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/*
* This program source code file is part of KiCad, a free EDA CAD application.
*
* Copyright The KiCad Developers, see AUTHORS.txt for contributors.
*
* This program is free software; you can redistribute it and/or
* modify it 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.
*
* This program 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 General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, you may find one here:
* http://www.gnu.org/licenses/old-licenses/gpl-2.0.html
* or you may search the http://www.gnu.org website for the version 2 license,
* or you may write to the Free Software Foundation, Inc.,
* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA
*/
#ifndef BEZIER_CURVES_H
#define BEZIER_CURVES_H
#include <vector>
#include <math/vector2d.h>
template <typename T> class ELLIPSE;
/**
* Bezier curves to polygon converter.
*
* Only quadratic and cubic Bezier curves are handled
*/
class BEZIER_POLY
{
public:
BEZIER_POLY( const VECTOR2I& aStart, const VECTOR2I& aCtrl1,
const VECTOR2I& aCtrl2, const VECTOR2I& aEnd );
BEZIER_POLY( const std::vector<VECTOR2I>& aControlPoints );
BEZIER_POLY( const std::vector<VECTOR2D>& aControlPoints )
: m_ctrlPts( aControlPoints )
{
m_minSegLen = 0.0;
}
/**
* Convert a Bezier curve to a polygon.
*
* @param aOutput will be used as an output vector storing polygon points.
* @param aMaxError maximum error in IU between the curve and the polygon.
*/
void GetPoly( std::vector<VECTOR2I>& aOutput, int aMaxError = 10 );
void GetPoly( std::vector<VECTOR2D>& aOutput, double aMaxError = 10.0 );
private:
void getQuadPoly( std::vector<VECTOR2D>& aOutput, double aMaxError );
void getCubicPoly( std::vector<VECTOR2D>& aOutput, double aMaxError );
int findInflectionPoints( double& aT1, double& aT2 );
int numberOfInflectionPoints();
double thirdControlPointDeviation();
void subdivide( double aT, BEZIER_POLY& aLeft, BEZIER_POLY& aRight );
void recursiveSegmentation( std::vector<VECTOR2D>& aOutput, double aMaxError );
void cubicParabolicApprox( std::vector<VECTOR2D>& aOutput, double aMaxError );
bool isNaN() const;
bool isFlat( double aMaxError ) const;
VECTOR2D eval( double t );
double m_minSegLen;
///< Control points
std::vector<VECTOR2D> m_ctrlPts;
};
// TODO: Refactor BEZIER_POLY to use BEZIER
/**
* Generic cubic Bezier representation
*/
template <typename NumericType>
class BEZIER
{
public:
BEZIER() = default;
constexpr BEZIER( const VECTOR2<NumericType>& aStart, const VECTOR2<NumericType>& aC1,
const VECTOR2<NumericType>& aC2, const VECTOR2<NumericType>& aEnd ) :
Start( aStart ), C1( aC1 ), C2( aC2 ), End( aEnd )
{
}
/**
* Evaluate the Bezier curve at a given t value
*
* aT doesn't have to be in the range [0, 1], but if it's not, the
* point will not be on the curve.
*
* @param aT the t value to evaluate the curve at (0 = start, 1 = end)
* @return the point on the curve at t (0 <= t <= 1)
*/
constexpr VECTOR2<NumericType> PointAt( double aT ) const
{
const double t2 = aT * aT;
const double t3 = t2 * aT;
const double t_m1 = 1.0 - aT;
const double t_m1_2 = t_m1 * t_m1;
const double t_m1_3 = t_m1_2 * t_m1;
return ( t_m1_3 * Start ) + ( 3.0 * aT * t_m1_2 * C1 ) + ( 3.0 * t2 * t_m1 * C2 )
+ ( t3 * End );
}
VECTOR2<NumericType> Start;
VECTOR2<NumericType> C1;
VECTOR2<NumericType> C2;
VECTOR2<NumericType> End;
};
/**
* Transforms an ellipse or elliptical arc into a set of quadratic Bezier curves that approximate it
*/
template<typename T>
void TransformEllipseToBeziers( const ELLIPSE<T>& aEllipse, std::vector<BEZIER<T>>& aBeziers );
#endif // BEZIER_CURVES_H
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