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cgal/Cartesian_kernel/include/CGAL/predicates/kernel_ftC3.h

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// Copyright (c) 2000 Utrecht University (The Netherlands),
// ETH Zurich (Switzerland), Freie Universitaet Berlin (Germany),
// INRIA Sophia-Antipolis (France), Martin-Luther-University Halle-Wittenberg
// (Germany), Max-Planck-Institute Saarbruecken (Germany), RISC Linz (Austria),
// and Tel-Aviv University (Israel). 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 Lesser General Public License as
// published by the Free Software Foundation; version 2.1 of the License.
// See the file LICENSE.LGPL 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.
//
// $Source$
// $Revision$ $Date$
// $Name$
//
// Author(s) : Herve Bronnimann, Sylvain Pion
#ifndef CGAL_PREDICATES_KERNEL_FTC3_H
#define CGAL_PREDICATES_KERNEL_FTC3_H
#include <CGAL/predicates/sign_of_determinant.h>
#include <CGAL/predicates/kernel_ftC2.h>
#include <CGAL/constructions/kernel_ftC3.h>
CGAL_BEGIN_NAMESPACE
template < class FT >
inline
typename Equal_to<FT>::result_type
parallelC3(const FT &v1x, const FT &v1y, const FT &v1z,
const FT &v2x, const FT &v2y, const FT &v2z)
{
return sign_of_determinant2x2(v1x, v2x, v1y, v2y) == ZERO
&& sign_of_determinant2x2(v1x, v2x, v1z, v2z) == ZERO
&& sign_of_determinant2x2(v1y, v2y, v1z, v2z) == ZERO;
}
template < class FT >
typename Equal_to<FT>::result_type
parallelC3(const FT &s1sx, const FT &s1sy, const FT &s1sz,
const FT &s1tx, const FT &s1ty, const FT &s1tz,
const FT &s2sx, const FT &s2sy, const FT &s2sz,
const FT &s2tx, const FT &s2ty, const FT &s2tz)
{
// NB : Could be made slightly more efficient by computing the z differences
// only when they are needed.
FT v1x = s1tx - s1sx;
FT v1y = s1ty - s1sy;
FT v1z = s1tz - s1sz;
FT v2x = s2tx - s2sx;
FT v2y = s2ty - s2sy;
FT v2z = s2tz - s2sz;
return parallelC3(v1x, v1y, v1z, v2x, v2y, v2z);
}
template < class FT >
/*CGAL_NO_FILTER*/
CGAL_KERNEL_MEDIUM_INLINE
typename Compare<FT>::result_type
compare_lexicographically_xyzC3(const FT &px, const FT &py, const FT &pz,
const FT &qx, const FT &qy, const FT &qz)
{
typedef typename Compare<FT>::result_type Cmp;
Cmp c = CGAL_NTS compare(px, qx);
if (c != EQUAL) return c;
c = CGAL_NTS compare(py, qy);
if (c != EQUAL) return c;
return CGAL_NTS compare(pz, qz);
}
template < class FT >
CGAL_KERNEL_MEDIUM_INLINE
typename Equal_to<FT>::result_type
strict_dominanceC3(const FT &px, const FT &py, const FT &pz,
const FT &qx, const FT &qy, const FT &qz)
{
return CGAL_NTS compare(px, qx) == LARGER &&
CGAL_NTS compare(py, qy) == LARGER &&
CGAL_NTS compare(pz, qz) == LARGER;
}
template < class FT >
CGAL_KERNEL_MEDIUM_INLINE
typename Equal_to<FT>::result_type
dominanceC3(const FT &px, const FT &py, const FT &pz,
const FT &qx, const FT &qy, const FT &qz)
{
return CGAL_NTS compare(px, qx) != SMALLER &&
CGAL_NTS compare(py, qy) != SMALLER &&
CGAL_NTS compare(pz, qz) != SMALLER;
}
template < class FT >
CGAL_KERNEL_MEDIUM_INLINE
typename Equal_to<FT>::result_type
collinearC3(const FT &px, const FT &py, const FT &pz,
const FT &qx, const FT &qy, const FT &qz,
