS square(qpx) + CGAL_NTS square(qpy) +
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CGAL_NTS square(qpz) - qw + pw;
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FT rpx = rx-px;
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FT rpy = ry-py;
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FT rpz = rz-pz;
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FT rp2 = CGAL_NTS square(rpx) + CGAL_NTS square(rpy) +
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CGAL_NTS square(rpz) - rw + pw;
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FT sx = qpy*rpz-qpz*rpy;
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FT sy = qpz*rpx-qpx*rpz;
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FT sz = qpx*rpy-qpy*rpx;
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// The following determinants can be developped and simplified.
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//
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// FT num_x = determinant(qpy,qpz,qp2,
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// rpy,rpz,rp2,
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// sy,sz,FT(0));
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// FT num_y = determinant(qpx,qpz,qp2,
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// rpx,rpz,rp2,
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// sx,sz,FT(0));
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// FT num_z = determinant(qpx,qpy,qp2,
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// rpx,rpy,rp2,
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// sx,sy,FT(0));
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num_x = qp2 * determinant(rpy,rpz,sy,sz)
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- rp2 * determinant(qpy,qpz,sy,sz);
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num_y = qp2 * determinant(rpx,rpz,sx,sz)
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- rp2 * determinant(qpx,qpz,sx,sz);
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num_z = qp2 * determinant(rpx,rpy,sx,sy)
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- rp2 * determinant(qpx,qpy,sx,sy);
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den = determinant(qpx,qpy,qpz,
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rpx,rpy,rpz,
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sx,sy,sz);
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}
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template < class FT >
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void
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weighted_circumcenterC3(
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const FT &px, const FT &py, const FT &pz, const FT &pw,
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const FT &qx, const FT &qy, const FT &qz, const FT &qw,
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const FT &rx, const FT &ry, const FT &rz, const FT &rw,
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FT &x, FT &y, FT &z)
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{
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// this function compute the weighted circumcenter point only
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// Translate p to origin and compute determinants
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FT num_x, num_y, num_z, den;
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determinants_for_weighted_circumcenterC3(px, py, pz, pw,
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qx, qy, qz, qw,
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rx, ry, rz, rw,
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num_x, num_y, num_z, den);
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CGAL_assertion( den != FT(0) );
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FT inv = FT(1)/(FT(2) * den);
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x = px + num_x*inv;
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y = py - num_y*inv;
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z = pz + num_z*inv;
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}
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template < class FT >
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void
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weighted_circumcenterC3(
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const FT &px, const FT &py, const FT &pz, const FT &pw,
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const FT &qx, const FT &qy, const FT &qz, const FT &qw,
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const FT &rx, const FT &ry, const FT &rz, const FT &rw,
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FT &x, FT &y, FT &z, FT &w)
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{
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// this function compute the weighted circumcenter and
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// the weighted squared circumradius
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// Translate p to origin and compute determinants
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FT num_x, num_y, num_z, den;
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determinants_for_weighted_circumcenterC3(px, py, pz, pw,
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qx, qy, qz, qw,
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rx, ry, rz, rw,
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num_x, num_y, num_z, den);
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CGAL_assertion( den != FT(0) );
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FT inv = FT(1)/(FT(2) * den);
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x = px + num_x*inv;
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y = py - num_y*inv;
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z = pz + num_z*inv;
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w = (CGAL_NTS square(num_x)+CGAL_NTS square(num_y)+CGAL_NTS square(num_z))
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*CGAL_NTS square(inv) - pw;
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}
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template< class FT >
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CGAL_MEDIUM_INLINE
