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elliptical-arc.h

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/**
 * \file
 * \brief  Elliptical Arc - implementation of the svg elliptical arc path element
 *
 * Authors:
 *          MenTaLguY <mental@rydia.net>
 *          Marco Cecchetti <mrcekets at gmail.com>
 * 
 * Copyright 2007-2008  authors
 *
 * This library is free software; you can redistribute it and/or
 * modify it either under the terms of the GNU Lesser General Public
 * License version 2.1 as published by the Free Software Foundation
 * (the "LGPL") or, at your option, under the terms of the Mozilla
 * Public License Version 1.1 (the "MPL"). If you do not alter this
 * notice, a recipient may use your version of this file under either
 * the MPL or the LGPL.
 *
 * You should have received a copy of the LGPL along with this library
 * in the file COPYING-LGPL-2.1; if not, write to the Free Software
 * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
 * You should have received a copy of the MPL along with this library
 * in the file COPYING-MPL-1.1
 *
 * The contents of this file are subject to the Mozilla Public License
 * Version 1.1 (the "License"); you may not use this file except in
 * compliance with the License. You may obtain a copy of the License at
 * http://www.mozilla.org/MPL/
 *
 * This software is distributed on an "AS IS" basis, WITHOUT WARRANTY
 * OF ANY KIND, either express or implied. See the LGPL or the MPL for
 * the specific language governing rights and limitations.
 */




#ifndef _2GEOM_ELLIPTICAL_ARC_H_
#define _2GEOM_ELLIPTICAL_ARC_H_


#include <2geom/curve.h>
#include <2geom/angle.h>
#include <2geom/utils.h>
#include <2geom/sbasis-curve.h>  // for non-native methods

#include <algorithm>


namespace Geom 
{

class EllipticalArc : public Curve
{
  public:
      EllipticalArc()
            : m_initial_point(Point(0,0)), m_final_point(Point(0,0)),
              m_rx(0), m_ry(0), m_rot_angle(0),
              m_large_arc(true), m_sweep(true)
      {
            m_start_angle = m_end_angle = 0;
            m_center = Point(0,0);
      }
      
    EllipticalArc( Point _initial_point, double _rx, double _ry,
                   double _rot_angle, bool _large_arc, bool _sweep,
                   Point _final_point
                  )
        : m_initial_point(_initial_point), m_final_point(_final_point),
          m_rx(_rx), m_ry(_ry), m_rot_angle(_rot_angle),
          m_large_arc(_large_arc), m_sweep(_sweep)
    {
            calculate_center_and_extreme_angles();
    }
        
    void set( Point _initial_point, double _rx, double _ry,
              double _rot_angle, bool _large_arc, bool _sweep,
              Point _final_point
             )
    {
      m_initial_point = _initial_point;
      m_final_point = _final_point;
      m_rx = _rx;
      m_ry = _ry;
      m_rot_angle = _rot_angle;
      m_large_arc = _large_arc;
      m_sweep = _sweep;
      calculate_center_and_extreme_angles();
    }

      Curve* duplicate() const
      {
            return new EllipticalArc(*this);
      }
      
    double center(unsigned int i) const
    {
        return m_center[i];
    }

    Point center() const
    {
        return m_center;
    }

    Point initialPoint() const
    {
        return m_initial_point;
    }

    Point finalPoint() const
    {
        return m_final_point;
    }

    double start_angle() const
    {
        return m_start_angle;
    }

    double end_angle() const
    {
        return m_end_angle;
    }

    double ray(unsigned int i) const
    {
        return (i == 0) ? m_rx : m_ry;
    }

    bool large_arc_flag() const
    {
        return m_large_arc;
    }

    bool sweep_flag() const
    {
        return m_sweep;
    }

    double rotation_angle() const
    {
        return m_rot_angle;
    }

    void setInitial( const Point _point)
    {
        m_initial_point = _point;
        calculate_center_and_extreme_angles();
    }

    void setFinal( const Point _point)
    {
        m_final_point = _point;
        calculate_center_and_extreme_angles();
    }

    void setExtremes( const Point& _initial_point, const Point& _final_point )
    {
        m_initial_point = _initial_point;
        m_final_point = _final_point;
        calculate_center_and_extreme_angles();
    }

    bool isDegenerate() const
    {
        return ( are_near(ray(X), 0) || are_near(ray(Y), 0) );
    }
    
    
    virtual OptRect boundsFast() const
    {
        return boundsExact();
    }
  
    virtual OptRect boundsExact() const;
    