const FT &rx, const FT &ry, const FT &rz)
{
FT dpx = px-rx;
FT dqx = qx-rx;
FT dpy = py-ry;
FT dqy = qy-ry;
if (sign_of_determinant2x2(dpx, dqx, dpy, dqy) != ZERO)
return false;
FT dpz = pz-rz;
FT dqz = qz-rz;
return sign_of_determinant2x2(dpx, dqx, dpz, dqz) == ZERO
&& sign_of_determinant2x2(dpy, dqy, dpz, dqz) == ZERO;
}
template < class FT >
CGAL_KERNEL_MEDIUM_INLINE
typename Same_uncertainty_nt<Orientation, FT>::type
orientationC3(const FT &px, const FT &py, const FT &pz,
const FT &qx, const FT &qy, const FT &qz,
const FT &rx, const FT &ry, const FT &rz,
const FT &sx, const FT &sy, const FT &sz)
{
return enum_cast<Orientation>(sign_of_determinant3x3<FT>(qx-px,rx-px,sx-px,
qy-py,ry-py,sy-py,
qz-pz,rz-pz,sz-pz));
}
template < class FT >
CGAL_KERNEL_MEDIUM_INLINE
typename Same_uncertainty_nt<Orientation, FT>::type
orientationC3(const FT &ux, const FT &uy, const FT &uz,
const FT &vx, const FT &vy, const FT &vz,
const FT &wx, const FT &wy, const FT &wz)
{
return enum_cast<Orientation>(sign_of_determinant3x3(ux, vx, wx,
uy, vy, wy,
uz, vz, wz));
}
template < class FT >
inline
typename Same_uncertainty_nt<Angle, FT>::type
angleC3(const FT &px, const FT &py, const FT &pz,
const FT &qx, const FT &qy, const FT &qz,
const FT &rx, const FT &ry, const FT &rz)
{
return enum_cast<Angle>(CGAL_NTS sign((px-qx)*(rx-qx)+
(py-qy)*(ry-qy)+
(pz-qz)*(rz-qz)));
}
template < class FT >
/*CGAL_NO_FILTER*/
CGAL_KERNEL_MEDIUM_INLINE
typename Same_uncertainty_nt<Orientation, FT>::type
coplanar_orientationC3(const FT &px, const FT &py, const FT &pz,
const FT &qx, const FT &qy, const FT &qz,
const FT &rx, const FT &ry, const FT &rz,
const FT &sx, const FT &sy, const FT &sz)
{
typedef typename Same_uncertainty_nt<Orientation, FT>::type Ori;
Ori oxy_pqr = orientationC2(px,py,qx,qy,rx,ry);
if (oxy_pqr != COLLINEAR)
return enum_cast<Orientation>( oxy_pqr * orientationC2(px,py,qx,qy,sx,sy));
Ori oyz_pqr = orientationC2(py,pz,qy,qz,ry,rz);
if (oyz_pqr != COLLINEAR)
return enum_cast<Orientation>( oyz_pqr * orientationC2(py,pz,qy,qz,sy,sz));
Ori oxz_pqr = orientationC2(px,pz,qx,qz,rx,rz);
CGAL_kernel_assertion(oxz_pqr != COLLINEAR);
return enum_cast<Orientation>( oxz_pqr * orientationC2(px,pz,qx,qz,sx,sz));
}
template < class FT >
/*CGAL_NO_FILTER*/
CGAL_KERNEL_MEDIUM_INLINE
typename Same_uncertainty_nt<Orientation, FT>::type
coplanar_orientationC3(const FT &px, const FT &py, const FT &pz,
const FT &qx, const FT &qy, const FT &qz,
const FT &rx, const FT &ry, const FT &rz)
{
typedef typename Same_uncertainty_nt<Orientation, FT>::type Ori;
Ori oxy_pqr = orientationC2(px,py,qx,qy,rx,ry);
if (oxy_pqr != COLLINEAR)
return oxy_pqr;
Ori oyz_pqr = orientationC2(py,pz,qy,qz,ry,rz);
if (oyz_pqr != COLLINEAR)
return oyz_pqr;
return orientationC2(px,pz,qx,qz,rx,rz);
}
template < class FT >
CGAL_KERNEL_LARGE_INLINE
typename Same_uncertainty_nt<Bounded_side, FT>::type
coplanar_side_of_bounded_circleC3(const FT &px, const FT &py, const FT &pz,
const FT &qx, const FT &qy, const FT &qz,
const FT &rx, const FT &ry, const FT &rz,
const FT &tx, const FT &ty, const FT &tz)
{
// The approach is to compute side_of_bounded_sphere(p,q,r,t+v,t),
// with v = pq ^ pr.
