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cgal/Packages/Cartesian_kernel/include/CGAL/predicates/kernel_ftC2.h

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// ======================================================================
//
// Copyright (c) 2000 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_ftC2.h
// revision : $Revision$
// revision_date : $Date$
// author(s) : Herve Bronnimann (Herve.Bronnimann@sophia.inria.fr)
// coordinator : INRIA Sophia-Antipolis (Mariette.Yvinec@sophia.inria.fr)
//
// ======================================================================
#ifndef CGAL_PREDICATES_KERNEL_FTC2_H
#define CGAL_PREDICATES_KERNEL_FTC2_H
#include <CGAL/number_utils.h>
#include <CGAL/predicates/sign_of_determinant.h>
#include <CGAL/constructions/kernel_ftC2.h>
CGAL_BEGIN_NAMESPACE
template < class FT >
CGAL_KERNEL_MEDIUM_INLINE
bool
equal_lineC2(const FT &l1a, const FT &l1b, const FT &l1c,
const FT &l2a, const FT &l2b, const FT &l2c)
{
if (sign_of_determinant2x2(l1a, l1b, l2a, l2b) != ZERO)
return false; // Not parallel.
CGAL::Sign s1a = CGAL_NTS sign(l1a);
if (s1a != ZERO)
return s1a == CGAL_NTS sign(l2a)
&& sign_of_determinant2x2(l1a, l1c, l2a, l2c) == ZERO;
return CGAL_NTS sign(l1b) == CGAL_NTS sign(l2b)
&& sign_of_determinant2x2(l1b, l1c, l2b, l2c) == ZERO;
}
template < class FT >
CGAL_KERNEL_MEDIUM_INLINE
Comparison_result
compare_xC2(const FT &px,
const FT &la, const FT &lb, const FT &lc,
const FT &ha, const FT &hb, const FT &hc)
{
// The abscissa of the intersection point is num/den.
FT num = det2x2_by_formula( lb, lc, hb, hc);
FT den = det2x2_by_formula( la, lb, ha, hb);
Sign s = CGAL_NTS sign(den);
CGAL_kernel_assertion( s != ZERO );
return Comparison_result( s * CGAL_NTS compare<FT>( px * den, num) );
}
template < class FT >
CGAL_KERNEL_MEDIUM_INLINE
Comparison_result
compare_xC2(const FT &la, const FT &lb, const FT &lc,
const FT &h1a, const FT &h1b, const FT &h1c,
const FT &h2a, const FT &h2b, const FT &h2c)
{
/*
FT num1 = det2x2_by_formula( lb, lc, h1b, h1c);
FT den1 = det2x2_by_formula( la, lb, h1a, h1b);
FT num2 = det2x2_by_formula( lb, lc, h2b, h2c);
FT den2 = det2x2_by_formula( la, lb, h2a, h2b);
Sign s = Sign (CGAL_NTS sign(den1) * CGAL_NTS sign(den2));
CGAL_kernel_assertion( s != ZERO );
return Comparison_result( s * sign_of_determinant2x2(num1,
num2, den1, den2));
*/
FT num1 = det2x2_by_formula( la, lc, h1a, h1c);
FT num2 = det2x2_by_formula( la, lc, h2a, h2c);
FT num = det2x2_by_formula(h1a,h1c,h2a,h2c)*lb
+ det2x2_by_formula(num1,num2,h1b,h2b);
FT den1 = det2x2_by_formula( la, lb, h1a, h1b);
FT den2 = det2x2_by_formula( la, lb, h2a, h2b);
return Comparison_result( CGAL_NTS sign(lb) * CGAL_NTS sign(num) *