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FT
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squared_radius_smallest_orthogonal_sphereC3(
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const FT &px, const FT &py, const FT &pz, const FT &pw,
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const FT &qx, const FT &qy, const FT &qz, const FT &qw,
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const FT &rx, const FT &ry, const FT &rz, const FT &rw)
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{
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// this function compute the weighted squared circumradius only
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// Translate p to origin and compute determinants
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FT num_x, num_y, num_z, den;
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determinants_for_weighted_circumcenterC3(px, py, pz, pw,
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qx, qy, qz, qw,
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rx, ry, rz, rw,
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num_x, num_y, num_z, den);
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CGAL_assertion( den != FT(0) );
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FT inv = FT(1)/(FT(2) * den);
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return
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(CGAL_NTS square(num_x)+CGAL_NTS square(num_y)+CGAL_NTS square(num_z))
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*CGAL_NTS square(inv) - pw;
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}
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template < class FT >
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void
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weighted_circumcenterC3(
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const FT &px, const FT &py, const FT &pz, const FT &pw,
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const FT &qx, const FT &qy, const FT &qz, const FT &qw,
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FT &x, FT &y, FT &z)
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{
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// this function compute the weighted circumcenter point only
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FT qpx = qx-px;
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FT qpy = qy-py;
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FT qpz = qz-pz;
|
||||||
|
FT qp2 = CGAL_NTS square(qpx) + CGAL_NTS square(qpy) +
|
||||||
|
CGAL_NTS square(qpz);
|
||||||
|
FT inv = FT(1)/(FT(2)*qp2);
|
||||||
|
FT alpha = 1/FT(2) + (pw-qw)*inv;
|
||||||
|
|
||||||
|
x = px + alpha * qpx;
|
||||||
|
y = py + alpha * qpy;
|
||||||
|
z = pz + alpha * qpz;
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
|
template < class FT >
|
||||||
|
void
|
||||||
|
weighted_circumcenterC3(
|
||||||
|
const FT &px, const FT &py, const FT &pz, const FT &pw,
|
||||||
|
const FT &qx, const FT &qy, const FT &qz, const FT &qw,
|
||||||
|
FT &x, FT &y, FT &z, FT &w)
|
||||||
|
{
|
||||||
|
// this function compute the weighted circumcenter point and
|
||||||
|
// the weighted circumradius
|
||||||
|
FT qpx = qx-px;
|
||||||
|
FT qpy = qy-py;
|
||||||
|
FT qpz = qz-pz;
|
||||||
|
FT qp2 = CGAL_NTS square(qpx) + CGAL_NTS square(qpy) +
|
||||||
|
CGAL_NTS square(qpz);
|
||||||
|
FT inv = FT(1)/(FT(2)*qp2);
|
||||||
|
FT alpha = 1/FT(2) + (pw-qw)*inv;
|
||||||
|
|
||||||
|
x = px + alpha * qpx;
|
||||||
|
y = py + alpha * qpy;
|
||||||
|
z = pz + alpha * qpz;
|
||||||
|
|
||||||
|
w = CGAL_NTS square(alpha)*qp2 - pw;
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
|
template< class FT >
|
||||||
|
CGAL_MEDIUM_INLINE
|
||||||
|
FT
|
||||||
|
squared_radius_smallest_orthogonal_sphereC3(
|
||||||
|
const FT &px, const FT &py, const FT &pz, const FT &pw,
|
||||||
|
const FT &qx, const FT &qy, const FT &qz, const FT &qw)
|
||||||
|
{
|
||||||
|
// this function computes
|
||||||
|
// the weighted circumradius only
|
||||||
|
FT qpx = qx-px;
|
||||||
|
FT qpy = qy-py;
|
||||||
|
FT qpz = qz-pz;
|
||||||
|
FT qp2 = CGAL_NTS square(qpx) + CGAL_NTS square(qpy) +
|
||||||
|
CGAL_NTS square(qpz);
|
||||||
|
FT inv = FT(1)/(FT(2)*qp2);
|
||||||
|
FT alpha = 1/FT(2) + (pw-qw)*inv;
|
||||||
|
|
||||||
|
return CGAL_NTS square(alpha)*qp2 - pw;
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
|
template< class FT >
|
||||||
|
FT
|
||||||
|
power_productC3(
|
||||||
|
const FT &px, const FT &py, const FT &pz, const FT &pw,
|
||||||
|
const FT &qx, const FT &qy, const FT &qz, const FT &qw)
|
||||||
|
{
|
||||||
|
// computes the power product of two weighted points
|
||||||
|
FT qpx = qx-px;
|
||||||
|
FT qpy = qy-py;
|
||||||
|
FT qpz = qz-pz;
|
||||||
|
FT qp2 = CGAL_NTS square(qpx) + CGAL_NTS square(qpy) +
|
||||||
|
CGAL_NTS square(qpz);
|
||||||
|
return qp2 - pw - qw ;
|
||||||
|
}
|
||||||
|
|
||||||
|
template < class RT , class We>
|
||||||
|
void
|
||||||
|
radical_axisC3(const RT &px, const RT &py, const RT &pz, const We & /* pw */,
|
||||||
|
const RT &qx, const RT &qy, const RT &qz, const We & /* qw */,
|
||||||
|
const RT &rx, const RT &ry, const RT &rz, const We & /* rw */,
|
||||||
|
RT &a, RT &b, RT& c )
|
||||||
|
{
|
||||||
|
RT dqx=qx-px, dqy=qy-py, dqz=qz-pz, drx=rx-px, dry=ry-py, drz=rz-pz;
|
||||||
|
|
||||||
|
//il manque des tests...
|
||||||
|
|
||||||
|
a= RT(1)*determinant(dqy, dqz, dry, drz);
|
||||||
|
b= - RT(1)*determinant(dqx, dqz, drx, drz);
|
||||||
|
c= RT(1)*determinant(dqx, dqy, drx, dry);
|
||||||
|
}
|
||||||
|
|
||||||
|
// function used in critical_squared_radiusC3
|
||||||
|
// power ( t, tw) with respect to
|
||||||
|
// circle orthogonal (p,pw), (q,qw), (r,rw), (s,sw)
|
||||||
|
template < class FT>
|
||||||
|
FT
|
||||||
|
power_to_orthogonal_sphereC3(
|
||||||
|
const FT &px, const FT &py, const FT &pz, const FT &pw,
|
||||||
|
const FT &qx, const FT &qy, const FT &qz, const FT &qw,
|
||||||
|
const FT &rx, const FT &ry, const FT &rz, const FT &rw,
|
||||||
|
const FT &sx, const FT &sy, const FT &sz, const FT &sw,
|
||||||
|
const FT &tx, const FT &ty, const FT &tz, const FT &tw)
|
||||||
|
{
|
||||||
|
//to get the value of the determinant
|
||||||
|
// We translate the points so that t becomes the origin.