// Note : since the circle defines the orientation of the plane, it can not
// be considered oriented.
FT ptx = px - tx;
FT pty = py - ty;
FT ptz = pz - tz;
FT pt2 = CGAL_NTS square(ptx) + CGAL_NTS square(pty) + CGAL_NTS square(ptz);
FT qtx = qx - tx;
FT qty = qy - ty;
FT qtz = qz - tz;
FT qt2 = CGAL_NTS square(qtx) + CGAL_NTS square(qty) + CGAL_NTS square(qtz);
FT rtx = rx - tx;
FT rty = ry - ty;
FT rtz = rz - tz;
FT rt2 = CGAL_NTS square(rtx) + CGAL_NTS square(rty) + CGAL_NTS square(rtz);
FT pqx = qx - px;
FT pqy = qy - py;
FT pqz = qz - pz;
FT prx = rx - px;
FT pry = ry - py;
FT prz = rz - pz;
FT vx = pqy*prz - pqz*pry;
FT vy = pqz*prx - pqx*prz;
FT vz = pqx*pry - pqy*prx;
FT v2 = CGAL_NTS square(vx) + CGAL_NTS square(vy) + CGAL_NTS square(vz);
return enum_cast<Bounded_side>(sign_of_determinant4x4(ptx,pty,ptz,pt2,
rtx,rty,rtz,rt2,
qtx,qty,qtz,qt2,
vx,vy,vz,v2));
}
template < class FT >
/*CGAL_NO_FILTER*/
CGAL_KERNEL_MEDIUM_INLINE
typename Equal_to<FT>::result_type
collinear_are_ordered_along_lineC3(
const FT &px, const FT &py, const FT &pz,
const FT &qx, const FT &qy, const FT &qz,
const FT &rx, const FT &ry, const FT &rz)
{
if (px < qx) return !(rx < qx);
if (qx < px) return !(qx < rx);
if (py < qy) return !(ry < qy);
if (qy < py) return !(qy < ry);
if (pz < qz) return !(rz < qz);
if (qz < pz) return !(qz < rz);
return true; // p==q
}
template < class FT >
/*CGAL_NO_FILTER*/
CGAL_KERNEL_MEDIUM_INLINE
typename Equal_to<FT>::result_type
collinear_are_strictly_ordered_along_lineC3(
const FT &px, const FT &py, const FT &pz,
const FT &qx, const FT &qy, const FT &qz,
const FT &rx, const FT &ry, const FT &rz)
{
if (px < qx) return (qx < rx);
if (qx < px) return (rx < qx);
if (py < qy) return (qy < ry);
if (qy < py) return (ry < qy);
if (pz < qz) return (qz < rz);
if (qz < pz) return (rz < qz);
return false; // p==q
}
template < class FT >
CGAL_KERNEL_MEDIUM_INLINE
typename Equal_to<FT>::result_type
equal_directionC3(const FT &dx1, const FT &dy1, const FT &dz1,
const FT &dx2, const FT &dy2, const FT &dz2)
{
return sign_of_determinant2x2(dx1, dy1, dx2, dy2) == ZERO
&& sign_of_determinant2x2(dx1, dz1, dx2, dz2) == ZERO
&& sign_of_determinant2x2(dy1, dz1, dy2, dz2) == ZERO
&& CGAL_NTS sign(dx1) == CGAL_NTS sign(dx2)
&& CGAL_NTS sign(dy1) == CGAL_NTS sign(dy2)
&& CGAL_NTS sign(dz1) == CGAL_NTS sign(dz2);
}
template < class FT >
CGAL_KERNEL_MEDIUM_INLINE
typename Equal_to<FT>::result_type
equal_planeC3(const FT &ha, const FT &hb, const FT &hc, const FT &hd,
const FT &pa, const FT &pb, const FT &pc, const FT &pd)
{
typedef typename Sgn<FT>::result_type Sg;
if (!equal_directionC3(ha, hb, hc, pa, pb, pc))
return false; // Not parallel.
