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cgal/Old_Packages/C3/include/CGAL/predicates/kernel_ftC3.h

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// ==========================================================================
//
// Copyright (c) 1998 The CGAL Consortium
//
// This software and related documentation is part of an INTERNAL release
// of the Computational Geometry Algorithms Library (CGAL). It is not
// intended for general use.
//
// --------------------------------------------------------------------------
//
// release :
// release_date :
//
// file : include/CGAL/predicates/kernel_ftC3.h
// source : include/CGAL/predicates/kernel_ftC3.h
// revision : $Revision$
// revision_date : $Date$
// author(s) : Herve.Bronnimann@sophia.inria.fr
//
// coordinator : INRIA Sophia-Antipolis (Herve.Bronnimann@sophia.inria.fr)
//
// ==========================================================================
#ifndef CGAL_PREDICATES_KERNEL_FTC3_H
#define CGAL_PREDICATES_KERNEL_FTC3_H
#ifndef CGAL_DETERMINANT_H
#include <CGAL/determinant.h>
#endif // CGAL_DETERMINANT_H
#ifndef CGAL_PREDICATES_KERNEL_FTC2_H
#include <CGAL/predicates/kernel_ftC2.h>
#endif // CGAL_PREDICATES_KERNEL_FTC2_H
#ifndef CGAL_CONSTRUCTIONS_KERNEL_FTC3_H
#include <CGAL/constructions/kernel_ftC3.h>
#endif // CGAL_CONSTRUCTIONS_KERNEL_FTC3_H
CGAL_BEGIN_NAMESPACE
template < class FT >
CGAL_KERNEL_MEDIUM_INLINE
Comparison_result
compare_lexicographically_xyzC3(const FT &x1, const FT &y1, const FT &z1,
const FT &x2, const FT &y2, const FT &z2)
{
if (x1 < x2) return SMALLER;
if (x2 < x1) return LARGER;
if (y1 < y2) return SMALLER;
if (y2 < y1) return LARGER;
if (z1 < z2) return SMALLER;
if (z2 < z1) return LARGER;
return EQUAL;
}
template < class FT >
CGAL_KERNEL_MEDIUM_INLINE
bool
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 dpy = py-ry;
FT dpz = pz-rz;
FT dqx = qx-rx;
FT dqy = qy-ry;
FT dqz = qz-rz;
return (sign_of_determinant2x2(dpx,dqx,dpy,dqy) == ZERO)
&& (sign_of_determinant2x2(dpx,dqx,dpz,dqz) == ZERO)
&& (sign_of_determinant2x2(dpy,dqy,dpz,dqz) == ZERO);
}
template < class FT >
CGAL_KERNEL_MEDIUM_INLINE
Orientation
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 Orientation(sign_of_determinant3x3(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
Orientation
coplanar_orientationC3(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 &px, const FT &py, const FT &pz)
{
Orientation oxy_qrs = orientationC2(qx,qy,rx,ry,sx,sy);
if (oxy_qrs != COLLINEAR)
return Orientation( oxy_qrs * orientationC2(qx,qy,rx,ry,px,py));
Orientation oyz_qrs = orientationC2(qy,qz,ry,rz,sy,sz);
if (oyz_qrs != COLLINEAR)
return Orientation( oyz_qrs * orientationC2(qy,qz,ry,rz,py,pz));
Orientation oxz_qrs = orientationC2(qx,qz,rx,rz,sx,sz);
assert(oxz_qrs != COLLINEAR);
return Orientation( oxz_qrs * orientationC2(qx,qz,rx,rz,px,pz));
}
template < class FT >
CGAL_KERNEL_MEDIUM_INLINE
bool
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)
{
CGAL_kernel_exactness_precondition( collinear(p, q, r) );
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_KERNEL_MEDIUM_INLINE
bool
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)
{
CGAL_kernel_exactness_precondition( collinear(p, q, r) );
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
bool
equal_directionC3(const FT &dx1, const FT &dy1, const FT &dz1,
const FT &dx2, const FT &dy2, const FT &dz2)
{
return ( dx1*dy2 == dy1*dx2 )
&&( dx1*dz2 == dz1*dx2 )
&&( dy1*dz2 == dz1*dy2 )
&&( CGAL::sign(dx1) == CGAL::sign(dx2) )
&&( CGAL::sign(dy1) == CGAL::sign(dy2) )
&&( CGAL::sign(dz1) == CGAL::sign(dz2) );
}
template <class FT >
CGAL_KERNEL_LARGE_INLINE
Oriented_side
