mirror of https://github.com/CGAL/cgal
314 lines
6.5 KiB
C++
314 lines
6.5 KiB
C++
// Copyright (c) 2003,2004 INRIA Sophia-Antipolis (France).
|
|
// All rights reserved.
|
|
//
|
|
// This file is part of CGAL (www.cgal.org); you may redistribute it under
|
|
// the terms of the Q Public License version 1.0.
|
|
// See the file LICENSE.QPL 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.
|
|
//
|
|
// $URL$
|
|
// $Id$
|
|
//
|
|
//
|
|
// Author(s) : Menelaos Karavelas <mkaravel@cse.nd.edu>
|
|
|
|
|
|
|
|
#ifndef CGAL_PARABOLA_2_H
|
|
#define CGAL_PARABOLA_2_H
|
|
|
|
#include <CGAL/determinant.h>
|
|
|
|
|
|
CGAL_BEGIN_NAMESPACE
|
|
|
|
|
|
template < class Gt >
|
|
class Parabola_2
|
|
{
|
|
public:
|
|
typedef typename Gt::Site_2 Site_2;
|
|
typedef typename Gt::Point_2 Point_2;
|
|
typedef typename Gt::Segment_2 Segment_2;
|
|
typedef typename Gt::Line_2 Line_2;
|
|
typedef typename Gt::FT FT;
|
|
// typedef CGAL::Point_2< Cartesian<double> > Point_2;
|
|
// typedef CGAL::Segment_2< Cartesian<double> > Segment_2;
|
|
// typedef CGAL::Line_2< Cartesian<double> > Line_2;
|
|
|
|
protected:
|
|
// static stuff
|
|
#if defined(__POWERPC__) && \
|
|
defined(__GNUC__) && (__GNUC__ == 3) && (__GNUC_MINOR__ == 4)
|
|
// hack to avoid nasty warning for G++ 3.4 on Darwin
|
|
static FT STEP()
|
|
{
|
|
return FT(2);
|
|
}
|
|
#else
|
|
static const FT& STEP()
|
|
{
|
|
static FT step_(2);
|
|
return step_;
|
|
}
|
|
#endif
|
|
|
|
inline static
|
|
FT square(const FT &x)
|
|
{
|
|
return x * x;
|
|
}
|
|
|
|
inline static
|
|
FT norm2(const Point_2& p)
|
|
{
|
|
return square(p.x()) + square(p.y());
|
|
}
|
|
|
|
inline static
|
|
FT distance2(const Point_2& p1, const Point_2& p2)
|
|
{
|
|
FT dx = p1.x()-p2.x();
|
|
FT dy = p1.y()-p2.y();
|
|
return square(dx) + square(dy);
|
|
}
|
|
|
|
inline static
|
|
FT distance(const Point_2& p1, const Point_2& p2)
|
|
{
|
|
return CGAL::sqrt( distance2(p1, p2) );
|
|
}
|
|
|
|
inline static
|
|
FT distance(const Point_2& p, const Line_2& l)
|
|
{
|
|
return ( p.x() * l.a() + p.y() * l.b() + l.c() ) /
|
|
CGAL::sqrt( square(l.a()) + square(l.b()) );
|
|
}
|
|
|
|
// instance stuff
|
|
Point_2 c;
|
|
Line_2 l;
|
|
Point_2 o;
|
|
|
|
inline
|
|
Point_2 lchain(const FT &t) const
|
|
{
|
|
std::vector< Point_2 > p = compute_points(t);
|
|
if ( right(p[0]) ) return p[1];
|
|
return p[0];
|
|
}
|
|
|
|
inline
|
|
Point_2 rchain(const FT &t) const
|
|
{
|
|
std::vector< Point_2 > p = compute_points(t);
|
|
if ( right(p[0]) ) return p[0];
|
|
return p[1];
|
|
}
|
|
|
|
std::vector< Point_2 > compute_points(const FT &d) const
|
|
{
|
|
assert(d >= 0);
|
|
FT d1 = distance(o, c) + d;
|
|
FT d2 = distance(o, l) + d;
|
|
d2 = d1;
|
|
d1 *= d1;
|
|
|
|
std::vector< Point_2 > p;
|
|
|
|
if ( l.a() == ZERO ) {
|
|
FT y = d2 * CGAL::sign(l.b()) - l.c() / l.b();
|
|
|
|
FT C = CGAL::square(y) - FT(2) * c.y() * y +
|
|
square(c.x()) + square(c.y()) - d1;
|
|
|
|
FT D = square(c.x()) - C;
|
|
|
|
D = CGAL::abs(D);
|
|
|
|
FT x1 = CGAL::sqrt(D) + c.x();
|
|
FT x2 = -CGAL::sqrt(D) + c.x();
|
|
|
|
p.push_back(Point_2(x1, y));
|
|
p.push_back(Point_2(x2, y));
|
|
|
|
return p;
|
|
}
|
|
|
|
FT A = d2 * CGAL::sqrt( CGAL::square(l.a()) +
|
|
CGAL::square(l.b()) ) - l.c();
|
|
FT B = CGAL::square(c.x()) + CGAL::square(c.y()) - d1;
|
|
|
|
FT alpha = FT(1) + CGAL::square(l.b() / l.a());
|
|
FT beta = A * l.b() / CGAL::square(l.a()) + c.y()