Sg s1a = CGAL_NTS sign(ha);
if (s1a != ZERO)
return s1a == CGAL_NTS sign(pa)
&& sign_of_determinant2x2(pa, pd, ha, hd) == ZERO;
Sg s1b = CGAL_NTS sign(hb);
if (s1b != ZERO)
return s1b == CGAL_NTS sign(pb)
&& sign_of_determinant2x2(pb, pd, hb, hd) == ZERO;
return CGAL_NTS sign(pc) == CGAL_NTS sign(hc)
&& sign_of_determinant2x2(pc, pd, hc, hd) == ZERO;
}
template <class FT >
CGAL_KERNEL_LARGE_INLINE
typename Same_uncertainty_nt<Oriented_side, FT>::type
side_of_oriented_planeC3(const FT &a, const FT &b, const FT &c, const FT &d,
const FT &px, const FT &py, const FT &pz)
{
return enum_cast<Oriented_side>(CGAL_NTS sign(a*px + b*py + c*pz +d));
}
template <class FT >
CGAL_KERNEL_LARGE_INLINE
typename Same_uncertainty_nt<Oriented_side, FT>::type
side_of_oriented_sphereC3(const FT &px, const FT &py, const FT &pz,
const FT &qx, const FT &qy, const FT &qz,
const FT &rx, const FT &ry, const FT &rz,
const FT &sx, const FT &sy, const FT &sz,
const FT &tx, const FT &ty, const FT &tz)
{
FT ptx = px - tx;
FT pty = py - ty;
FT ptz = pz - tz;
FT pt2 = CGAL_NTS square(ptx) + CGAL_NTS square(pty) + CGAL_NTS square(ptz);
FT qtx = qx - tx;
FT qty = qy - ty;
FT qtz = qz - tz;
FT qt2 = CGAL_NTS square(qtx) + CGAL_NTS square(qty) + CGAL_NTS square(qtz);
FT rtx = rx - tx;
FT rty = ry - ty;
FT rtz = rz - tz;
FT rt2 = CGAL_NTS square(rtx) + CGAL_NTS square(rty) + CGAL_NTS square(rtz);
FT stx = sx - tx;
FT sty = sy - ty;
FT stz = sz - tz;
FT st2 = CGAL_NTS square(stx) + CGAL_NTS square(sty) + CGAL_NTS square(stz);
return enum_cast<Oriented_side>(sign_of_determinant4x4(ptx,pty,ptz,pt2,
rtx,rty,rtz,rt2,
qtx,qty,qtz,qt2,
stx,sty,stz,st2));
}
template <class FT >
CGAL_KERNEL_MEDIUM_INLINE
typename Same_uncertainty_nt<Bounded_side, FT>::type
side_of_bounded_sphereC3(const FT &px, const FT &py, const FT &pz,
const FT &qx, const FT &qy, const FT &qz,
const FT &rx, const FT &ry, const FT &rz,
const FT &sx, const FT &sy, const FT &sz,
const FT &tx, const FT &ty, const FT &tz)
{
return enum_cast<Bounded_side>( side_of_oriented_sphereC3(px, py, pz,
qx, qy, qz,
rx, ry, rz,
sx, sy, sz,
tx, ty, tz)
* orientationC3(px, py, pz,
qx, qy, qz,
rx, ry, rz,
sx, sy, sz) );
}
template <class FT >
CGAL_KERNEL_MEDIUM_INLINE
typename Same_uncertainty_nt<Bounded_side, FT>::type
side_of_bounded_sphereC3(const FT &px, const FT &py, const FT &pz,
const FT &qx, const FT &qy, const FT &qz,
const FT &tx, const FT &ty, const FT &tz)
{
// Returns whether T lies inside or outside the sphere which diameter is PQ.
