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//----------------------------------------------------------------------------
// 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));
}
}