CGAL_NTS sign(den1) * CGAL_NTS sign(den2));
}
template < class FT >
CGAL_KERNEL_MEDIUM_INLINE
Comparison_result
compare_xC2(const FT &l1a, const FT &l1b, const FT &l1c,
const FT &h1a, const FT &h1b, const FT &h1c,
const FT &l2a, const FT &l2b, const FT &l2c,
const FT &h2a, const FT &h2b, const FT &h2c)
{
FT num1 = det2x2_by_formula( l1b, l1c, h1b, h1c);
FT den1 = det2x2_by_formula( l1a, l1b, h1a, h1b);
FT num2 = det2x2_by_formula( l2b, l2c, h2b, h2c);
FT den2 = det2x2_by_formula( l2a, l2b, h2a, h2b);
Sign s = Sign (CGAL_NTS sign(den1) * CGAL_NTS sign(den2));
CGAL_kernel_assertion( s != ZERO );
return Comparison_result( s * sign_of_determinant2x2(num1, num2,
den1, den2));
}
template < class FT >
CGAL_KERNEL_MEDIUM_INLINE
Comparison_result
compare_y_at_xC2(const FT &px, const FT &py,
const FT &la, const FT &lb, const FT &lc)
{
Sign s = CGAL_NTS sign(lb);
CGAL_kernel_assertion( s != ZERO );
return Comparison_result (s * CGAL_NTS sign<FT>(la*px + lb*py + lc));
}
template < class FT >
CGAL_KERNEL_MEDIUM_INLINE
Comparison_result
compare_y_at_xC2(const FT &px,
const FT &l1a, const FT &l1b, const FT &l1c,
const FT &l2a, const FT &l2b, const FT &l2c)
{
Sign s = Sign (CGAL_NTS sign(l1b) * CGAL_NTS sign(l2b));
CGAL_kernel_assertion( s != ZERO );
return Comparison_result ( s * sign_of_determinant2x2<FT>(l2a*px+l2c, l2b,
l1a*px+l1c, l1b));
}
template < class FT >
CGAL_KERNEL_LARGE_INLINE
Comparison_result
compare_y_at_xC2(const FT &l1a, const FT &l1b, const FT &l1c,
const FT &l2a, const FT &l2b, const FT &l2c,
const FT &ha, const FT &hb, const FT &hc)
{
Sign s = Sign (sign_of_determinant2x2(l1a, l1b, l2a, l2b) *
CGAL_NTS sign(hb));
CGAL_kernel_assertion( s != ZERO );
return Comparison_result( s * sign_of_determinant3x3(l1a, l1b, l1c,
l2a, l2b, l2c,
ha, hb, hc));
}
template < class FT >
CGAL_KERNEL_LARGE_INLINE
Comparison_result
compare_y_at_xC2(const FT &l1a, const FT &l1b, const FT &l1c,
const FT &l2a, const FT &l2b, const FT &l2c,
const FT &h1a, const FT &h1b, const FT &h1c,
const FT &h2a, const FT &h2b, const FT &h2c)
{
// The abscissa of the intersection point is num/den.
FT num = det2x2_by_formula( l1b, l1c, l2b, l2c);
FT den = det2x2_by_formula( l1a, l1b, l2a, l2b);
Sign s = Sign (CGAL_NTS sign(h1b) * CGAL_NTS sign(h2b) * CGAL_NTS sign(den));
CGAL_kernel_assertion( s != ZERO );
return Comparison_result ( s *
sign_of_determinant2x2<FT>(h2a*num+h2c*den, h2b,
h1a*num+h1c*den, h1b));
}
template < class FT >
/*CGAL_NO_FILTER*/
CGAL_KERNEL_LARGE_INLINE
Comparison_result
compare_y_at_xC2(const FT &px, const FT &py,
const FT &ssx, const FT &ssy,
const FT &stx, const FT &sty)
{
// compares the y-coordinates of p and the vertical projection of p on s.
// Precondition : p is in the x-range of s.