return enum_cast<Bounded_side>( CGAL_NTS sign((tx-px)*(qx-tx)
+ (ty-py)*(qy-ty)
+ (tz-pz)*(qz-tz)) );
}
template < class FT >
CGAL_KERNEL_INLINE
typename Compare<FT>::result_type
cmp_dist_to_pointC3(const FT &px, const FT &py, const FT &pz,
const FT &qx, const FT &qy, const FT &qz,
const FT &rx, const FT &ry, const FT &rz)
{
return CGAL_NTS compare(squared_distanceC3(px,py,pz,qx,qy,qz),
squared_distanceC3(px,py,pz,rx,ry,rz));
}
// Because of the way the filtered predicates generator script works,
// cmp_dist_to_pointC3() must be defined _before_ ths following one.
template <class FT >
CGAL_KERNEL_MEDIUM_INLINE
typename Same_uncertainty_nt<Bounded_side, FT>::type
side_of_bounded_sphereC3(const FT &px, const FT &py, const FT &pz,
const FT &qx, const FT &qy, const FT &qz,
const FT &sx, const FT &sy, const FT &sz,
const FT &tx, const FT &ty, const FT &tz)
{
// Returns whether T lies inside or outside the sphere which equatorial
// circle is PQR.
// This code is inspired by the one of circumcenterC3(3 points).
FT psx = px-sx;
FT psy = py-sy;
FT psz = pz-sz;
FT ps2 = CGAL_NTS square(psx) + CGAL_NTS square(psy) + CGAL_NTS square(psz);
FT qsx = qx-sx;
FT qsy = qy-sy;
FT qsz = qz-sz;
FT qs2 = CGAL_NTS square(qsx) + CGAL_NTS square(qsy) + CGAL_NTS square(qsz);
FT rsx = psy*qsz-psz*qsy;
FT rsy = psz*qsx-psx*qsz;
FT rsz = psx*qsy-psy*qsx;
FT tsx = tx-sx;
FT tsy = ty-sy;
FT tsz = tz-sz;
FT num_x = ps2 * det2x2_by_formula(qsy,qsz,rsy,rsz)
- qs2 * det2x2_by_formula(psy,psz,rsy,rsz);
FT num_y = ps2 * det2x2_by_formula(qsx,qsz,rsx,rsz)
- qs2 * det2x2_by_formula(psx,psz,rsx,rsz);
FT num_z = ps2 * det2x2_by_formula(qsx,qsy,rsx,rsy)
- qs2 * det2x2_by_formula(psx,psy,rsx,rsy);
FT den2 = 2 * det3x3_by_formula(psx,psy,psz,
qsx,qsy,qsz,
rsx,rsy,rsz);
// The following could be simplified a bit.
