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/* 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_distance_epsilon = 1e-15;
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;
}
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);
}
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