|
||||||
|
FT dpx = px - tx;
|
||||||
|
FT dpy = py - ty;
|
||||||
|
FT dpz = pz - tz;
|
||||||
|
FT dpt = CGAL_NTS square(dpx) + CGAL_NTS square(dpy) +
|
||||||
|
CGAL_NTS square(dpz) - pw + tw ;
|
||||||
|
FT dqx = qx - tx;
|
||||||
|
FT dqy = qy - ty;
|
||||||
|
FT dqz = qz - tz;
|
||||||
|
FT dqt = CGAL_NTS square(dqx) + CGAL_NTS square(dqy) +
|
||||||
|
CGAL_NTS square(dqz) - qw + tw;
|
||||||
|
FT drx = rx - tx;
|
||||||
|
FT dry = ry - ty;
|
||||||
|
FT drz = rz - tz;
|
||||||
|
FT drt = CGAL_NTS square(drx) + CGAL_NTS square(dry) +
|
||||||
|
CGAL_NTS square(drz) - rw + tw;
|
||||||
|
FT dsx = sx - tx;
|
||||||
|
FT dsy = sy - ty;
|
||||||
|
FT dsz = sz - tz;
|
||||||
|
FT dst = CGAL_NTS square(dsx) + CGAL_NTS square(dsy) +
|
||||||
|
CGAL_NTS square(dsz) - sw + tw;
|
||||||
|
|
||||||
|
return determinant(dpx, dpy, dpz, dpt,
|
||||||
|
dqx, dqy, dqz, dqt,
|
||||||
|
drx, dry, drz, drt,
|
||||||
|
dsx, dsy, dsz, dst);
|
||||||
|
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
// compute the critical weight tw
|
||||||
|
// where weighted point t is orthogonal to weighted points p, q,r,s
|
||||||
|
template < class FT>
|
||||||
|
FT
|
||||||
|
critical_squared_radiusC3(
|
||||||
|
const FT &px, const FT &py, const FT &pz, const FT &pw,
|
||||||
|
const FT &qx, const FT &qy, const FT &qz, const FT &qw,
|
||||||
|
const FT &rx, const FT &ry, const FT &rz, const FT &rw,
|
||||||
|
const FT &sx, const FT &sy, const FT &sz, const FT &sw,
|
||||||
|
const FT &tx, const FT &ty, const FT &tz, const FT & )
|
||||||
|
{
|
||||||
|
// the 5x5 det is a linear function of tw ff(tw)= ff(0) + tw ff(1)
|
||||||
|
// the critical value for tw is - ff(0)/( ff(1) - ff(0))
|
||||||
|
|
||||||
|
|
||||||
|
FT ff0 = power_to_orthogonal_sphereC3(px, py, pz, pw,
|
||||||
|
qx, qy, qz, qw,
|
||||||
|
rx, ry, rz, rw,
|
||||||
|
sx, sy, sz, sw,
|
||||||
|
tx, ty, tz, FT(0));
|
||||||
|
|
||||||
|
FT ff1 = power_to_orthogonal_sphereC3(px, py, pz, pw,
|
||||||
|
qx, qy, qz, qw,
|
||||||
|
rx, ry, rz, rw,
|
||||||
|
sx, sy, sz, sw,
|
||||||
|
tx, ty, tz, FT(1));
|
||||||
|
|
||||||
|
return -ff0/(ff1 - ff0);
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
// I will use this to test if the radial axis of three spheres
|
||||||
|
// intersect the triangle formed by the centers.
|
||||||
|
// // resolution of the system (where we note c the center)
|
||||||
|
// // | dc^2 = cw + rw
|
||||||
|
// // | (dp-dc)^2 = pw + cw
|
||||||
|
// // | (dq-dc)^2 = qw + cw
|
||||||
|
// // | dc = Lamdba*dp + Mu*dq
|
||||||
|
|
||||||
|
// FT FT2(2);
|
||||||
|
// FT dpx = px-rx;
|
||||||
|
// FT dpy = py-ry;
|
||||||
|
// FT dpz = pz-rz;
|
||||||
|
// FT dp = CGAL_NTS square(dpx)+CGAL_NTS square(dpy)+CGAL_NTS square(dpz);
|
||||||
|
// FT dpp = dp-pw+rw;
|
||||||
|
// FT dqx = qx-rx;
|
||||||
|
// FT dqy = qy-ry;
|
||||||
|
// FT dqz = qz-rz;
|
||||||
|
// FT dq = CGAL_NTS square(dqx)+CGAL_NTS square(dqy)+CGAL_NTS square(dqz);
|
||||||
|
// FT dqq = dq-qw+rw;
|
||||||
|
// FT dpdq = dpx*dqx+dpy*dqy+dpz*dqz;
|
||||||
|
// FT denom = FT2*(dp*dq-CGAL_NTS square(dpdq));
|
||||||
|
// FT Lambda = (dpp*dq-dqq*dpdq)/denom;
|
||||||
|
// FT Mu = (dqq*dp-dpp*dpdq)/denom;
|
||||||
|
|
||||||
|
// return (CGAL_NTS square(Lambda)*dp+CGAL_NTS square(Mu)*dq
|
||||||
|
// +FT2*Lambda*Mu*dpdq - rw);
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
} //namespace CGAL
|
} //namespace CGAL
|
||||||
|
|
||||||
#endif // CGAL_CONSTRUCTIONS_KERNEL_FTC3_H
|
#endif // CGAL_CONSTRUCTIONS_KERNEL_FTC3_H
|
||||||
|
|
|
||||||
|
|
@ -555,6 +555,137 @@ has_smaller_signed_dist_to_planeC3(
|
||||||
prx, pry, prz, px, py, pz, qx, qy, qz) == SMALLER;
|
prx, pry, prz, px, py, pz, qx, qy, qz) == SMALLER;
|
||||||
}
|
}
|
||||||
|
|
||||||
|
// return minus the sign of the 5x5 determinant [P,Q,R,S,T]
|
||||||
|
// where column [P] = transpose[px,py,pz,p^2 -wp,1]
|
||||||
|
template <class FT>
|
||||||
|
Oriented_side
|
||||||
|
power_testC3( const FT &px, const FT &py, const FT &pz, const FT &pwt,
|
||||||
|
const FT &qx, const FT &qy, const FT &qz, const FT &qwt,
|
||||||
|
const FT &rx, const FT &ry, const FT &rz, const FT &rwt,
|
||||||
|
const FT &sx, const FT &sy, const FT &sz, const FT &swt,
|
||||||
|
const FT &tx, const FT &ty, const FT &tz, const FT &twt)
|
||||||
|
{
|
||||||
|
// We translate the points so that T becomes the origin.
