//------------------------------------------------------------------------
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 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 recursive_bezier( int x1, int y1, int x2, int y2, int x3, int y3, int level )
{
if( abs( level ) > bezier_recursion_limit )
{
return;
}
// Calculate all the mid-points of the line segments
//----------------------
int x12 = (x1 + x2) / 2;
int y12 = (y1 + y2) / 2;
int x23 = (x2 + x3) / 2;
int y23 = (y2 + y3) / 2;
int x123 = (x12 + x23) / 2;
int y123 = (y12 + y23) / 2;
int dx = x3 - x1;
int dy = y3 - y1;
double d = fabs( ((double) (x2 - x3) * dy) - ((double) (y2 - y3) * dx ) );
double da;
if( d > bezier_curve_collinearity_epsilon )
{
// Regular case
//-----------------
if( d * d <= bezier_distance_tolerance_square * (dx * dx + dy * dy) )
{
// If the curvature doesn't exceed the distance_tolerance value
// we tend to finish subdivisions.
//----------------------
if( bezier_angle_tolerance < bezier_curve_angle_tolerance_epsilon )
{
add_segment( wxPoint( x123, y123 ) );
return;
}
// Angle & Cusp Condition
//----------------------
da = fabs( atan2( (double) ( y3 - y2 ), (double) ( x3 - x2 ) ) -
atan2( (double) ( y2 - y1 ), (double) ( x2 - x1 ) ) );
if( da >=M_PI )
da = 2 * M_PI - da;
if( da < bezier_angle_tolerance )
{
// Finally we can stop the recursion
//----------------------
add_segment( wxPoint( x123, y123 ) );
return;
}
}
}
else
{
// Collinear case
//------------------
da = sqrt_len(dx, dy);
if( da == 0 )
{
d = calc_sq_distance( x1, y1, x2, y2 );
}
else
{
d = ( (double)(x2 - x1) * dx + (double)(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 + (int) d * dx,
y1 + (int) d * dy );
}
if( d < bezier_distance_tolerance_square )
{
add_segment( wxPoint( 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) );
}