CGAL_kernel_precondition(px >= min(ssx, stx) && px <= max(ssx, stx));
if (ssx < stx)
return (Comparison_result) orientationC2(px, py, ssx, ssy, stx, sty);
else if (ssx > stx)
return (Comparison_result) orientationC2(px, py, stx, sty, ssx, ssy);
else {
if (py < min(sty, ssy))
return SMALLER;
if (py > max(sty, ssy))
return LARGER;
return EQUAL;
}
}
template < class FT >
CGAL_KERNEL_LARGE_INLINE
Comparison_result
compare_y_at_x_segment_C2(const FT &px,
const FT &s1sx, const FT &s1sy,
const FT &s1tx, const FT &s1ty,
const FT &s2sx, const FT &s2sy,
const FT &s2tx, const FT &s2ty)
{
// compares the y-coordinates of the vertical projections of p on s1 and s2
// Precondition : p is in the x-range of s1 and s2.
// - if one or two segments are vertical :
// - if the segments intersect, return EQUAL
// - if not, return the obvious SMALLER/LARGER.
CGAL_kernel_precondition(px >= min(s1sx, s1tx) && px <= max(s1sx, s1tx));
CGAL_kernel_precondition(px >= min(s2sx, s2tx) && px <= max(s2sx, s2tx));
if (s1sx != s1tx && s2sx != s2tx) {
FT s1stx = s1sx-s1tx;
FT s2stx = s2sx-s2tx;
return Comparison_result(
CGAL_NTS compare(s1sx, s1tx) *
CGAL_NTS compare(s2sx, s2tx) *
CGAL_NTS compare<FT>(-(s1sx-px)*(s1sy-s1ty)*s2stx,
(s2sy-s1sy)*s2stx*s1stx
-(s2sx-px)*(s2sy-s2ty)*s1stx ));
}
else {
if (s1sx == s1tx) { // s1 is vertical
Comparison_result c1, c2;
c1 = compare_y_at_xC2(px, s1sy, s2sx, s2sy, s2tx, s2ty);
c2 = compare_y_at_xC2(px, s1ty, s2sx, s2sy, s2tx, s2ty);
if (c1 == c2)
return c1;
return EQUAL;
}
// s2 is vertical
Comparison_result c3, c4;
c3 = compare_y_at_xC2(px, s2sy, s1sx, s1sy, s1tx, s1ty);
c4 = compare_y_at_xC2(px, s2ty, s1sx, s1sy, s1tx, s1ty);
if (c3 == c4)
return opposite(c3);
return EQUAL;
}
}
template < class FT >
CGAL_KERNEL_MEDIUM_INLINE
bool
equal_directionC2(const FT &dx1, const FT &dy1,
const FT &dx2, const FT &dy2)
{
return CGAL_NTS sign(dx1) == CGAL_NTS sign(dx2)
&& CGAL_NTS sign(dy1) == CGAL_NTS sign(dy2)
&& sign_of_determinant2x2(dx1, dy1, dx2, dy2) == ZERO;
}
template < class FT >
/*CGAL_NO_FILTER*/
CGAL_KERNEL_MEDIUM_INLINE
Comparison_result
compare_angle_with_x_axisC2(const FT &dx1, const FT &dy1,
const FT &dx2, const FT &dy2)
{
// angles are in [-pi,pi], and the angle between Ox and d1 is compared
// with the angle between Ox and d2
int quadrant_1 = (dx1 >= FT(0)) ? ((dy1 >= FT(0))?1:4)
: ((dy1 >= FT(0))?2:3);
int quadrant_2 = (dx2 >= FT(0)) ? ((dy2 >= FT(0))?1:4)
: ((dy2 >= FT(0))?2:3);
// We can't use CGAL_NTS compare(quadrant_1,quadrant_2) because in case
// of tie, we need additional computation
if (quadrant_1 > quadrant_2)
return LARGER;
else if (quadrant_1 < quadrant_2)
return SMALLER;
return Comparison_result(-sign_of_determinant2x2(dx1,dy1,dx2,dy2));
}