|
||||||
|
FT dpx = px - tx;
|
||||||
|
FT dpy = py - ty;
|
||||||
|
FT dpz = pz - tz;
|
||||||
|
FT dpt = CGAL_NTS square(dpx) + CGAL_NTS square(dpy) +
|
||||||
|
CGAL_NTS square(dpz) + (twt - pwt);
|
||||||
|
FT dqx = qx - tx;
|
||||||
|
FT dqy = qy - ty;
|
||||||
|
FT dqz = qz - tz;
|
||||||
|
FT dqt = CGAL_NTS square(dqx) + CGAL_NTS square(dqy) +
|
||||||
|
CGAL_NTS square(dqz) + (twt - qwt);
|
||||||
|
FT drx = rx - tx;
|
||||||
|
FT dry = ry - ty;
|
||||||
|
FT drz = rz - tz;
|
||||||
|
FT drt = CGAL_NTS square(drx) + CGAL_NTS square(dry) +
|
||||||
|
CGAL_NTS square(drz) + (twt - rwt);
|
||||||
|
FT dsx = sx - tx;
|
||||||
|
FT dsy = sy - ty;
|
||||||
|
FT dsz = sz - tz;
|
||||||
|
FT dst = CGAL_NTS square(dsx) + CGAL_NTS square(dsy) +
|
||||||
|
CGAL_NTS square(dsz) + (twt - swt);
|
||||||
|
|
||||||
|
return - sign_of_determinant(dpx, dpy, dpz, dpt,
|
||||||
|
dqx, dqy, dqz, dqt,
|
||||||
|
drx, dry, drz, drt,
|
||||||
|
dsx, dsy, dsz, dst);
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
|
template <class FT>
|
||||||
|
Oriented_side
|
||||||
|
power_testC3( const FT &px, const FT &py, const FT &pz, const FT &pwt,
|
||||||
|
const FT &qx, const FT &qy, const FT &qz, const FT &qwt,
|
||||||
|
const FT &rx, const FT &ry, const FT &rz, const FT &rwt,
|
||||||
|
const FT &tx, const FT &ty, const FT &tz, const FT &twt)
|
||||||
|
{
|
||||||
|
// Same translation as above.
|
||||||
|
FT dpx = px - tx;
|
||||||
|
FT dpy = py - ty;
|
||||||
|
FT dpz = pz - tz;
|
||||||
|
FT dpt = CGAL_NTS square(dpx) + CGAL_NTS square(dpy) +
|
||||||
|
CGAL_NTS square(dpz) + (twt - pwt);
|
||||||
|
FT dqx = qx - tx;
|
||||||
|
FT dqy = qy - ty;
|
||||||
|
FT dqz = qz - tz;
|
||||||
|
FT dqt = CGAL_NTS square(dqx) + CGAL_NTS square(dqy) +
|
||||||
|
CGAL_NTS square(dqz) + (twt - qwt);
|
||||||
|
FT drx = rx - tx;
|
||||||
|
FT dry = ry - ty;
|
||||||
|
FT drz = rz - tz;
|
||||||
|
FT drt = CGAL_NTS square(drx) + CGAL_NTS square(dry) +
|
||||||
|
CGAL_NTS square(drz) + (twt - rwt);
|
||||||
|
Sign cmp;
|
||||||
|
|
||||||
|
// Projection on the (xy) plane.
|
||||||
|
cmp = sign_of_determinant(dpx, dpy, dpt,
|
||||||
|
dqx, dqy, dqt,
|
||||||
|
drx, dry, drt);
|
||||||
|
if (cmp != ZERO)
|
||||||
|
return cmp * sign_of_determinant(px-rx, py-ry,
|
||||||
|
qx-rx, qy-ry);
|
||||||
|
|
||||||
|
// Projection on the (xz) plane.
|
||||||
|
cmp = sign_of_determinant(dpx, dpz, dpt,
|
||||||
|
dqx, dqz, dqt,
|
||||||
|
drx, drz, drt);
|
||||||
|
if (cmp != ZERO)
|
||||||
|
return cmp * sign_of_determinant(px-rx, pz-rz,
|
||||||
|
qx-rx, qz-rz);
|
||||||
|
|
||||||
|
// Projection on the (yz) plane.