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 Oriented_side(CGAL::sign(a*px + b*py + c*pz +d));
}
template <class FT >
CGAL_KERNEL_LARGE_INLINE
Oriented_side
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 = square(ptx) + square(pty) + square(ptz);
FT qtx = qx - tx;
FT qty = qy - ty;
FT qtz = qz - tz;
FT qt2 = square(qtx) + square(qty) + square(qtz);
FT rtx = rx - tx;
FT rty = ry - ty;
FT rtz = rz - tz;
FT rt2 = square(rtx) + square(rty) + square(rtz);
FT stx = sx - tx;
FT sty = sy - ty;
FT stz = sz - tz;
FT st2 = square(stx) + square(sty) + square(stz);
return 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
Bounded_side
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)
{
Oriented_side s = side_of_oriented_sphereC3(px, py, pz,
qx, qy, qz,
rx, ry, rz,
sx, sy, sz,
tx, ty, tz);
Orientation o = orientationC3(px, py, pz,
qx, qy, qz,
rx, ry, rz,
sx, sy, sz);
return Bounded_side(s * o);
}
template < class FT >
CGAL_KERNEL_INLINE
Comparison_result
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::compare(squared_distanceC3(px,py,pz,qx,qy,qz),
squared_distanceC3(px,py,pz,rx,ry,rz));
}
template < class FT >
CGAL_KERNEL_MEDIUM_INLINE
bool
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 squared_distanceC3(px,py,pz,rx,ry,rz)
< squared_distanceC3(px,py,pz,qx,qy,qz);
}
template < class FT >
CGAL_KERNEL_MEDIUM_INLINE
bool
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 squared_distanceC3(px,py,pz,qx,qy,qz)
< squared_distanceC3(px,py,pz,rx,ry,rz);
}
template < class FT >
CGAL_KERNEL_MEDIUM_INLINE
Comparison_result
cmp_signed_dist_to_planeC3(
const FT &pa, const FT &pb, const FT &pc, const FT &pd,
const FT &px, const FT &py, const FT &pz,
const FT &qx, const FT &qy, const FT &qz)
{
return CGAL::compare(scaled_distance_to_planeC3(pa,pb,pc,pd,px,py,pz),
scaled_distance_to_planeC3(pa,pb,pc,pd,qx,qy,qz));
}
template < class FT >
CGAL_KERNEL_MEDIUM_INLINE
bool
has_larger_signed_dist_to_planeC3(
const FT &pa, const FT &pb, const FT &pc, const FT &pd,
const FT &px, const FT &py, const FT &pz,
const FT &qx, const FT &qy, const FT &qz)
{
return scaled_distance_to_planeC3(pa,pb,pc,pd,qx,qy,qz)
< scaled_distance_to_planeC3(pa,pb,pc,pd,px,py,pz);
}
template < class FT >
CGAL_KERNEL_MEDIUM_INLINE
bool
has_smaller_signed_dist_to_planeC3(
const FT &pa, const FT &pb, const FT &pc, const FT &pd,
const FT &px, const FT &py, const FT &pz,
const FT &qx, const FT &qy, const FT &qz)
{
return scaled_distance_to_planeC3(pa,pb,pc,pd,px,py,pz)
< scaled_distance_to_planeC3(pa,pb,pc,pd,qx,qy,qz);
}
template < class FT >
CGAL_KERNEL_MEDIUM_INLINE
Comparison_result
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 CGAL::compare(
scaled_distance_to_planeC3(ppx,ppy,ppz,pqx,pqy,pqz,
prx,pry,prz,psx,psy,psz,
px,py,pz),
scaled_distance_to_planeC3(ppx,ppy,ppz,pqx,pqy,pqz,
prx,pry,prz,psx,psy,psz,
qx,qy,qz) );
}
template < class FT >
CGAL_KERNEL_MEDIUM_INLINE
bool
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 scaled_distance_to_planeC3(ppx,ppy,ppz,pqx,pqy,pqz,
prx,pry,prz,psx,psy,psz,
qx,qy,qz)
< scaled_distance_to_planeC3(ppx,ppy,ppz,pqx,pqy,pqz,
prx,pry,prz,psx,psy,psz,
px,py,pz);
}
template < class FT >
CGAL_KERNEL_MEDIUM_INLINE
bool
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 scaled_distance_to_planeC3(ppx,ppy,ppz,pqx,pqy,pqz,
prx,pry,prz,psx,psy,psz,
px,py,pz)
< scaled_distance_to_planeC3(ppx,ppy,ppz,pqx,pqy,pqz,
prx,pry,prz,psx,psy,psz,
qx,qy,qz);
}
CGAL_END_NAMESPACE
#ifdef CGAL_ARITHMETIC_FILTER_H
#ifndef CGAL_ARITHMETIC_FILTER_PREDICATES_ON_FTC3_H
#include <CGAL/Arithmetic_filter/predicates_on_ftC3.h>
#endif // CGAL_ARITHMETIC_FILTER_PREDICATES_ON_FTC3_H
#endif
#endif // CGAL_PREDICATES_KERNEL_FTC3_H
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