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cgal/Cartesian_kernel/include/CGAL/constructions/kernel_ftC2.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) : Sven Schoenherr, Herve Bronnimann, Sylvain Pion
#ifndef CGAL_CONSTRUCTIONS_KERNEL_FTC2_H
#define CGAL_CONSTRUCTIONS_KERNEL_FTC2_H
#include <CGAL/determinant.h>
CGAL_BEGIN_NAMESPACE
template < class FT >
CGAL_KERNEL_INLINE
void
midpointC2( const FT &px, const FT &py,
const FT &qx, const FT &qy,
FT &x, FT &y )
{
x = (px+qx) / 2;
y = (py+qy) / 2;
}
template < class FT >
CGAL_KERNEL_LARGE_INLINE
void
circumcenter_translateC2(const FT &dqx, const FT &dqy,
const FT &drx, const FT &dry,
FT &dcx, FT &dcy)
{
// Given 3 points P, Q, R, this function takes as input:
// qx-px, qy-py, rx-px, ry-py. And returns cx-px, cy-py,
// where (cx, cy) are the coordinates of the circumcenter C.
// What we do is intersect the bisectors.
FT r2 = CGAL_NTS square(drx) + CGAL_NTS square(dry);
FT q2 = CGAL_NTS square(dqx) + CGAL_NTS square(dqy);
FT den = 2 * det2x2_by_formula(dqx, dqy, drx, dry);
// The 3 points aren't collinear.
// Hopefully, this is already checked at the upper level.
CGAL_kernel_assertion ( ! CGAL_NTS is_zero(den) );
// One possible optimization here is to precompute 1/den, to avoid one
// division. However, we loose precision, and it's maybe not worth it (?).
dcx = det2x2_by_formula (dry, dqy, r2, q2) / den;
dcy = - det2x2_by_formula (drx, dqx, r2, q2) / den;
}
template < class FT >
CGAL_KERNEL_MEDIUM_INLINE
void
circumcenterC2( const FT &px, const FT &py,
const FT &qx, const FT &qy,
const FT &rx, const FT &ry,
FT &x, FT &y )
{
circumcenter_translateC2<FT>(qx-px, qy-py, rx-px, ry-py, x, y);
x += px;
y += py;
}
template < class FT >
CGAL_KERNEL_MEDIUM_INLINE
void
centroidC2( const FT &px, const FT &py,
const FT &qx, const FT &qy,
const FT &rx, const FT &ry,
FT &x, FT &y)
{
x = (px + qx + rx) / 3;
y = (py + qy + ry) / 3;
}
template < class FT >
CGAL_KERNEL_MEDIUM_INLINE
void
centroidC2( const FT &px, const FT &py,
const FT &qx, const FT &qy,
const FT &rx, const FT &ry,
const FT &sx, const FT &sy,
FT &x, FT &y)
{
x = (px + qx + rx + sx) / 4;
y = (py + qy + ry + sy) / 4;
}
template < class FT >
inline
void
line_from_pointsC2(const FT &px, const FT &py,
const FT &qx, const FT &qy,
FT &a, FT &b, FT &c)
{
// The horizontal and vertical line get a special treatment
// in order to make the intersection code robust for doubles
if(py == qy){
a = 0 ;
if(qx > px){
b = 1;
c = -py;
} else if(qx == px){
b = 0;
c = 0;
}else{
b = -1;
c = py;
}
} else if(qx == px){
b = 0;
if(qy > py){
a = -1;
c = px;
} else if (qy == py){
a = 0;
c = 0;
} else {
a = 1;
c = -px;
}
} else {
a = py - qy;
b = qx - px;
c = -px*a - py*b;
}
}
template < class FT >
inline
void
line_from_point_directionC2(const FT &px, const FT &py,
const FT &dx, const FT &dy,
FT &a, FT &b, FT &c)
{
a = - dy;
b = dx;
c = px*dy - py*dx;
}
template < class FT >
CGAL_KERNEL_INLINE
void
bisector_of_pointsC2(const FT &px, const FT &py,
const FT &qx, const FT &qy,
FT &a, FT &b, FT& c )
{
a = 2 * (px - qx);
b = 2 * (py - qy);
c = CGAL_NTS square(qx) + CGAL_NTS square(qy) -
CGAL_NTS square(px) - CGAL_NTS square(py);
}
template < class FT >
CGAL_KERNEL_INLINE
void
bisector_of_linesC2(const FT &pa, const FT &pb, const FT &pc,
const FT &qa, const FT &qb, const FT &qc,
FT &a, FT &b, FT &c)
{
// We normalize the equations of the 2 lines, and we then add them.
