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139 lines
4.2 KiB
C++
139 lines
4.2 KiB
C++
/*
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* This program source code file is part of KiCad, a free EDA CAD application.
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*
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* Copyright (C) 2014-2021 KiCad Developers, see AUTHORS.txt for contributors.
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*
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* This program is free software; you can redistribute it and/or
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* modify it under the terms of the GNU General Public License
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* as published by the Free Software Foundation; either version 2
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* of the License, or (at your option) any later version.
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*
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* This program is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with this program; if not, you may find one here:
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* http://www.gnu.org/licenses/old-licenses/gpl-2.0.html
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* or you may search the http://www.gnu.org website for the version 2 license,
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* or you may write to the Free Software Foundation, Inc.,
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* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA
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*/
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#ifndef BEZIER_CURVES_H
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#define BEZIER_CURVES_H
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#include <vector>
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#include <math/vector2d.h>
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template <typename T> class ELLIPSE;
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/**
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* Bezier curves to polygon converter.
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*
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* Only quadratic and cubic Bezier curves are handled
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*/
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class BEZIER_POLY
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{
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public:
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BEZIER_POLY( const VECTOR2I& aStart, const VECTOR2I& aCtrl1,
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const VECTOR2I& aCtrl2, const VECTOR2I& aEnd );
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BEZIER_POLY( const std::vector<VECTOR2I>& aControlPoints );
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BEZIER_POLY( const std::vector<VECTOR2D>& aControlPoints )
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: m_ctrlPts( aControlPoints )
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{
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m_minSegLen = 0.0;
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}
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/**
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* Convert a Bezier curve to a polygon.
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*
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* @param aOutput will be used as an output vector storing polygon points.
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* @param aMaxError maximum error in IU between the curve and the polygon.
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*/
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void GetPoly( std::vector<VECTOR2I>& aOutput, int aMaxError = 10 );
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void GetPoly( std::vector<VECTOR2D>& aOutput, double aMaxError = 10.0 );
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private:
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void getQuadPoly( std::vector<VECTOR2D>& aOutput, double aMaxError );
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void getCubicPoly( std::vector<VECTOR2D>& aOutput, double aMaxError );
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int findInflectionPoints( double& aT1, double& aT2 );
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int numberOfInflectionPoints();
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double thirdControlPointDeviation();
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void subdivide( double aT, BEZIER_POLY& aLeft, BEZIER_POLY& aRight );
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void recursiveSegmentation( std::vector<VECTOR2D>& aOutput, double aMaxError );
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void cubicParabolicApprox( std::vector<VECTOR2D>& aOutput, double aMaxError );
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bool isNaN() const;
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bool isFlat( double aMaxError ) const;
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VECTOR2D eval( double t );
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double m_minSegLen;
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///< Control points
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std::vector<VECTOR2D> m_ctrlPts;
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};
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// TODO: Refactor BEZIER_POLY to use BEZIER
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/**
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* Generic cubic Bezier representation
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*/
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template <typename NumericType>
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class BEZIER
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{
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public:
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BEZIER() = default;
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constexpr BEZIER( const VECTOR2<NumericType>& aStart, const VECTOR2<NumericType>& aC1,
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const VECTOR2<NumericType>& aC2, const VECTOR2<NumericType>& aEnd ) :
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Start( aStart ), C1( aC1 ), C2( aC2 ), End( aEnd )
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{
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}
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/**
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* Evaluate the Bezier curve at a given t value
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*
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* aT doesn't have to be in the range [0, 1], but if it's not, the
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* point will not be on the curve.
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*
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* @param aT the t value to evaluate the curve at (0 = start, 1 = end)
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* @return the point on the curve at t (0 <= t <= 1)
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*/
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constexpr VECTOR2<NumericType> PointAt( double aT ) const
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{
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const double t2 = aT * aT;
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const double t3 = t2 * aT;
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const double t_m1 = 1.0 - aT;
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const double t_m1_2 = t_m1 * t_m1;
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const double t_m1_3 = t_m1_2 * t_m1;
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return ( t_m1_3 * Start ) + ( 3.0 * aT * t_m1_2 * C1 ) + ( 3.0 * t2 * t_m1 * C2 )
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+ ( t3 * End );
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}
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VECTOR2<NumericType> Start;
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VECTOR2<NumericType> C1;
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VECTOR2<NumericType> C2;
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VECTOR2<NumericType> End;
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};
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/**
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* Transforms an ellipse or elliptical arc into a set of quadratic Bezier curves that approximate it
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*/
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template<typename T>
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void TransformEllipseToBeziers( const ELLIPSE<T>& aEllipse, std::vector<BEZIER<T>>& aBeziers );
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#endif // BEZIER_CURVES_H
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