|
||||||
|
cmp = sign_of_determinant(dpy, dpz, dpt,
|
||||||
|
dqy, dqz, dqt,
|
||||||
|
dry, drz, drt);
|
||||||
|
return cmp * sign_of_determinant(py-ry, pz-rz,
|
||||||
|
qy-ry, qz-rz);
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
|
template <class FT>
|
||||||
|
Oriented_side
|
||||||
|
power_testC3( const FT &px, const FT &py, const FT &pz, const FT &pwt,
|
||||||
|
const FT &qx, const FT &qy, const FT &qz, const FT &qwt,
|
||||||
|
const FT &tx, const FT &ty, const FT &tz, const FT &twt)
|
||||||
|
{
|
||||||
|
// Same translation as above.
|
||||||
|
FT dpx = px - tx;
|
||||||
|
FT dpy = py - ty;
|
||||||
|
FT dpz = pz - tz;
|
||||||
|
FT dpt = CGAL_NTS square(dpx) + CGAL_NTS square(dpy) +
|
||||||
|
CGAL_NTS square(dpz) + (twt - pwt);
|
||||||
|
FT dqx = qx - tx;
|
||||||
|
FT dqy = qy - ty;
|
||||||
|
FT dqz = qz - tz;
|
||||||
|
FT dqt = CGAL_NTS square(dqx) + CGAL_NTS square(dqy) +
|
||||||
|
CGAL_NTS square (dqz) + (twt - qwt);
|
||||||
|
Comparison_result cmp;
|
||||||
|
|
||||||
|
// We do an orthogonal projection on the (x) axis, if possible.
|
||||||
|
cmp = CGAL_NTS compare(px, qx);
|
||||||
|
if (cmp != EQUAL)
|
||||||
|
return cmp * sign_of_determinant(dpx, dpt, dqx, dqt);
|
||||||
|
|
||||||
|
// We do an orthogonal projection on the (y) axis, if possible.
|
||||||
|
cmp = CGAL_NTS compare(py, qy);
|
||||||
|
if (cmp != EQUAL)
|
||||||
|
return cmp * sign_of_determinant(dpy, dpt, dqy, dqt);
|
||||||
|
|
||||||
|
// We do an orthogonal projection on the (z) axis.
|
||||||
|
cmp = CGAL_NTS compare(pz, qz);
|
||||||
|
return cmp * sign_of_determinant(dpz, dpt, dqz, dqt);
|
||||||
|
}
|
||||||
|
|
||||||
|
template <class FT>
|
||||||
|
Oriented_side
|
||||||
|
power_testC3(const FT &pwt, const FT &qwt)
|
||||||
|
{
|
||||||
|
return CGAL_NTS compare(qwt, pwt);
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
} //namespace CGAL
|
} //namespace CGAL
|
||||||
|
|
||||||
#endif // CGAL_PREDICATES_KERNEL_FTC3_H
|
#endif // CGAL_PREDICATES_KERNEL_FTC3_H
|
||||||
|
|
|
||||||
|
|
@ -1,10 +1,10 @@
|
||||||
// Copyright (c) 2009 INRIA Sophia-Antipolis (France).
|
// Copyright (c) 2009 INRIA Sophia-Antipolis (France).
|
||||||
// All rights reserved.
|
// All rights reserved.
|
||||||
//
|
//
|
||||||
// This file is part of CGAL (www.cgal.org).
|
// This file is part of CGAL (www.cgal.org); you can redistribute it and/or
|
||||||
// You can redistribute it and/or modify it under the terms of the GNU
|
// modify it under the terms of the GNU Lesser General Public License as
|
||||||
// General Public License as published by the Free Software Foundation,
|
// published by the Free Software Foundation; either version 3 of the License,
|
||||||
// either version 3 of the License, or (at your option) any later version.
|
// or (at your option) any later version.
|
||||||
//
|
//
|
||||||
// Licensees holding a valid commercial license may use this file in
|
// Licensees holding a valid commercial license may use this file in
|
||||||
// accordance with the commercial license agreement provided with the software.
|
// accordance with the commercial license agreement provided with the software.
|
||||||
|
|
|
||||||
|
|
@ -6,8 +6,10 @@
|
||||||
// General Public License as published by the Free Software Foundation,
|
// General Public License as published by the Free Software Foundation,
|
||||||
// either version 3 of the License, or (at your option) any later version.
|
// either version 3 of the License, or (at your option) any later version.
|
||||||
//
|
//
|
||||||
// Licensees holding a valid commercial license may use this file in
|
// This file is part of CGAL (www.cgal.org); you can redistribute it and/or
|
||||||
// accordance with the commercial license agreement provided with the software.
|
// modify it under the terms of the GNU Lesser General Public License as
|
||||||
|
// published by the Free Software Foundation; either version 3 of the License,
|
||||||
|
// or (at your option) any later version.
|
||||||
//
|
//
|
||||||
// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
|
// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
|
||||||
// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
|
// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
|
||||||
|
|
|
||||||
|
|
@ -1,10 +1,10 @@
|
||||||
// Copyright (c) 1999 INRIA Sophia-Antipolis (France).
|
// Copyright (c) 1999 INRIA Sophia-Antipolis (France).
|
||||||
// All rights reserved.
|
// All rights reserved.
|
||||||
//
|
//
|
||||||
// This file is part of CGAL (www.cgal.org).
|
// This file is part of CGAL (www.cgal.org); you can redistribute it and/or
|
||||||
// You can redistribute it and/or modify it under the terms of the GNU
|
// modify it under the terms of the GNU Lesser General Public License as
|
||||||
// General Public License as published by the Free Software Foundation,
|
// published by the Free Software Foundation; either version 3 of the License,
|
||||||
// either version 3 of the License, or (at your option) any later version.
