path: root/svg-flatten/src/flatten.cpp

/* Copied from Antigrain Graphics (AGG) v2.4 */
/* Mirror: https://github.com/pelson/antigrain/blob/master/agg-2.4/src/agg_curves.cpp */

#include <flatten.hpp>
#include <cmath>

using namespace gerbolyze;

namespace gerbolyze {
    const double curve_collinearity_epsilon              = 1e-15;
    const double curve_angle_tolerance_epsilon           = 0.1;
    constexpr unsigned curve_recursion_limit             = 20;
}

static inline double calc_sq_distance(double x1, double y1, double x2, double y2)
{
    double dx = x2-x1;
    double dy = y2-y1;
    return dx * dx + dy * dy;
}

/* Quadratic beziers */

void curve3_div::run(double x1, double y1, double x2, double y2, double x3, double y3)
{
    m_points.clear();
    m_points.emplace_back(d2p{x1, y1});
    recursive_bezier(x1, y1, x2, y2, x3, y3, 0);
    m_points.emplace_back(d2p{x3, y3});
}

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;
    double pi = M_PI;

    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.emplace_back(d2p{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.emplace_back(d2p{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.emplace_back(d2p{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); 
}


/* Cubic beziers */

void curve4_div::run(double x1, double y1, double x2, double y2, double x3, double y3, double x4, double y4)
{
    m_points.clear();
    m_points.emplace_back(d2p{x1, y1});
    recursive_bezier(x1, y1, x2, y2, x3, y3, x4, y4, 0);
    m_points.emplace_back(d2p{x4, y4});
}

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;
    }

    double pi = M_PI;

    // 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.emplace_back(d2p{x2, y2});
                return;
            }
        } else {
            if(d3 < m_distance_tolerance_square) {
                m_points.emplace_back(d2p{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.emplace_back(d2p{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.emplace_back(d2p{x2, y2});
                m_points.emplace_back(d2p{x3, y3});
                return;
            }

            if(m_cusp_limit != 0.0) {
                if(da1 > m_cusp_limit)
                {
                    m_points.emplace_back(d2p{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.emplace_back(d2p{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.emplace_back(d2p{x2, y2});
                m_points.emplace_back(d2p{x3, y3});
                return;
            }

            if(m_cusp_limit != 0.0) {
                if(da1 > m_cusp_limit) {
                    m_points.emplace_back(d2p{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.emplace_back(d2p{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.emplace_back(d2p{x23, y23});
                return;
            }

            if(m_cusp_limit != 0.0) {
                if(da1 > m_cusp_limit) {
                    m_points.emplace_back(d2p{x2, y2});
                    return;
                }

                if(da2 > m_cusp_limit) {
                    m_points.emplace_back(d2p{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); 
}