FT n1 = CGAL_NTS sqrt(CGAL_NTS square(pa) + CGAL_NTS square(pb));
FT n2 = CGAL_NTS sqrt(CGAL_NTS square(qa) + CGAL_NTS square(qb));
a = n2 * pa + n1 * qa;
b = n2 * pb + n1 * qb;
c = n2 * pc + n1 * qc;
// Care must be taken for the case when this produces a degenerate line.
if (a == 0 && b == 0) {
a = n2 * pa - n1 * qa;
b = n2 * pb - n1 * qb;
c = n2 * pc - n1 * qc;
}
}
template < class FT >
inline
FT
line_y_at_xC2(const FT &a, const FT &b, const FT &c, const FT &x)
{
return (-a*x-c) / b;
}
template < class FT >
inline
void
line_get_pointC2(const FT &a, const FT &b, const FT &c, int i,
FT &x, FT &y)
{
if (CGAL_NTS is_zero(b))
{
x = (-b-c)/a + i * b;
y = 1 - i * a;
}
else
{
x = 1 + i * b;
y = -(a+c)/b - i * a;
}
}
template < class FT >
inline
void
perpendicular_through_pointC2(const FT &la, const FT &lb,
const FT &px, const FT &py,
FT &a, FT &b, FT &c)
{
a = -lb;
b = la;
c = lb * px - la * py;
}
template < class FT >
CGAL_KERNEL_MEDIUM_INLINE
void
line_project_pointC2(const FT &la, const FT &lb, const FT &lc,
const FT &px, const FT &py,
FT &x, FT &y)
{
#if 1 // FIXME
// Original old version
if (CGAL_NTS is_zero(la)) // horizontal line
{
x = px;
y = -lc/lb;
}
else if (CGAL_NTS is_zero(lb)) // vertical line
{
x = -lc/la;
y = py;
}
else
{
FT ab = la/lb, ba = lb/la, ca = lc/la;
y = ( -px + ab*py - ca ) / ( ba + ab );
x = -ba * y - ca;
}
#else
// New version, with more multiplications, but less divisions and tests.
// Let's compare the results of the 2, benchmark them, as well as check
// the precision with the intervals.
FT a2 = CGAL_NTS square(la);
FT b2 = CGAL_NTS square(lb);
FT d = a2 + b2;
x = (la * (lb * py - lc) - px * b2) / d;
y = (lb * (lc - la * px) + py * a2) / d;
#endif
}
template < class FT >
CGAL_KERNEL_MEDIUM_INLINE
FT
squared_radiusC2(const FT &px, const FT &py,
const FT &qx, const FT &qy,
const FT &rx, const FT &ry,
FT &x, FT &y )
{
circumcenter_translateC2(qx-px, qy-py, rx-px, ry-py, x, y);
FT r2 = CGAL_NTS square(x) + CGAL_NTS square(y);
x += px;
y += py;
return r2;
}
template < class FT >
CGAL_KERNEL_MEDIUM_INLINE
FT
squared_radiusC2(const FT &px, const FT &py,
const FT &qx, const FT &qy,
const FT &rx, const FT &ry)
{
FT x, y;
circumcenter_translateC2<FT>(qx-px, qy-py, rx-px, ry-py, x, y);
return CGAL_NTS square(x) + CGAL_NTS square(y);
}
template < class FT >
inline
FT
squared_distanceC2( const FT &px, const FT &py,
const FT &qx, const FT &qy)
{
return CGAL_NTS square(px-qx) + CGAL_NTS square(py-qy);
}
template < class FT >
inline
FT
squared_radiusC2(const FT &px, const FT &py,
const FT &qx, const FT &qy)
{
return squared_distanceC2(px, py,qx, qy) / 4;
}
template < class FT >
CGAL_KERNEL_INLINE
FT
scaled_distance_to_lineC2( const FT &la, const FT &lb, const FT &lc,
const FT &px, const FT &py)
{
// for comparisons, use distance_to_directionsC2 instead
// since lc is irrelevant
return la*px + lb*py + lc;
}
template < class FT >
CGAL_KERNEL_INLINE
FT
scaled_distance_to_directionC2( const FT &la, const FT &lb,
const FT &px, const FT &py)
{
// scalar product with direction
return la*px + lb*py;
}
template < class FT >
CGAL_KERNEL_MEDIUM_INLINE
FT
scaled_distance_to_lineC2( const FT &px, const FT &py,
const FT &qx, const FT &qy,
const FT &rx, const FT &ry)
{
return det2x2_by_formula<FT>(px-rx, py-ry, qx-rx, qy-ry);
}
CGAL_END_NAMESPACE
#endif // CGAL_CONSTRUCTIONS_KERNEL_FTC2_H
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