|
|
- c.x() * l.b() / l.a();
|
|
FT gamma = CGAL::square(A / l.a()) + B
|
|
- FT(2) * c.x() * A / l.a();
|
|
|
|
FT D = CGAL::square(beta) - alpha * gamma;
|
|
|
|
D = CGAL::abs(D);
|
|
|
|
FT y1 = (beta + CGAL::sqrt(D)) / alpha;
|
|
FT y2 = (beta - CGAL::sqrt(D)) / alpha;
|
|
|
|
FT x1 = (A - l.b() * y1) / l.a();
|
|
FT x2 = (A - l.b() * y2) / l.a();
|
|
|
|
p.push_back(Point_2(x1, y1));
|
|
p.push_back(Point_2(x2, y2));
|
|
|
|
return p;
|
|
}
|
|
|
|
bool right(const Point_2& p) const
|
|
{
|
|
return
|
|
CGAL::is_positive( det3x3_by_formula<FT>(c.x(), c.y(), FT(1),
|
|
o.x(), o.y(), FT(1),
|
|
p.x(), p.y(), FT(1)) );
|
|
}
|
|
|
|
inline
|
|
Point_2 midpoint(const Point_2& p1, const Point_2& p2) const
|
|
{
|
|
FT t1 = t(p1);
|
|
FT t2 = t(p2);
|
|
FT midt = (t1+t2)/2;
|
|
return f(midt);
|
|
}
|
|
|
|
inline
|
|
Point_2 f(FT t) const
|
|
{
|
|
if ( CGAL::is_negative(t) ) return rchain(-t);
|
|
return lchain(t);
|
|
}
|
|
|
|
inline
|
|
FT t(const Point_2 &p) const
|
|
{
|
|
FT tt = distance(p, c) - distance(c, o);
|
|
if ( right(p) ) return -tt;
|
|
return tt;
|
|
}
|
|
|
|
void compute_origin()
|
|
{
|
|
FT d = (l.a() * c.x() + l.b() * c.y() + l.c())
|
|
/ ( FT(2) * ( square(l.a()) + square(l.b()) ) );
|
|
o = Point_2(c.x() - l.a() * d, c.y() - l.b() * d);
|
|
}
|
|
|
|
public:
|
|
Parabola_2() {}
|
|
|
|
template<class ApolloniusSite>
|
|
Parabola_2(const ApolloniusSite &p, const Line_2 &l1)
|
|
{
|
|
this->c = p.point();
|
|
|
|
FT d_a = CGAL::to_double(l1.a());
|
|
FT d_b = CGAL::to_double(l1.b());
|
|
FT len = CGAL::sqrt(CGAL::square(d_a) + CGAL::square(d_b));
|
|
|
|
FT r = p.weight() * len;
|
|
|
|
this->l = Line_2(-l1.a(), -l1.b(), -l1.c() + r);
|
|
compute_origin();
|
|
}
|
|
|
|
Parabola_2(const Point_2 &p, const Line_2 &line)
|
|
{
|
|
this->c = p;
|
|
|
|
if ( line.has_on_positive_side(p) ) {
|
|
this->l = line;
|
|
} else {
|
|
this->l = line.opposite();
|
|
}
|
|
compute_origin();
|
|
}
|
|
|
|
|
|
Oriented_side
|
|
side_of_parabola(const Point_2& p) const
|
|
{
|
|
Point_2 q(CGAL::to_double(p.x()), CGAL::to_double(p.y()));
|
|
|
|
FT d = distance(q, c) - fabs(distance(q, l));
|
|
if ( d < 0 ) return ON_NEGATIVE_SIDE;
|
|
if ( d > 0 ) return ON_POSITIVE_SIDE;
|
|
return ON_ORIENTED_BOUNDARY;
|
|
}
|
|
|
|
|
|
inline Line_2 line() const
|
|
{
|
|
return l;
|
|
}
|
|
|
|
inline Point_2 center() const
|
|
{
|
|
return c;
|
|
}
|
|
|
|
template< class Stream >
|
|
void draw(Stream& W) const
|
|
{
|
|
std::vector< Point_2 > p;
|
|
std::vector< Point_2 > pleft, pright;
|
|
|
|
pleft.push_back(o);
|
|
pright.push_back(o);
|
|
|
|
for (int i = 1; i <= 100; i++) {
|
|
p = compute_points(i * i * STEP());
|
|
|
|
W << p[0];
|
|
W << p[1];
|
|
|
|
if ( p.size() > 0 ) {
|
|
if ( right(p[0]) ) {
|
|
pright.push_back(p[0]);
|
|
pleft.push_back(p[1]);
|
|
} else {
|
|
pright.push_back(p[1]);
|
|
pleft.push_back(p[0]);
|
|
}
|
|
}
|
|
}
|
|
|
|
for (unsigned int i = 0; i < pleft.size() - 1; i++) {
|
|
W << Segment_2(pleft[i], pleft[i+1]);
|
|
}
|
|
|
|
for (unsigned int i = 0; i < pright.size() - 1; i++) {
|
|
W << Segment_2(pright[i], pright[i+1]);
|
|
}
|
|
|
|
W << o;
|
|
}
|
|
};
|
|
|
|
template< class Stream, class Gt >
|
|
inline
|
|
Stream& operator<<(Stream& s, const Parabola_2<Gt> &P)
|
|
{
|
|
P.draw(s);
|
|
return s;
|
|
}
|
|
|
|
|
|
|
|
|
|
CGAL_END_NAMESPACE
|
|
|
|
#endif // CGAL_PARABOLA_2_H
|