agg_curves.h

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//----------------------------------------------------------------------------
// Anti-Grain Geometry - Version 2.4
// Copyright (C) 2002-2005 Maxim Shemanarev (http://www.antigrain.com)
// Copyright (C) 2005 Tony Juricic ([e-mail])
//
// Permission to copy, use, modify, sell and distribute this software 
// is granted provided this copyright notice appears in all copies. 
// This software is provided "as is" without express or implied
// warranty, and with no claim as to its suitability for any purpose.
//
//----------------------------------------------------------------------------
// Contact: [e-mail]
//          [e-mail]
//          http://www.antigrain.com
//----------------------------------------------------------------------------

#ifndef AGG_CURVES_INCLUDED
#define AGG_CURVES_INCLUDED

#include "agg_array.h"

namespace agg
{

    // See Implementation agg_curves.cpp

    //--------------------------------------------curve_approximation_method_e
    enum curve_approximation_method_e
    {
        curve_inc,
        curve_div
    };
    
    //--------------------------------------------------------------curve3_inc
    class curve3_inc
    {
    public:
        curve3_inc() :
          m_num_steps(0), m_step(0), m_scale(1.0) { }

        curve3_inc(double x1, double y1, 
                   double x2, double y2, 
                   double x3, double y3) :
            m_num_steps(0), m_step(0), m_scale(1.0) 
        { 
            init(x1, y1, x2, y2, x3, y3);
        }

        void reset() { m_num_steps = 0; m_step = -1; }
        void init(double x1, double y1, 
                  double x2, double y2, 
                  double x3, double y3);

        void approximation_method(curve_approximation_method_e) {}
        curve_approximation_method_e approximation_method() const { return curve_inc; }

        void approximation_scale(double s);
        double approximation_scale() const;

        void angle_tolerance(double) {}
        double angle_tolerance() const { return 0.0; }

        void cusp_limit(double) {}
        double cusp_limit() const { return 0.0; }

        void     rewind(unsigned path_id);
        unsigned vertex(double* x, double* y);

    private:
        int      m_num_steps;
        int      m_step;
        double   m_scale;
        double   m_start_x; 
        double   m_start_y;
        double   m_end_x; 
        double   m_end_y;
        double   m_fx; 
        double   m_fy;
        double   m_dfx; 
        double   m_dfy;
        double   m_ddfx; 
        double   m_ddfy;
        double   m_saved_fx; 
        double   m_saved_fy;
        double   m_saved_dfx; 
        double   m_saved_dfy;
    };





    //-------------------------------------------------------------curve3_div
    class curve3_div
    {
    public:
        curve3_div() : 
            m_approximation_scale(1.0),
            m_angle_tolerance(0.0),
            m_count(0)
        {}

        curve3_div(double x1, double y1, 
                   double x2, double y2, 
                   double x3, double y3) :
            m_approximation_scale(1.0),
            m_angle_tolerance(0.0),
            m_count(0)
        { 
            init(x1, y1, x2, y2, x3, y3);
        }

        void reset() { m_points.remove_all(); m_count = 0; }
        void init(double x1, double y1, 
                  double x2, double y2, 
                  double x3, double y3);

        void approximation_method(curve_approximation_method_e) {}
        curve_approximation_method_e approximation_method() const { return curve_div; }

        void approximation_scale(double s) { m_approximation_scale = s; }
        double approximation_scale() const { return m_approximation_scale;  }

        void angle_tolerance(double a) { m_angle_tolerance = a; }
        double angle_tolerance() const { return m_angle_tolerance;  }

        void cusp_limit(double) {}
        double cusp_limit() const { return 0.0; }

        void rewind(unsigned)
        {
            m_count = 0;
        }

        unsigned vertex(double* x, double* y)
        {
            if(m_count >= m_points.size()) return path_cmd_stop;
            const point_d& p = m_points[m_count++];
            *x = p.x;
            *y = p.y;
            return (m_count == 1) ? path_cmd_move_to : path_cmd_line_to;
        }

    private:
        void bezier(double x1, double y1, 
                    double x2, double y2, 
                    double x3, double y3);
        void recursive_bezier(double x1, double y1, 
                              double x2, double y2, 
                              double x3, double y3,
                              unsigned level);

        double               m_approximation_scale;
        double               m_distance_tolerance_square;
        double               m_distance_tolerance_manhattan;
        double               m_angle_tolerance;
        unsigned             m_count;
        pod_bvector<point_d> m_points;
    };







    //-------------------------------------------------------------curve4_points
    struct curve4_points
    {
        double cp[8];
        curve4_points() {}
        curve4_points(double x1, double y1,
                      double x2, double y2,
                      double x3, double y3,
                      double x4, double y4)
        {
            cp[0] = x1; cp[1] = y1; cp[2] = x2; cp[3] = y2;
            cp[4] = x3; cp[5] = y3; cp[6] = x4; cp[7] = y4;
        }
        void init(double x1, double y1,
                  double x2, double y2,
                  double x3, double y3,
                  double x4, double y4)
        {
            cp[0] = x1; cp[1] = y1; cp[2] = x2; cp[3] = y2;
            cp[4] = x3; cp[5] = y3; cp[6] = x4; cp[7] = y4;
        }
        double  operator [] (unsigned i) const { return cp[i]; }
        double& operator [] (unsigned i)       { return cp[i]; }
    };



