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/* This file is part of the libdepixelize project
Copyright (C) 2013 Vinícius dos Santos Oliveira <vini.ipsmaker@gmail.com>
GNU Lesser General Public License Usage
This library is free software; 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; either version 2.1 of the License, or (at your
option) any later version.
You should have received a copy of the GNU Lesser General Public License
along with this library. If not, see <http://www.gnu.org/licenses/>.
GNU General Public License Usage
Alternatively, this library may be used under the terms of the GNU General
Public License as published by the Free Software Foundation, either version
2 of the License, or (at your option) any later version.
You should have received a copy of the GNU General Public License along with
this library. If not, see <http://www.gnu.org/licenses/>.
This library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
*/
#ifndef LIBDEPIXELIZE_TRACER_CURVATURE_H
#define LIBDEPIXELIZE_TRACER_CURVATURE_H
#include "point.h"
#include <cmath>
namespace Tracer {
/**
* Curvature function for a quadratic Bézier curve where the points are know.
* Its main use is to numerically integrate the curvature function and then
* smooth the B-Splines generated by the Kopf-Lischinski algorithm.
*/
template<class T>
struct Curvature
{
Curvature(Point<T> p0, Point<T> c1, Point<T> p2) :
p0(p0), c1(c1), p2(p2)
{}
T operator()(T t) const;
/**
* The derivative of x
*/
T xPrime(T t) const;
/**
* The derivative of y
*/
T yPrime(T t) const;
/**
* The second derivative of x
*/
T xPrimePrime() const;
/**
* The second derivative of y
*/
T yPrimePrime() const;
Point<T> p0, c1, p2;
};
template<class T>
T Curvature<T>::operator()(T t) const
{
T num = xPrime(t) * yPrimePrime() - yPrime(t) * xPrimePrime();
T den = std::pow(xPrime(t) * xPrime(t) + yPrime(t) * yPrime(t), T(3) / 2);
return num / den;
}
template<class T>
T Curvature<T>::xPrime(T t) const
{
return (1-t)*2*(c1.x-p0.x) + t*2*(p2.x-c1.x);
}
template<class T>
T Curvature<T>::yPrime(T t) const
{
return (1-t)*2*(c1.y-p0.y) + t*2*(p2.y-c1.y);
}
template<class T>
T Curvature<T>::xPrimePrime() const
{
return 2 * (p2.x - 2*c1.x + p0.x);
}
template<class T>
T Curvature<T>::yPrimePrime() const
{
return 2 * (p2.y - 2*c1.y + p0.y);
}
} // namespace Tracer
#endif // LIBDEPIXELIZE_TRACER_CURVATURE_H
/*
Local Variables:
mode:c++
c-file-style:"stroustrup"
c-file-offsets:((innamespace . 0)(inline-open . 0)(case-label . +))
indent-tabs-mode:nil
fill-column:99
End:
*/
// vim: filetype=cpp:expandtab:shiftwidth=4:tabstop=8:softtabstop=4:encoding=utf-8:textwidth=99 :
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