614 lines
19 KiB
C++
614 lines
19 KiB
C++
|
//----------------------------------------------------------------------------
|
||
|
|
// 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));
|
||
|
|
}
|
||
|
|
|
||
|
|
}
|
||
|
|
|