template < class FT >
CGAL_KERNEL_MEDIUM_INLINE
Comparison_result
compare_slopesC2(const FT &l1a, const FT &l1b, const FT &l2a, const FT &l2b)
{
if (l1a == FT(0)) // l1 is horizontal
return l2b == FT(0) ? SMALLER
: Comparison_result(CGAL_NTS sign<FT>(l2a*l2b));
if (l2a == FT(0)) // l2 is horizontal
return l1b == FT(0) ? LARGER
: Comparison_result(-CGAL_NTS sign<FT>(l1a*l1b));
if (l1b == FT(0)) return l2b == FT(0) ? EQUAL : LARGER;
if (l2b == FT(0)) return SMALLER;
int l1_sign = CGAL_NTS sign<FT>(-l1a * l1b);
int l2_sign = CGAL_NTS sign<FT>(-l2a * l2b);
if (l1_sign < l2_sign) return SMALLER;
if (l1_sign > l2_sign) return LARGER;
if (l1_sign > 0)
return CGAL_NTS compare ( CGAL_NTS abs<FT>(l1a * l2b),
CGAL_NTS abs<FT>(l2a * l1b) );
return CGAL_NTS compare ( CGAL_NTS abs<FT>(l2a * l1b),
CGAL_NTS abs<FT>(l1a * l2b) );
}
template < class FT >
CGAL_KERNEL_MEDIUM_INLINE
Comparison_result
compare_slopesC2(const FT &s1_src_x, const FT &s1_src_y, const FT &s1_tgt_x,
const FT &s1_tgt_y, const FT &s2_src_x, const FT &s2_src_y,
const FT &s2_tgt_x, const FT &s2_tgt_y)
{
Comparison_result cmp_y1 = CGAL_NTS compare(s1_src_y, s1_tgt_y);
if (cmp_y1 == EQUAL) // horizontal
{
Comparison_result cmp_x2 = CGAL_NTS compare(s2_src_x, s2_tgt_x);
if (cmp_x2 == EQUAL) return SMALLER;
return Comparison_result (- CGAL_NTS sign<FT>((s2_src_y - s2_tgt_y) *
(s2_src_x - s2_tgt_x)) );
}
Comparison_result cmp_y2 = CGAL_NTS compare(s2_src_y, s2_tgt_y);
if (cmp_y2 == EQUAL)
{
Comparison_result cmp_x1 = CGAL_NTS compare(s1_src_x, s1_tgt_x);
if (cmp_x1 == EQUAL) return LARGER;
return Comparison_result ( CGAL_NTS sign<FT>((s1_src_y - s1_tgt_y) *
(s1_src_x - s1_tgt_x)) );
}
Comparison_result cmp_x1 = CGAL_NTS compare(s1_src_x, s1_tgt_x);
Comparison_result cmp_x2 = CGAL_NTS compare(s2_src_x, s2_tgt_x);
if (cmp_x1 == EQUAL) return cmp_x2 == EQUAL ? EQUAL : LARGER;
if (cmp_x2 == EQUAL) return SMALLER;
FT s1_xdiff = s1_src_x - s1_tgt_x;
FT s1_ydiff = s1_src_y - s1_tgt_y;
FT s2_xdiff = s2_src_x - s2_tgt_x;
FT s2_ydiff = s2_src_y - s2_tgt_y;
Sign s1_sign = CGAL_NTS sign<FT>(s1_ydiff * s1_xdiff);
Sign s2_sign = CGAL_NTS sign<FT>(s2_ydiff * s2_xdiff);
if (s1_sign < s2_sign) return SMALLER;
if (s1_sign > s2_sign) return LARGER;
if (s1_sign > 0)
return CGAL_NTS compare( CGAL_NTS abs<FT>(s1_ydiff * s2_xdiff),
CGAL_NTS abs<FT>(s2_ydiff * s1_xdiff));
return CGAL_NTS compare( CGAL_NTS abs<FT>(s2_ydiff * s1_xdiff),
CGAL_NTS abs<FT>(s1_ydiff * s2_xdiff));
}
template < class FT >
inline
Comparison_result
compare_deltax_deltayC2(const FT &px, const FT &qx,
const FT &ry, const FT &sy)
{
return CGAL_NTS compare(CGAL_NTS abs(px-qx), CGAL_NTS abs(ry-sy));
}
template < class FT >
/*CGAL_NO_FILTER*/
inline
Comparison_result