|
// or (at your option) any later version.
|
||||||
//
|
//
|
||||||
// Licensees holding a valid commercial license may use this file in
|
// Licensees holding a valid commercial license may use this file in
|
||||||
// accordance with the commercial license agreement provided with the software.
|
// accordance with the commercial license agreement provided with the software.
|
||||||
|
|
@ -24,7 +24,7 @@
|
||||||
// This file contains the low level homogeneous predicates
|
// This file contains the low level homogeneous predicates
|
||||||
// used by the 3D regular triangulation.
|
// used by the 3D regular triangulation.
|
||||||
|
|
||||||
#include <CGAL/predicates/Regular_triangulation_ftC3.h>
|
#include <CGAL/predicates/kernel_ftC3.h>
|
||||||
|
|
||||||
namespace CGAL {
|
namespace CGAL {
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -29,7 +29,7 @@
|
||||||
#include <CGAL/Cartesian/function_objects.h>
|
#include <CGAL/Cartesian/function_objects.h>
|
||||||
#include <CGAL/Kernel/Return_base_tag.h>
|
#include <CGAL/Kernel/Return_base_tag.h>
|
||||||
#include <CGAL/predicates/sign_of_determinant.h>
|
#include <CGAL/predicates/sign_of_determinant.h>
|
||||||
#include <CGAL/predicates/Regular_triangulation_rtH3.h>
|
#include <CGAL/Homogeneous/Regular_triangulation_rtH3.h>
|
||||||
|
|
||||||
namespace CGAL {
|
namespace CGAL {
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -78,7 +78,6 @@ public:
|
||||||
Weighted_point_3(const Rep& p)
|
Weighted_point_3(const Rep& p)
|
||||||
: Rep(p) {}
|
: Rep(p) {}
|
||||||
|
|
||||||
|
|
||||||
Weighted_point_3(const Point_3& p)
|
Weighted_point_3(const Point_3& p)
|
||||||
: Rep(typename R::Construct_weighted_point_3()(Return_base_tag(), p, 0))
|
: Rep(typename R::Construct_weighted_point_3()(Return_base_tag(), p, 0))
|
||||||
{}
|
{}
|
||||||
|
|
|
||||||
|
|
@ -1,10 +1,10 @@
|
||||||
// Copyright (c) 1997 INRIA Sophia-Antipolis (France).
|
// Copyright (c) 1997 INRIA Sophia-Antipolis (France).
|
||||||
// All rights reserved.
|
// All rights reserved.
|
||||||
//
|
//
|
||||||
// This file is part of CGAL (www.cgal.org).
|
// This file is part of CGAL (www.cgal.org); you can redistribute it and/or
|
||||||
// You can redistribute it and/or modify it under the terms of the GNU
|
// modify it under the terms of the GNU Lesser General Public License as
|
||||||
// General Public License as published by the Free Software Foundation,
|
// published by the Free Software Foundation; either version 3 of the License,
|
||||||
// either version 3 of the License, or (at your option) any later version.
|
// or (at your option) any later version.
|
||||||
//
|
//
|
||||||
// Licensees holding a valid commercial license may use this file in
|
// Licensees holding a valid commercial license may use this file in
|
||||||
// accordance with the commercial license agreement provided with the software.
|
// accordance with the commercial license agreement provided with the software.
|
||||||
|
|
@ -127,156 +127,6 @@ in_smallest_orthogonal_sphereC3(
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
// return ON_UNBOUNDED_SIDE, ON_BOUNDARY or ON_BOUNDED_SIDE according
|
|
||||||
// to the position of the weighted circumcenter of pqrs
|
|
||||||
// with respect with the tertraedron formed by bare points in p, q,r,s
|
|
||||||
template <class FT>
|
|
||||||
Bounded_side
|
|
||||||
does_simplex_intersect_weighted_dual_supportC3(
|
|
||||||
const FT &px, const FT &py, const FT &pz, const FT &pw,
|
|
||||||
const FT &qx, const FT &qy, const FT &qz, const FT &qw,
|
|
||||||
const FT &rx, const FT &ry, const FT &rz, const FT &rw,
|
|
||||||
const FT &sx, const FT &sy, const FT &sz, const FT &sw)
|
|
||||||
{
|
|
||||||
FT qpx = qx-px;
|
|
||||||
FT qpy = qy-py;
|
|
||||||
FT qpz = qz-pz;
|
|
||||||
|
|
||||||
FT rpx = rx-px;
|
|
||||||
FT rpy = ry-py;
