mapnik/deps/agg/src/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 <math.h>
#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 = sqrt(dx1 * dx1 + dy1 * dy1) + 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 = 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 = fabs(atan2(y3 - y2, x3 - x2) - 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 = (sqrt(dx1 * dx1 + dy1 * dy1) +
                  sqrt(dx2 * dx2 + dy2 * dy2) +
                  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 = fabs(((x2 - x4) * dy - (y2 - y4) * dx));
    double d3 = 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 = fabs(atan2(y4 - y3, x4 - x3) - 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 = fabs(atan2(y3 - y2, x3 - x2) - 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   = atan2(y3 - y2, x3 - x2);
            da1 = fabs(k - atan2(y2 - y1, x2 - x1));
            da2 = fabs(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));
}

}