agg_curves.cpp

来自「这是VCF框架的代码」· C++ 代码 · 共 572 行 · 第 1/2 页

        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;
        m_distance_tolerance_manhattan = 4.0 / m_approximation_scale;
        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;

        switch((int(d2 > curve_collinearity_epsilon) << 1) +
                int(d3 > curve_collinearity_epsilon))
        {
        case 0:
            // All collinear OR p1==p4
            //----------------------
            if(fabs(x1 + x3 - x2 - x2) +
               fabs(y1 + y3 - y2 - y2) +
               fabs(x2 + x4 - x3 - x3) +
               fabs(y2 + y4 - y3 - y3) <= m_distance_tolerance_manhattan)
            {
                m_points.add(point_d(x1234, y1234));
                return;
            }    
            break;

        case 1:
            // p1,p2,p4 are collinear, p3 is considerable
            //----------------------
            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 considerable
            //----------------------
            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 care
            //-----------------
            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
                //----------------------
                double a23 = atan2(y3 - y2, x3 - x2);
                da1 = fabs(a23 - atan2(y2 - y1, x2 - x1));
                da2 = fabs(atan2(y4 - y3, x4 - x3) - a23);
                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));
    }

}