|
|
||||||
FT rpz = rz-pz;
|
|
||||||
|
|
||||||
FT spx = sx-px;
|
|
||||||
FT spy = sy-py;
|
|
||||||
FT spz = sz-pz;
|
|
||||||
|
|
||||||
FT qq = CGAL_NTS square(qpx) + CGAL_NTS square(qpy) + CGAL_NTS square(qpz);
|
|
||||||
FT rr = CGAL_NTS square(rpx) + CGAL_NTS square(rpy) + CGAL_NTS square(rpz);
|
|
||||||
FT ss = CGAL_NTS square(spx) + CGAL_NTS square(spy) + CGAL_NTS square(spz);
|
|
||||||
FT qr = qpx*rpx + qpy*rpy + qpz*rpz;
|
|
||||||
FT rs = rpx*spx + rpy*spy + rpz*spz;
|
|
||||||
FT qs = spx*qpx + spy*qpy + spz*qpz;
|
|
||||||
FT qpw = qq - qw + pw ;
|
|
||||||
FT rpw = rr - rw + pw ;
|
|
||||||
FT spw = ss - sw + pw ;
|
|
||||||
|
|
||||||
FT den = determinant(qq,qr,qs,
|
|
||||||
qr,rr,rs,
|
|
||||||
qs,rs,ss);
|
|
||||||
FT detq = determinant(qpw,qr,qs,
|
|
||||||
rpw,rr,rs,
|
|
||||||
spw,rs,ss);
|
|
||||||
FT detr = determinant(qq,qpw,qs,
|
|
||||||
qr,rpw,rs,
|
|
||||||
qs,spw,ss);
|
|
||||||
FT dets = determinant(qq,qr,qpw,
|
|
||||||
qr,rr,rpw,
|
|
||||||
qs,rs,spw);
|
|
||||||
CGAL_assertion( ! CGAL_NTS is_zero(den) );
|
|
||||||
|
|
||||||
|
|
||||||
// The barycentrique coordinate of the smallest orthogonal sphere center
|
|
||||||
// are detq/2*den detr/2*den dets/2*den
|
|
||||||
// and 1-(detq+ detr+dets)/2*den
|
|
||||||
|
|
||||||
CGAL::Sign sign1 = CGAL_NTS sign(FT(2)*den - detq -detr -dets);
|
|
||||||
if (
|
|
||||||
(CGAL_NTS sign(detq) == CGAL_NTS sign(den) || CGAL_NTS sign(detq)== ZERO) &&
|
|
||||||
(CGAL_NTS sign(detr) == CGAL_NTS sign(den) || CGAL_NTS sign(detr)== ZERO) &&
|
|
||||||
(CGAL_NTS sign(dets) == CGAL_NTS sign(den) || CGAL_NTS sign(dets)== ZERO) &&
|
|
||||||
( sign1 == POSITIVE || sign1 == ZERO )) { // inside or on boundary
|
|
||||||
if (CGAL_NTS sign(detq) != ZERO &&
|
|
||||||
CGAL_NTS sign(detr) != ZERO &&
|
|
||||||
CGAL_NTS sign(dets) != ZERO &&
|
|
||||||
sign1 != ZERO)
|
|
||||||
return ON_BOUNDED_SIDE;
|
|
||||||
else return ON_BOUNDARY ;
|
|
||||||
}
|
|
||||||
return ON_UNBOUNDED_SIDE;
|
|
||||||
}
|
|
||||||
|
|
||||||
// return ON_UNBOUNDED_SIDE, ON_BOUNDARY or ON_BOUNDED_SIDE according
|
|
||||||
// to the position of the intersection if the radialaxis
|
|
||||||
// of weighted circumcenter of pqr with affine hull of bare p,q,r
|
|
||||||
// with respect with the triangle formed by bare points in p, q,r.
|
|
||||||
template <class FT>
|
|
||||||
Bounded_side
|
|
||||||
does_simplex_intersect_weighted_dual_supportC3(
|
|
||||||
const FT &px, const FT &py, const FT &pz, const FT &pw,
|
|
||||||
const FT &qx, const FT &qy, const FT &qz, const FT &qw,
|
|
||||||
const FT &rx, const FT &ry, const FT &rz, const FT &rw)
|
|
||||||
{
|
|
||||||
// returns true if weighted circumcenter of pqr is in
|
|
||||||
// triangle pqr or on boundary
|
|
||||||
FT qpx = qx-px;
|
|
||||||
FT qpy = qy-py;
|
|
||||||
FT qpz = qz-pz;
|
|
||||||
|
|
||||||
FT rpx = rx-px;
|
|
||||||
FT rpy = ry-py;
|
|
||||||
FT rpz = rz-pz;
|
|
||||||
|
|
||||||
FT qq = CGAL_NTS square(qpx) + CGAL_NTS square(qpy) + CGAL_NTS square(qpz);
|
|
||||||
FT rr = CGAL_NTS square(rpx) + CGAL_NTS square(rpy) + CGAL_NTS square(rpz);
|
|
||||||
FT qr = qpx*rpx + qpy*rpy + qpz*rpz;
|
|
||||||
|
|
||||||
FT qpw = qq - qw + pw ;
|
|
||||||
FT rpw = rr - rw + pw ;
|
|
||||||
|
|
||||||
FT den = determinant(qq,qr,
|
|
||||||
qr,rr);
|
|
||||||
FT detq = determinant(qpw,qr,
|
|
||||||
rpw,rr);
|
|
||||||
FT detr = determinant(qq,qpw,
|
|
||||||
qr,rpw);
|
|
||||||
|
|
||||||
CGAL_assertion( ! CGAL_NTS is_zero(den) );
|
|
||||||
|
|
||||||
// The barycentrique coordinate of the smallest orthogonal sphere center
|
|
||||||
// are detq/2*den detr/2*den
|
|
||||||
// and 1-(detq+ detr)/2*den
|
|
||||||
|
|
||||||
CGAL::Sign sign1 = CGAL_NTS sign(FT(2)*den - detq - detr);
|
|
||||||
if (
|
|
||||||
(CGAL_NTS sign(detq) == CGAL_NTS sign(den) || CGAL_NTS sign(detq)== ZERO) &&
|
|
||||||