    //-------------------------------------------------------------curve4_inc
    class curve4_inc
    {
    public:
        curve4_inc() :
            m_num_steps(0), m_step(0), m_scale(1.0) { }

        curve4_inc(double x1, double y1, 
                   double x2, double y2, 
                   double x3, double y3,
                   double x4, double y4) :
            m_num_steps(0), m_step(0), m_scale(1.0) 
        { 
            init(x1, y1, x2, y2, x3, y3, x4, y4);
        }

        curve4_inc(const curve4_points& cp) :
            m_num_steps(0), m_step(0), m_scale(1.0) 
        { 
            init(cp[0], cp[1], cp[2], cp[3], cp[4], cp[5], cp[6], cp[7]);
        }

        void reset() { m_num_steps = 0; m_step = -1; }
        void init(double x1, double y1, 
                  double x2, double y2, 
                  double x3, double y3,
                  double x4, double y4);

        void init(const curve4_points& cp)
        {
            init(cp[0], cp[1], cp[2], cp[3], cp[4], cp[5], cp[6], cp[7]);
        }

        void approximation_method(curve_approximation_method_e) {}
        curve_approximation_method_e approximation_method() const { return curve_inc; }

        void approximation_scale(double s);
        double approximation_scale() const;

        void angle_tolerance(double) {}
        double angle_tolerance() const { return 0.0; }

        void cusp_limit(double) {}
        double cusp_limit() const { return 0.0; }

        void     rewind(unsigned path_id);
        unsigned vertex(double* x, double* y);

    private:
        int      m_num_steps;
        int      m_step;
        double   m_scale;
        double   m_start_x; 
        double   m_start_y;
        double   m_end_x; 
        double   m_end_y;
        double   m_fx; 
        double   m_fy;
        double   m_dfx; 
        double   m_dfy;
        double   m_ddfx; 
        double   m_ddfy;
        double   m_dddfx; 
        double   m_dddfy;
        double   m_saved_fx; 
        double   m_saved_fy;
        double   m_saved_dfx; 
        double   m_saved_dfy;
        double   m_saved_ddfx; 
        double   m_saved_ddfy;
    };



    //-------------------------------------------------------catrom_to_bezier
    inline curve4_points catrom_to_bezier(double x1, double y1, 
                                          double x2, double y2, 
                                          double x3, double y3,
                                          double x4, double y4)
    {
        // Trans. matrix Catmull-Rom to Bezier
        //
        //  0       1       0       0
        //  -1/6    1       1/6     0
        //  0       1/6     1       -1/6
        //  0       0       1       0
        //
        return curve4_points(
            x2,
            y2,
            (-x1 + 6*x2 + x3) / 6,
            (-y1 + 6*y2 + y3) / 6,
            ( x2 + 6*x3 - x4) / 6,
            ( y2 + 6*y3 - y4) / 6,
            x3,
            y3);
    }


    //-----------------------------------------------------------------------
    inline curve4_points
    catrom_to_bezier(const curve4_points& cp)
    {
        return catrom_to_bezier(cp[0], cp[1], cp[2], cp[3], 
                                cp[4], cp[5], cp[6], cp[7]);
    }



    //-----------------------------------------------------ubspline_to_bezier
    inline curve4_points ubspline_to_bezier(double x1, double y1, 
                                            double x2, double y2, 
                                            double x3, double y3,
                                            double x4, double y4)
    {
        // Trans. matrix Uniform BSpline to Bezier
        //
        //  1/6     4/6     1/6     0
        //  0       4/6     2/6     0
        //  0       2/6     4/6     0
        //  0       1/6     4/6     1/6
        //
        return curve4_points(
            (x1 + 4*x2 + x3) / 6,
            (y1 + 4*y2 + y3) / 6,
            (4*x2 + 2*x3) / 6,
            (4*y2 + 2*y3) / 6,
            (2*x2 + 4*x3) / 6,
            (2*y2 + 4*y3) / 6,
            (x2 + 4*x3 + x4) / 6,
            (y2 + 4*y3 + y4) / 6);
    }


    //-----------------------------------------------------------------------
    inline curve4_points 
    ubspline_to_bezier(const curve4_points& cp)
    {
        return ubspline_to_bezier(cp[0], cp[1], cp[2], cp[3], 
                                  cp[4], cp[5], cp[6], cp[7]);
    }




    //------------------------------------------------------hermite_to_bezier
    inline curve4_points hermite_to_bezier(double x1, double y1, 
                                           double x2, double y2, 
                                           double x3, double y3,
                                           double x4, double y4)
    {
        // Trans. matrix Hermite to Bezier
        //
        //  1       0       0       0
        //  1       0       1/3     0