agg_curves.cpp

//----------------------------------------------------------------------------
// Anti-Grain Geometry - Version 2.4
// Copyright (C) 2002-2005 Maxim Shemanarev (http://www.antigrain.com)
//
// 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: mcseem@antigrain.com
//          mcseemagg@yahoo.com
//          http://www.antigrain.com
//----------------------------------------------------------------------------

#include <cmath>
#include "agg_curves.h"
#include "agg_math.h"

namespace agg
{

    //------------------------------------------------------------------------
    const double curve_distance_epsilon                  = 1e-30;
    const double curve_collinearity_epsilon              = 1e-30;
    const double curve_angle_tolerance_epsilon           = 0.01;
    enum curve_recursion_limit_e { curve_recursion_limit = 32 };



    //------------------------------------------------------------------------
    void curve3_inc::approximation_scale(double s) 
    { 
        m_scale = s;
    }

    //------------------------------------------------------------------------
    double curve3_inc::approximation_scale() const 
    { 
        return m_scale;
    }

    //------------------------------------------------------------------------
    void curve3_inc::init(double x1, double y1, 
                          double x2, double y2, 
                          double x3, double y3)
    {
        m_start_x = x1;
        m_start_y = y1;
        m_end_x   = x3;
        m_end_y   = y3;

        double dx1 = x2 - x1;
        double dy1 = y2 - y1;
        double dx2 = x3 - x2;
        double dy2 = y3 - y2;

        double len = std::sqrt(dx1 * dx1 + dy1 * dy1) + std::sqrt(dx2 * dx2 + dy2 * dy2); 

        m_num_steps = uround(len * 0.25 * m_scale);

        if(m_num_steps < 4)
        {
            m_num_steps = 4;   
        }

        double subdivide_step  = 1.0 / m_num_steps;
        double subdivide_step2 = subdivide_step * subdivide_step;

        double tmpx = (x1 - x2 * 2.0 + x3) * subdivide_step2;
        double tmpy = (y1 - y2 * 2.0 + y3) * subdivide_step2;

        m_saved_fx = m_fx = x1;
        m_saved_fy = m_fy = y1;
        
        m_saved_dfx = m_dfx = tmpx + (x2 - x1) * (2.0 * subdivide_step);
        m_saved_dfy = m_dfy = tmpy + (y2 - y1) * (2.0 * subdivide_step);

        m_ddfx = tmpx * 2.0;
        m_ddfy = tmpy * 2.0;

        m_step = m_num_steps;
    }

    //------------------------------------------------------------------------
    void curve3_inc::rewind(unsigned)
    {
        if(m_num_steps == 0)
        {
            m_step = -1;
            return;
        }
        m_step = m_num_steps;
        m_fx   = m_saved_fx;
        m_fy   = m_saved_fy;
        m_dfx  = m_saved_dfx;
        m_dfy  = m_saved_dfy;
    }

    //------------------------------------------------------------------------
    unsigned curve3_inc::vertex(double* x, double* y)
    {
        if(m_step < 0) return path_cmd_stop;
        if(m_step == m_num_steps)
        {
            *x = m_start_x;
            *y = m_start_y;
            --m_step;
            return path_cmd_move_to;
        }
        if(m_step == 0)
        {
            *x = m_end_x;
            *y = m_end_y;
            --m_step;
            return path_cmd_line_to;
        }
        m_fx  += m_dfx; 
        m_fy  += m_dfy;
        m_dfx += m_ddfx; 
        m_dfy += m_ddfy; 
        *x = m_fx;
        *y = m_fy;
        --m_step;
        return path_cmd_line_to;
    }

    //------------------------------------------------------------------------
    void curve3_div::init(double x1, double y1, 
                          double x2, double y2, 
                          double x3, double y3)
    {
        m_points.remove_all();
        m_distance_tolerance_square = 0.5 / m_approximation_scale;
        m_distance_tolerance_square *= m_distance_tolerance_square;
        bezier(x1, y1, x2, y2, x3, y3);
        m_count = 0;
    }

    //------------------------------------------------------------------------
    void curve3_div::recursive_bezier(double x1, double y1, 
                                      double x2, double y2, 
                                      double x3, double y3,
                                      unsigned level)
    {
        if(level > curve_recursion_limit) 
        {
            return;
        }

