135 lines
3.2 KiB
C
135 lines
3.2 KiB
C
|
// Copyright (c) 2016-2018 INRIA Sophia Antipolis, INRIA Nancy (France).
|
||
|
|
// All rights reserved.
|
||
|
|
//
|
||
|
|
// This file is part of CGAL (www.cgal.org).
|
||
|
|
//
|
||
|
|
// $URL: https://github.com/CGAL/cgal/blob/v5.1/Hyperbolic_triangulation_2/include/CGAL/internal/Exact_complex.h $
|
||
|
|
// $Id: Exact_complex.h 254d60f 2019-10-19T15:23:19+02:00 Sébastien Loriot
|
||
|
|
// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
|
||
|
|
//
|
||
|
|
// Author(s) : Iordan Iordanov
|
||
|
|
//
|
||
|
|
|
||
|
|
#ifndef CGAL_EXACT_COMPLEX_H
|
||
|
|
#define CGAL_EXACT_COMPLEX_H
|
||
|
|
|
||
|
|
#include <CGAL/license/Hyperbolic_triangulation_2.h>
|
||
|
|
|
||
|
|
#include <CGAL/assertions.h>
|
||
|
|
#include <CGAL/number_utils.h>
|
||
|
|
|
||
|
|
#include <iostream>
|
||
|
|
#include <fstream>
|
||
|
|
|
||
|
|
// Complex number in the form a + bi, where a and b are of type NT.
|
||
|
|
// NT must be an exact number type, model of:
|
||
|
|
// + FieldWithRootOf
|
||
|
|
// + RealEmbeddable
|
||
|
|
// + FromDoubleConstructible
|
||
|
|
//
|
||
|
|
|
||
|
|
namespace CGAL {
|
||
|
|
|
||
|
|
template <class NumberType>
|
||
|
|
class Exact_complex
|
||
|
|
{
|
||
|
|
typedef Exact_complex<NumberType> Self;
|
||
|
|
|
||
|
|
private:
|
||
|
|
NumberType _a, _b;
|
||
|
|
|
||
|
|
public:
|
||
|
|
typedef NumberType NT;
|
||
|
|
|
||
|
|
Exact_complex() : _a(0), _b(0) {}
|
||
|
|
Exact_complex(NT a, NT b) : _a(a), _b(b) {}
|
||
|
|
|
||
|
|
NT real() const { return _a; }
|
||
|
|
void set_real(NT val) { _a = val; }
|
||
|
|
|
||
|
|
NT imag() const { return _b; }
|
||
|
|
void set_imag(NT val) { _b = val; }
|
||
|
|
|
||
|
|
Self conj() const { return Self(_a, -_b); }
|
||
|
|
NT square_modulus() const { return (_a*_a + _b*_b); }
|
||
|
|
NT modulus() const { return CGAL::sqrt(this->square_modulus()); }
|
||
|
|
|
||
|
|
Self reciprocal()
|
||
|
|
{
|
||
|
|
NT denom = _a*_a + _b*_b;
|
||
|
|
if(denom == NT(0))
|
||
|
|
return Self(0,0);
|
||
|
|
else
|
||
|
|
return Self(_a/denom, -_b/denom);
|
||
|
|
}
|
||
|
|
|
||
|
|
Self invert_in_unit_circle() { return this->reciprocal().conj(); }
|
||
|
|
|
||
|
|
template <class Circle_2>
|
||
|
|
Self invert_in_circle(Circle_2 c)
|
||
|
|
{
|
||
|
|
NT r2 = c.squared_radius();
|
||
|
|
NT xc = c.center().x();
|
||
|
|
NT yc = c.center().y();
|
||
|
|
NT denom = (_a - xc)*(_a - xc) + (_b - yc)*(_b - yc);
|
||
|
|
return Self(xc + r2*(_a-xc)/denom, yc + r2*(_b-yc)/denom);
|
||
|
|
}
|
||
|
|
|
||
|
|
Self operator+(const Self& other) const
|
||
|
|
{
|
||
|
|
return Self(this->_a + other._a, this->_b + other._b);
|
||
|
|
}
|
||
|
|
|
||
|
|
Self operator-(const Self& other) const
|
||
|
|
{
|
||
|
|
return Self(this->_a - other._a, this->_b - other._b);
|
||
|
|
}
|
||
|
|
|
||
|
|
Self operator*(const Self& other) const
|
||
|
|
{
|
||
|
|
NT rp = _a*other._a - _b*other._b;
|
||
|
|
NT ip = _b*other._a + _a*other._b;
|
||
|
|
return Self(rp, ip);
|
||
|
|
}
|
||
|
|
|
||
|
|
Self operator/(const Self& other) const
|
||
|
|
{
|
||
|
|
NT denom = other._a*other._a + other._b*other._b;
|
||
|
|
CGAL_assertion(denom != 0);
|
||
|
|
NT rp = _a*other._a + _b*other._b;
|
||
|
|
NT ip = _b*other._a - _a*other._b;
|
||
|
|
return Self(rp/denom, ip/denom);
|
||
|
|
}
|
||
|
|
};
|
||
|
|
|
||
|
|
template <class NT>
|
||
|
|
std::ostream& operator<<(std::ostream& s, const Exact_complex<NT>& c)
|
||
|
|
{
|
||
|
|
s << c.real() << (c.imag() >= 0 ? " + " : " - ") << abs(c.imag()) << "i";
|
||
|
|
return s;
|
||
|
|
}
|
||
|
|
|
||
|
|
// just to give an ordering
|
||
|
|
template<class NT>
|
||
|
|
bool operator==(const Exact_complex<NT>& lh, const Exact_complex<NT>& rh)
|
||
|
|
{
|
||
|
|
return (lh.real() == rh.real() && lh.imag() == rh.imag());
|
||
|
|
}
|
||
|
|
|
||
|
|
template<class NT>
|
||
|
|
bool operator!=(const Exact_complex<NT>& lh, const Exact_complex<NT>& rh)
|
||
|
|
{
|
||
|
|
return !operator==(lh, rh);
|
||
|
|
}
|
||
|
|
|
||
|
|
// just to give an ordering
|
||
|
|
template<class NT>
|
||
|
|
bool operator<(const Exact_complex<NT>& lh, const Exact_complex<NT>& rh)
|
||
|
|
{
|
||
|
|
return lh.square_modulus() < rh.square_modulus();
|
||
|
|
}
|
||
|
|
|
||
|
|
} // namespace CGAL
|
||
|
|
|
||
|
|
#endif // CGAL_EXACT_COMPLEX_H
|