compare_lexicographically_xyC2(const FT &px, const FT &py,
const FT &qx, const FT &qy)
{
Comparison_result c = CGAL_NTS compare(px,qx);
return (c != EQUAL) ? c : CGAL_NTS compare(py,qy);
}
template < class FT >
inline
Orientation
orientationC2(const FT &px, const FT &py,
const FT &qx, const FT &qy,
const FT &rx, const FT &ry)
{
return Orientation (sign_of_determinant2x2(qx-px, qy-py,
rx-px, ry-py));
}
template < class FT >
inline
Angle
angleC2(const FT &px, const FT &py,
const FT &qx, const FT &qy,
const FT &rx, const FT &ry)
{
return (Angle) CGAL_NTS sign<FT> ((px-qx)*(rx-qx)+(py-qy)*(ry-qy));
}
template < class FT >
/*CGAL_NO_FILTER*/
CGAL_KERNEL_MEDIUM_INLINE
bool
collinear_are_ordered_along_lineC2(const FT &px, const FT &py,
const FT &qx, const FT &qy,
const FT &rx, const FT &ry)
{
if (px < qx) return !(rx < qx);
if (qx < px) return !(qx < rx);
if (py < qy) return !(ry < qy);
if (qy < py) return !(qy < ry);
return true; // p==q
}
template < class FT >
/*CGAL_NO_FILTER*/
CGAL_KERNEL_MEDIUM_INLINE
bool
collinear_are_strictly_ordered_along_lineC2(const FT &px, const FT &py,
const FT &qx, const FT &qy,
const FT &rx, const FT &ry)
{
if (px < qx) return (qx < rx);
if (qx < px) return (rx < qx);
if (py < qy) return (qy < ry);
if (qy < py) return (ry < qy);
return false;
}
template < class FT >
CGAL_KERNEL_LARGE_INLINE
Oriented_side
side_of_oriented_circleC2(const FT &px, const FT &py,
const FT &qx, const FT &qy,
const FT &rx, const FT &ry,
const FT &tx, const FT &ty)
{
// Oriented_side(
// sign_of_determinant4x4(px, py, px*px + py*py, 1,
// qx, qy, qx*qx + qy*qy, 1,
// rx, ry, rx*rx + ry*ry, 1,
// tx, ty, tx*tx + ty*ty, 1));
// We first translate so that p is the new origin.
FT qpx = qx-px;
FT qpy = qy-py;
FT rpx = rx-px;
FT rpy = ry-py;
FT tpx = tx-px;
FT tpy = ty-py;
// The usual 3x3 formula can be simplified a little bit to a 2x2.
// - sign_of_determinant3x3(qpx, qpy, square(qpx) + square(qpy),
// rpx, rpy, square(rpx) + square(rpy),
// tpx, tpy, square(tpx) + square(tpy)));
return Oriented_side(sign_of_determinant2x2<FT>(
qpx*tpy - qpy*tpx, tpx*(tx-qx) + tpy*(ty-qy),
qpx*rpy - qpy*rpx, rpx*(rx-qx) + rpy*(ry-qy)));
}
template < class FT >
CGAL_KERNEL_LARGE_INLINE
Bounded_side
side_of_bounded_circleC2(const FT &px, const FT &py,
const FT &qx, const FT &qy,
const FT &rx, const FT &ry,
const FT &tx, const FT &ty)
{
return Bounded_side( side_of_oriented_circleC2(px,py,qx,qy,rx,ry,tx,ty)
* orientationC2(px,py,qx,qy,rx,ry) );
}
template < class FT >
CGAL_KERNEL_LARGE_INLINE
Bounded_side
side_of_bounded_circleC2(const FT &px, const FT &py,
const FT &qx, const FT &qy,
const FT &tx, const FT &ty)
{
// Returns whether T lies inside or outside the circle which diameter is PQ.