        // Calculate all the mid-points of the line segments
        //----------------------
        double x12   = (x1 + x2) / 2;                
        double y12   = (y1 + y2) / 2;
        double x23   = (x2 + x3) / 2;
        double y23   = (y2 + y3) / 2;
        double x123  = (x12 + x23) / 2;
        double y123  = (y12 + y23) / 2;

        double dx = x3-x1;
        double dy = y3-y1;
        double d = std::fabs(((x2 - x3) * dy - (y2 - y3) * dx));
        double da;

        if(d > curve_collinearity_epsilon)
        { 
            // Regular case
            //-----------------
            if(d * d <= m_distance_tolerance_square * (dx*dx + dy*dy))
            {
                // If the curvature doesn't exceed the distance_tolerance value
                // we tend to finish subdivisions.
                //----------------------
                if(m_angle_tolerance < curve_angle_tolerance_epsilon)
                {
                    m_points.add(point_d(x123, y123));
                    return;
                }

                // Angle & Cusp Condition
                //----------------------
                da = std::fabs(std::atan2(y3 - y2, x3 - x2) - std::atan2(y2 - y1, x2 - x1));
                if(da >= pi) da = 2*pi - da;

                if(da < m_angle_tolerance)
                {
                    // Finally we can stop the recursion
                    //----------------------
                    m_points.add(point_d(x123, y123));
                    return;                 
                }
            }
        }
        else
        {
            // Collinear case
            //------------------
            da = dx*dx + dy*dy;
            if(da == 0)
            {
                d = calc_sq_distance(x1, y1, x2, y2);
            }
            else
            {
                d = ((x2 - x1)*dx + (y2 - y1)*dy) / da;
                if(d > 0 && d < 1)
                {
                    // Simple collinear case, 1---2---3
                    // We can leave just two endpoints
                    return;
                }
                     if(d <= 0) d = calc_sq_distance(x2, y2, x1, y1);
                else if(d >= 1) d = calc_sq_distance(x2, y2, x3, y3);
                else            d = calc_sq_distance(x2, y2, x1 + d*dx, y1 + d*dy);
            }
            if(d < m_distance_tolerance_square)
            {
                m_points.add(point_d(x2, y2));
                return;
            }
        }

        // Continue subdivision
        //----------------------
        recursive_bezier(x1, y1, x12, y12, x123, y123, level + 1); 
        recursive_bezier(x123, y123, x23, y23, x3, y3, level + 1); 
    }

    //------------------------------------------------------------------------
    void curve3_div::bezier(double x1, double y1, 
                            double x2, double y2, 
                            double x3, double y3)
    {
        m_points.add(point_d(x1, y1));
        recursive_bezier(x1, y1, x2, y2, x3, y3, 0);
        m_points.add(point_d(x3, y3));
    }





    //------------------------------------------------------------------------
    void curve4_inc::approximation_scale(double s) 
    { 
        m_scale = s;
    }

    //------------------------------------------------------------------------
    double curve4_inc::approximation_scale() const 
    { 
        return m_scale;
    }

#if defined(_MSC_VER) && _MSC_VER <= 1200
    //------------------------------------------------------------------------
    static double MSC60_fix_ICE(double v) { return v; }
#endif

    //------------------------------------------------------------------------
    void curve4_inc::init(double x1, double y1, 
                          double x2, double y2, 
                          double x3, double y3,
                          double x4, double y4)
    {
        m_start_x = x1;
        m_start_y = y1;
        m_end_x   = x4;
        m_end_y   = y4;

        double dx1 = x2 - x1;
        double dy1 = y2 - y1;
        double dx2 = x3 - x2;
        double dy2 = y3 - y2;
        double dx3 = x4 - x3;
        double dy3 = y4 - y3;

        double len = (std::sqrt(dx1 * dx1 + dy1 * dy1) + 
                      std::sqrt(dx2 * dx2 + dy2 * dy2) + 
                      std::sqrt(dx3 * dx3 + dy3 * dy3)) * 0.25 * m_scale;

#if defined(_MSC_VER) && _MSC_VER <= 1200
        m_num_steps = uround(MSC60_fix_ICE(len));
#else
        m_num_steps = uround(len);
#endif

        if(m_num_steps < 4)
        {
            m_num_steps = 4;   
        }

        double subdivide_step  = 1.0 / m_num_steps;
        double subdivide_step2 = subdivide_step * subdivide_step;
        double subdivide_step3 = subdivide_step * subdivide_step * subdivide_step;

        double pre1 = 3.0 * subdivide_step;
        double pre2 = 3.0 * subdivide_step2;
        double pre4 = 6.0 * subdivide_step2;
        double pre5 = 6.0 * subdivide_step3;
    
        double tmp1x = x1 - x2 * 2.0 + x3;
        double tmp1y = y1 - y2 * 2.0 + y3;

        double tmp2x = (x2 - x3) * 3.0 - x1 + x4;
        double tmp2y = (y2 - y3) * 3.0 - y1 + y4;

        m_saved_fx = m_fx = x1;
        m_saved_fy = m_fy = y1;