    // TODO: native implementation of the following methods
    virtual OptRect boundsLocal(OptInterval i, unsigned int deg) const
    {
        return SBasisCurve(toSBasis()).boundsLocal(i, deg);
    }
    
    std::vector<double> roots(double v, Dim2 d) const;
    
    std::vector<double> 
    allNearestPoints( Point const& p, double from = 0, double to = 1 ) const;
    
    double nearestPoint( Point const& p, double from = 0, double to = 1 ) const
    {
      if ( are_near(ray(X), ray(Y)) && are_near(center(), p) )
      {
            return from;
      }
      return allNearestPoints(p, from, to).front();
    }
    
    // TODO: native implementation of the following methods
    int winding(Point p) const
    {
      return SBasisCurve(toSBasis()).winding(p);
    }

    int degreesOfFreedom() const { return 7;}
    
    Curve *derivative() const;
    
    // TODO: native implementation of the following methods
    Curve *transformed(Matrix const &m) const
    {
      return SBasisCurve(toSBasis()).transformed(m);
    }
    
    std::vector<Point> pointAndDerivatives(Coord t, unsigned int n) const;
    
    D2<SBasis> toSBasis() const;
    
    bool containsAngle(Coord angle) const;
    
    double valueAtAngle(Coord t, Dim2 d) const;
    
    Point pointAtAngle(Coord t) const
    {
        double sin_rot_angle = std::sin(rotation_angle());
        double cos_rot_angle = std::cos(rotation_angle());
        Matrix m( ray(X) * cos_rot_angle, ray(X) * sin_rot_angle,
                 -ray(Y) * sin_rot_angle, ray(Y) * cos_rot_angle,
                  center(X),              center(Y) );
        Point p( std::cos(t), std::sin(t) );
        return p * m;
    }
    
    double valueAt(Coord t, Dim2 d) const
    {
      Coord tt = map_to_02PI(t);
      return valueAtAngle(tt, d);
    }

    Point pointAt(Coord t) const
    {
        Coord tt = map_to_02PI(t);
        return pointAtAngle(tt);
    }

    std::pair<EllipticalArc, EllipticalArc>
    subdivide(Coord t) const
    {
        EllipticalArc* arc1 = static_cast<EllipticalArc*>(portion(0, t));
        EllipticalArc* arc2 = static_cast<EllipticalArc*>(portion(t, 1));
        assert( arc1 != NULL && arc2 != NULL);
        std::pair<EllipticalArc, EllipticalArc> arc_pair(*arc1, *arc2);        
        delete arc1;
        delete arc2;
        return arc_pair;
    }

    Curve* portion(double f, double t) const;
    
    // the arc is the same but traversed in the opposite direction
    Curve* reverse() const
    {
        EllipticalArc* rarc = new EllipticalArc( *this );
        rarc->m_sweep = !m_sweep;
        rarc->m_initial_point = m_final_point;
        rarc->m_final_point = m_initial_point;
        rarc->m_start_angle = m_end_angle;
        rarc->m_end_angle = m_start_angle;
        return rarc;
    }

    double sweep_angle() const
    {
        Coord d = end_angle() - start_angle();
        if ( !sweep_flag() ) d = -d;
        if ( d < 0 )
            d += 2*M_PI;
        return d;
    }
    
  private:
    Coord map_to_02PI(Coord t) const;
    Coord map_to_01(Coord angle) const; 
    void calculate_center_and_extreme_angles();
  private:
    Point m_initial_point, m_final_point;
    double m_rx, m_ry, m_rot_angle;
    bool m_large_arc, m_sweep;
    double m_start_angle, m_end_angle;
    Point m_center;
    
}; // end class EllipticalArc


} // end namespace Geom

#endif // _2GEOM_ELLIPTICAL_ARC_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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