private static float max_error_location(Arc arc, float begin_point_angle, float end_point_angle)
{
OctahedronUVCoordinates begin_point = new NormalizedCartesianCoordinates(arc.position(begin_point_angle));
OctahedronUVCoordinates end_point = new NormalizedCartesianCoordinates(arc.position(end_point_angle));
float begin = begin_point_angle;
float end = end_point_angle;
// 2) use binary / bisection search to find the point of maximal error
while (end - begin > Precision.delta)
{
float midpoint = (begin + end) / 2;
OctahedronUVCoordinates left_midpoint = new NormalizedCartesianCoordinates(arc.position(midpoint - Precision.delta));
OctahedronUVCoordinates right_midpoint = new NormalizedCartesianCoordinates(arc.position(midpoint + Precision.delta));
float error_left = PlanetariaMath.point_line_distance(begin_point.data, end_point.data, left_midpoint.data);
float error_right = PlanetariaMath.point_line_distance(begin_point.data, end_point.data, right_midpoint.data);
if (error_left < error_right) //error begin should be replaced since it has less error
{
begin = midpoint;
}
else //error end should be replaced since it has less error
{
end = midpoint;
}
}
return((begin + end) / 2); // return location of max error
}
private static void subdivide(Arc arc, float begin_point_angle, float end_point_angle)
{
float middle_point_angle = max_error_location(arc, begin_point_angle, end_point_angle);
Vector3 begin = arc.position(begin_point_angle);
Vector3 middle = arc.position(middle_point_angle);
Vector3 end = arc.position(end_point_angle);
OctahedronUVCoordinates begin_point = new NormalizedCartesianCoordinates(begin);
OctahedronUVCoordinates middle_point = new NormalizedCartesianCoordinates(middle);
OctahedronUVCoordinates end_point = new NormalizedCartesianCoordinates(end);
if (PlanetariaMath.point_line_distance(begin_point.data, end_point.data, middle_point.data) > Precision.threshold) // if the max error is greater than a threshold, recursively add the left and right halves into the list of lines
{
subdivide(arc, begin_point_angle, middle_point_angle);
subdivide(arc, middle_point_angle, end_point_angle);
}
else
{
QuadraticBezierCurve curve = new QuadraticBezierCurve(begin_point.data, middle_point.data, end_point.data);
VectorGraphicsWriter.set_edge(curve);
}
}