        m_saved_dfx = m_dfx = (x2 - x1) * pre1 + tmp1x * pre2 + tmp2x * subdivide_step3;
        m_saved_dfy = m_dfy = (y2 - y1) * pre1 + tmp1y * pre2 + tmp2y * subdivide_step3;

        m_saved_ddfx = m_ddfx = tmp1x * pre4 + tmp2x * pre5;
        m_saved_ddfy = m_ddfy = tmp1y * pre4 + tmp2y * pre5;

        m_dddfx = tmp2x * pre5;
        m_dddfy = tmp2y * pre5;

        m_step = m_num_steps;
    }

    //------------------------------------------------------------------------
    void curve4_inc::rewind(unsigned)
    {
        if(m_num_steps == 0)
        {
            m_step = -1;
            return;
        }
        m_step = m_num_steps;
        m_fx   = m_saved_fx;
        m_fy   = m_saved_fy;
        m_dfx  = m_saved_dfx;
        m_dfy  = m_saved_dfy;
        m_ddfx = m_saved_ddfx;
        m_ddfy = m_saved_ddfy;
    }

    //------------------------------------------------------------------------
    unsigned curve4_inc::vertex(double* x, double* y)
    {
        if(m_step < 0) return path_cmd_stop;
        if(m_step == m_num_steps)
        {
            *x = m_start_x;
            *y = m_start_y;
            --m_step;
            return path_cmd_move_to;
        }

        if(m_step == 0)
        {
            *x = m_end_x;
            *y = m_end_y;
            --m_step;
            return path_cmd_line_to;
        }

        m_fx   += m_dfx;
        m_fy   += m_dfy;
        m_dfx  += m_ddfx; 
        m_dfy  += m_ddfy; 
        m_ddfx += m_dddfx; 
        m_ddfy += m_dddfy; 

        *x = m_fx;
        *y = m_fy;
        --m_step;
        return path_cmd_line_to;
    }




    //------------------------------------------------------------------------
    void curve4_div::init(double x1, double y1, 
                          double x2, double y2, 
                          double x3, double y3,
                          double x4, double y4)
    {
        m_points.remove_all();
        m_distance_tolerance_square = 0.5 / m_approximation_scale;
        m_distance_tolerance_square *= m_distance_tolerance_square;
        bezier(x1, y1, x2, y2, x3, y3, x4, y4);
        m_count = 0;
    }

    //------------------------------------------------------------------------
    void curve4_div::recursive_bezier(double x1, double y1, 
                                      double x2, double y2, 
                                      double x3, double y3, 
                                      double x4, double y4,
                                      unsigned level)
    {
        if(level > curve_recursion_limit) 
        {
            return;
        }

        // Calculate all the mid-points of the line segments
        //----------------------
        double x12   = (x1 + x2) / 2;
        double y12   = (y1 + y2) / 2;
        double x23   = (x2 + x3) / 2;
        double y23   = (y2 + y3) / 2;
        double x34   = (x3 + x4) / 2;
        double y34   = (y3 + y4) / 2;
        double x123  = (x12 + x23) / 2;
        double y123  = (y12 + y23) / 2;
        double x234  = (x23 + x34) / 2;
        double y234  = (y23 + y34) / 2;
        double x1234 = (x123 + x234) / 2;
        double y1234 = (y123 + y234) / 2;


        // Try to approximate the full cubic curve by a single straight line
        //------------------
        double dx = x4-x1;
        double dy = y4-y1;

        double d2 = std::fabs(((x2 - x4) * dy - (y2 - y4) * dx));
        double d3 = std::fabs(((x3 - x4) * dy - (y3 - y4) * dx));
        double da1, da2, k;

        switch((int(d2 > curve_collinearity_epsilon) << 1) +
                int(d3 > curve_collinearity_epsilon))
        {
        case 0:
            // All collinear OR p1==p4
            //----------------------
            k = dx*dx + dy*dy;
            if(k == 0)
            {
                d2 = calc_sq_distance(x1, y1, x2, y2);
                d3 = calc_sq_distance(x4, y4, x3, y3);
            }
            else
            {
                k   = 1 / k;
                da1 = x2 - x1;
                da2 = y2 - y1;
                d2  = k * (da1*dx + da2*dy);
                da1 = x3 - x1;
                da2 = y3 - y1;
                d3  = k * (da1*dx + da2*dy);
                if(d2 > 0 && d2 < 1 && d3 > 0 && d3 < 1)
                {
                    // Simple collinear case, 1---2---3---4
                    // We can leave just two endpoints
                    return;
                }
                     if(d2 <= 0) d2 = calc_sq_distance(x2, y2, x1, y1);
                else if(d2 >= 1) d2 = calc_sq_distance(x2, y2, x4, y4);
                else             d2 = calc_sq_distance(x2, y2, x1 + d2*dx, y1 + d2*dy);