return Bounded_side( CGAL_NTS compare((tx-px)*(qx-tx), (ty-py)*(ty-qy)) );
}
template < class FT >
inline
Comparison_result
cmp_dist_to_pointC2(const FT &px, const FT &py,
const FT &qx, const FT &qy,
const FT &rx, const FT &ry)
{
return CGAL_NTS compare(squared_distanceC2(px,py,qx,qy),
squared_distanceC2(px,py,rx,ry));
}
template < class FT >
/*CGAL_NO_FILTER*/
inline
bool
has_larger_dist_to_pointC2(const FT &px, const FT &py,
const FT &qx, const FT &qy,
const FT &rx, const FT &ry)
{
return cmp_dist_to_pointC2(px,py,qx,qy,rx,ry) == LARGER;
}
template < class FT >
/*CGAL_NO_FILTER*/
inline
bool
has_smaller_dist_to_pointC2(const FT &px, const FT &py,
const FT &qx, const FT &qy,
const FT &rx, const FT &ry)
{
return cmp_dist_to_pointC2(px,py,qx,qy,rx,ry) == SMALLER;
}
template < class FT >
inline
Comparison_result
cmp_signed_dist_to_directionC2(const FT &la, const FT &lb,
const FT &px, const FT &py,
const FT &qx, const FT &qy)
{
return CGAL_NTS compare(scaled_distance_to_directionC2(la,lb,px,py),
scaled_distance_to_directionC2(la,lb,qx,qy));
}
template < class FT >
/*CGAL_NO_FILTER*/
inline
bool
has_larger_signed_dist_to_directionC2(const FT &la, const FT &lb,
const FT &px, const FT &py,
const FT &qx, const FT &qy)
{
return cmp_signed_dist_to_directionC2(la,lb,px,py,qx,qy) == LARGER;
}
template < class FT >
/*CGAL_NO_FILTER*/
inline
bool
has_smaller_signed_dist_to_directionC2(const FT &la, const FT &lb,
const FT &px, const FT &py,
const FT &qx, const FT &qy)
{
return cmp_signed_dist_to_directionC2(la,lb,px,py,qx,qy) == SMALLER;
}
template <class FT>
inline
Comparison_result
cmp_signed_dist_to_lineC2(const FT &px, const FT &py,
const FT &qx, const FT &qy,
const FT &rx, const FT &ry,
const FT &sx, const FT &sy)
{
return CGAL_NTS compare(scaled_distance_to_lineC2(px,py,qx,qy,rx,ry),
scaled_distance_to_lineC2(px,py,qx,qy,sx,sy));
}
template <class FT>
/*CGAL_NO_FILTER*/
inline
bool
has_larger_signed_dist_to_lineC2(const FT &px, const FT &py,
const FT &qx, const FT &qy,
const FT &rx, const FT &ry,
const FT &sx, const FT &sy)
{
return cmp_signed_dist_to_lineC2(px,py,qx,qy,rx,ry,sx,sy) == LARGER;
}
template <class FT>
/*CGAL_NO_FILTER*/
inline
bool
has_smaller_signed_dist_to_lineC2(const FT &px, const FT &py,
const FT &qx, const FT &qy,
const FT &rx, const FT &ry,
const FT &sx, const FT &sy)
{
return cmp_signed_dist_to_lineC2(px,py,qx,qy,rx,ry,sx,sy) == SMALLER;
}
template <class FT>
inline
Oriented_side
side_of_oriented_lineC2(const FT &a, const FT &b, const FT &c,
const FT &x, const FT &y)
{
return Oriented_side(CGAL_NTS sign<FT>(a*x+b*y+c));
}
CGAL_END_NAMESPACE
#ifdef CGAL_ARITHMETIC_FILTER_H
#include <CGAL/Arithmetic_filter/predicates/kernel_ftC2.h>
#endif
#endif // CGAL_PREDICATES_KERNEL_FTC2_H
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