return enum_cast<Bounded_side>(
cmp_dist_to_pointC3<FT>(num_x, - num_y, num_z,
psx*den2, psy*den2, psz*den2,
tsx*den2, tsy*den2, tsz*den2) );
}
template < class FT >
/*CGAL_NO_FILTER*/
CGAL_KERNEL_MEDIUM_INLINE
typename Equal_to<FT>::result_type
has_larger_dist_to_pointC3(const FT &px, const FT &py, const FT &pz,
const FT &qx, const FT &qy, const FT &qz,
const FT &rx, const FT &ry, const FT &rz)
{
return cmp_dist_to_pointC3(px,py,pz,qx,qy,qz,rx,ry,rz) == LARGER;
}
template < class FT >
/*CGAL_NO_FILTER*/
CGAL_KERNEL_MEDIUM_INLINE
typename Equal_to<FT>::result_type
has_smaller_dist_to_pointC3(const FT &px, const FT &py, const FT &pz,
const FT &qx, const FT &qy, const FT &qz,
const FT &rx, const FT &ry, const FT &rz)
{
return cmp_dist_to_pointC3(px,py,pz,qx,qy,qz,rx,ry,rz) == SMALLER;
}
template < class FT >
CGAL_KERNEL_MEDIUM_INLINE
typename Compare<FT>::result_type
cmp_signed_dist_to_directionC3( const FT &pa, const FT &pb, const FT &pc,
const FT &px, const FT &py, const FT &pz,
const FT &qx, const FT &qy, const FT &qz)
{
return CGAL_NTS compare(scaled_distance_to_directionC3(pa,pb,pc,px,py,pz),
scaled_distance_to_directionC3(pa,pb,pc,qx,qy,qz));
}
template < class FT >
/*CGAL_NO_FILTER*/
CGAL_KERNEL_MEDIUM_INLINE
typename Equal_to<FT>::result_type
has_larger_signed_dist_to_directionC3(
const FT &pa, const FT &pb, const FT &pc,
const FT &px, const FT &py, const FT &pz,
const FT &qx, const FT &qy, const FT &qz)
{
return cmp_signed_dist_to_directionC3(pa,pb,pc,px,py,pz,qx,qy,qz) == LARGER;
}
template < class FT >
/*CGAL_NO_FILTER*/
CGAL_KERNEL_MEDIUM_INLINE
typename Equal_to<FT>::result_type
has_smaller_signed_dist_to_directionC3(
const FT &pa, const FT &pb, const FT &pc,
const FT &px, const FT &py, const FT &pz,
const FT &qx, const FT &qy, const FT &qz)
{
return cmp_signed_dist_to_directionC3(pa,pb,pc,px,py,pz,qx,qy,qz) == SMALLER;
}
template < class FT >
CGAL_KERNEL_MEDIUM_INLINE
typename Compare<FT>::result_type
cmp_signed_dist_to_planeC3(
const FT &ppx, const FT &ppy, const FT &ppz,
const FT &pqx, const FT &pqy, const FT &pqz,
const FT &prx, const FT &pry, const FT &prz,
const FT &px, const FT &py, const FT &pz,
const FT &qx, const FT &qy, const FT &qz)
{
return enum_cast<Comparison_result>(sign_of_determinant3x3<FT>(
pqx-ppx, pqy-ppy, pqz-ppz,
prx-ppx, pry-ppy, prz-ppz,
px-qx, py-qy, pz-qz));
}
template < class FT >
/*CGAL_NO_FILTER*/
CGAL_KERNEL_MEDIUM_INLINE
typename Equal_to<FT>::result_type
has_larger_signed_dist_to_planeC3(
const FT &ppx, const FT &ppy, const FT &ppz,
const FT &pqx, const FT &pqy, const FT &pqz,
const FT &prx, const FT &pry, const FT &prz,
const FT &px, const FT &py, const FT &pz,
const FT &qx, const FT &qy, const FT &qz)
{
return cmp_signed_dist_to_planeC3(ppx, ppy, ppz, pqx, pqy, pqz,
prx, pry, prz, px, py, pz, qx, qy, qz) == LARGER;
}
template < class FT >
/*CGAL_NO_FILTER*/
CGAL_KERNEL_MEDIUM_INLINE
typename Equal_to<FT>::result_type
has_smaller_signed_dist_to_planeC3(
const FT &ppx, const FT &ppy, const FT &ppz,
const FT &pqx, const FT &pqy, const FT &pqz,
const FT &prx, const FT &pry, const FT &prz,
const FT &px, const FT &py, const FT &pz,
const FT &qx, const FT &qy, const FT &qz)
{
return cmp_signed_dist_to_planeC3(ppx, ppy, ppz, pqx, pqy, pqz,
prx, pry, prz, px, py, pz, qx, qy, qz) == SMALLER;
}
CGAL_END_NAMESPACE
#ifdef CGAL_ARITHMETIC_FILTER_H
#include <CGAL/Arithmetic_filter/predicates/kernel_ftC3.h>
#endif
#endif // CGAL_PREDICATES_KERNEL_FTC3_H
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