                     if(d3 <= 0) d3 = calc_sq_distance(x3, y3, x1, y1);
                else if(d3 >= 1) d3 = calc_sq_distance(x3, y3, x4, y4);
                else             d3 = calc_sq_distance(x3, y3, x1 + d3*dx, y1 + d3*dy);
            }
            if(d2 > d3)
            {
                if(d2 < m_distance_tolerance_square)
                {
                    m_points.add(point_d(x2, y2));
                    return;
                }
            }
            else
            {
                if(d3 < m_distance_tolerance_square)
                {
                    m_points.add(point_d(x3, y3));
                    return;
                }
            }
            break;

        case 1:
            // p1,p2,p4 are collinear, p3 is significant
            //----------------------
            if(d3 * d3 <= m_distance_tolerance_square * (dx*dx + dy*dy))
            {
                if(m_angle_tolerance < curve_angle_tolerance_epsilon)
                {
                    m_points.add(point_d(x23, y23));
                    return;
                }

                // Angle Condition
                //----------------------
                da1 = std::fabs(std::atan2(y4 - y3, x4 - x3) - std::atan2(y3 - y2, x3 - x2));
                if(da1 >= pi) da1 = 2*pi - da1;

                if(da1 < m_angle_tolerance)
                {
                    m_points.add(point_d(x2, y2));
                    m_points.add(point_d(x3, y3));
                    return;
                }

                if(m_cusp_limit != 0.0)
                {
                    if(da1 > m_cusp_limit)
                    {
                        m_points.add(point_d(x3, y3));
                        return;
                    }
                }
            }
            break;

        case 2:
            // p1,p3,p4 are collinear, p2 is significant
            //----------------------
            if(d2 * d2 <= m_distance_tolerance_square * (dx*dx + dy*dy))
            {
                if(m_angle_tolerance < curve_angle_tolerance_epsilon)
                {
                    m_points.add(point_d(x23, y23));
                    return;
                }

                // Angle Condition
                //----------------------
                da1 = std::fabs(std::atan2(y3 - y2, x3 - x2) - std::atan2(y2 - y1, x2 - x1));
                if(da1 >= pi) da1 = 2*pi - da1;

                if(da1 < m_angle_tolerance)
                {
                    m_points.add(point_d(x2, y2));
                    m_points.add(point_d(x3, y3));
                    return;
                }

                if(m_cusp_limit != 0.0)
                {
                    if(da1 > m_cusp_limit)
                    {
                        m_points.add(point_d(x2, y2));
                        return;
                    }
                }
            }
            break;

        case 3: 
            // Regular case
            //-----------------
            if((d2 + d3)*(d2 + d3) <= m_distance_tolerance_square * (dx*dx + dy*dy))
            {
                // If the curvature doesn't exceed the distance_tolerance value
                // we tend to finish subdivisions.
                //----------------------
                if(m_angle_tolerance < curve_angle_tolerance_epsilon)
                {
                    m_points.add(point_d(x23, y23));
                    return;
                }

                // Angle & Cusp Condition
                //----------------------
                k   = std::atan2(y3 - y2, x3 - x2);
                da1 = std::fabs(k - std::atan2(y2 - y1, x2 - x1));
                da2 = std::fabs(std::atan2(y4 - y3, x4 - x3) - k);
                if(da1 >= pi) da1 = 2*pi - da1;
                if(da2 >= pi) da2 = 2*pi - da2;

                if(da1 + da2 < m_angle_tolerance)
                {
                    // Finally we can stop the recursion
                    //----------------------
                    m_points.add(point_d(x23, y23));
                    return;
                }

                if(m_cusp_limit != 0.0)
                {
                    if(da1 > m_cusp_limit)
                    {
                        m_points.add(point_d(x2, y2));
                        return;
                    }

                    if(da2 > m_cusp_limit)
                    {
                        m_points.add(point_d(x3, y3));
                        return;
                    }
                }
            }
            break;
        }

        // Continue subdivision
        //----------------------
        recursive_bezier(x1, y1, x12, y12, x123, y123, x1234, y1234, level + 1); 
        recursive_bezier(x1234, y1234, x234, y234, x34, y34, x4, y4, level + 1); 
    }

    //------------------------------------------------------------------------
    void curve4_div::bezier(double x1, double y1, 
                            double x2, double y2, 
                            double x3, double y3, 
                            double x4, double y4)
    {
        m_points.add(point_d(x1, y1));
        recursive_bezier(x1, y1, x2, y2, x3, y3, x4, y4, 0);
        m_points.add(point_d(x4, y4));
    }

}