(CGAL_NTS sign(detr) == CGAL_NTS sign(den) || CGAL_NTS sign(detr)== ZERO) &&
|
|
||||||
( sign1 == POSITIVE || sign1 == ZERO )) { // inside or on boundary
|
|
||||||
if ( CGAL_NTS sign(detq) != ZERO &&
|
|
||||||
CGAL_NTS sign(detr) != ZERO &&
|
|
||||||
sign1 != ZERO)
|
|
||||||
return ON_BOUNDED_SIDE;
|
|
||||||
else return ON_BOUNDARY;
|
|
||||||
}
|
|
||||||
return ON_UNBOUNDED_SIDE;
|
|
||||||
}
|
|
||||||
|
|
||||||
|
|
||||||
template <class FT>
|
|
||||||
Bounded_side
|
|
||||||
does_simplex_intersect_weighted_dual_supportC3(
|
|
||||||
const FT &px, const FT &py, const FT &pz, const FT &pw,
|
|
||||||
const FT &qx, const FT &qy, const FT &qz, const FT &qw)
|
|
||||||
{
|
|
||||||
// returns true if weighted circumcenter of pq is in
|
|
||||||
// segment pq or on boundary
|
|
||||||
FT qpx = qx-px;
|
|
||||||
FT qpy = qy-py;
|
|
||||||
FT qpz = qz-pz;
|
|
||||||
|
|
||||||
FT qq = CGAL_NTS square(qpx) + CGAL_NTS square(qpy) + CGAL_NTS square(qpz);
|
|
||||||
FT dw = pw - qw;
|
|
||||||
|
|
||||||
CGAL::Sign sign1 = CGAL_NTS sign( qq + dw);
|
|
||||||
CGAL::Sign sign2 = CGAL_NTS sign( qq - dw);
|
|
||||||
|
|
||||||
if( ( sign1 == POSITIVE || sign1 == ZERO ) &&
|
|
||||||
( sign2 == POSITIVE || sign2 == ZERO )) { // inside or on boundary
|
|
||||||
if (sign1 != ZERO && sign2 != ZERO) return ON_BOUNDED_SIDE;
|
|
||||||
else return ON_BOUNDARY;
|
|
||||||
}
|
|
||||||
return ON_UNBOUNDED_SIDE;
|
|
||||||
}
|
|
||||||
|
|
||||||
//-------------------------------------------------------------------
|
//-------------------------------------------------------------------
|
||||||
} //namespace CGAL
|
} //namespace CGAL
|
||||||
//-------------------------------------------------------------------
|
//-------------------------------------------------------------------
|
||||||
|
|
|
||||||
|
|
@ -32,7 +32,7 @@
|
||||||
#include <CGAL/Robust_construction.h>
|
#include <CGAL/Robust_construction.h>
|
||||||
#include <CGAL/Exact_predicates_exact_constructions_kernel.h>
|
#include <CGAL/Exact_predicates_exact_constructions_kernel.h>
|
||||||
#include <CGAL/Regular_triangulation_euclidean_traits_3.h>
|
#include <CGAL/Regular_triangulation_euclidean_traits_3.h>
|
||||||
#include <CGAL/constructions/constructions_on_weighted_points_cartesian_3.h>
|
#include <CGAL/constructions/kernel_ftC3.h>
|
||||||
|
|
||||||
namespace CGAL {
|
namespace CGAL {
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -33,9 +33,8 @@
|
||||||
bool del=true;
|
bool del=true;
|
||||||
|
|
||||||
typedef CGAL::Exact_predicates_inexact_constructions_kernel FK;
|
typedef CGAL::Exact_predicates_inexact_constructions_kernel FK;
|
||||||
// typedef CGAL::Regular_triangulation_euclidean_traits_3<FK> traits;
|
typedef CGAL::Regular_triangulation_euclidean_traits_3<FK> traits;
|
||||||
|
|
||||||
typedef FK traits;
|
|
||||||
|
|
||||||
// Explicit instantiation of the whole class :
|
// Explicit instantiation of the whole class :
|
||||||
template class CGAL::Regular_triangulation_3<traits>;
|
template class CGAL::Regular_triangulation_3<traits>;
|
||||||
|
|
@ -449,7 +448,7 @@ int main()
|
||||||
typedef CGAL::Spatial_lock_grid_3<
|
typedef CGAL::Spatial_lock_grid_3<
|
||||||
CGAL::Tag_priority_blocking> Lock_ds;
|
CGAL::Tag_priority_blocking> Lock_ds;
|
||||||
typedef CGAL::Triangulation_data_structure_3<
|
typedef CGAL::Triangulation_data_structure_3<
|
||||||
CGAL::Triangulation_vertex_base_3<CGAL::Weighted_point_triangulation_traits_3<traits> >,
|
CGAL::Triangulation_vertex_base_3<traits>,
|
||||||
CGAL::Regular_triangulation_cell_base_3<traits>,
|
CGAL::Regular_triangulation_cell_base_3<traits>,
|
||||||
CGAL::Parallel_tag > Tds_parallel;
|
CGAL::Parallel_tag > Tds_parallel;
|
||||||
typedef CGAL::Regular_triangulation_3<
|
typedef CGAL::Regular_triangulation_3<
|
||||||
|
|
|
||||||
Loading…
Reference in New Issue