private static float MaxErrorLocation(ArcOfSphere arc, float begin, float end)
{
Vector2 L1 = SpaceConverter.SphereToUV(arc.Evaluate(begin));
Vector2 L2 = SpaceConverter.SphereToUV(arc.Evaluate(end));
// 2) use binary / bisection search to find the point of maximal error
while (end - begin > delta)
{
float midpoint = (begin + end) / 2;
float error_left = Point_Line_Distance(L1, L2, SpaceConverter.SphereToUV(arc.Evaluate(midpoint - delta)));
float error_right = Point_Line_Distance(L1, L2, SpaceConverter.SphereToUV(arc.Evaluate(midpoint + delta)));
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
}
public static void AddLine(ArcOfSphere edge, float begin, float end)
{
Vector2 begin_UV = SpaceConverter.SphereToUV(edge.Evaluate(begin));
Vector2 end_UV = SpaceConverter.SphereToUV(edge.Evaluate(end));
if (Vector2.Distance(begin_UV, end_UV) > threshold)
{
Vector2 delta_begin_UV = SpaceConverter.SphereToUV(edge.Evaluate(begin + 64 * delta));
Vector2 delta_end_UV = SpaceConverter.SphereToUV(edge.Evaluate(end - 64 * delta));
Vector2 control_point = Intersection(begin_UV, delta_begin_UV, delta_end_UV, end_UV);
DebugUtility.Log("AddLine:", begin_UV, end_UV);
lines.Add(new QuadraticBezier(edge, begin_UV, control_point, end_UV, begin, end));
}
}
private static void Subdivide(ArcOfSphere arc, float begin, float end)
{
float midpoint = MaxErrorLocation(arc, begin, end);
Vector2 L1 = SpaceConverter.SphereToUV(arc.Evaluate(begin));
Vector2 L2 = SpaceConverter.SphereToUV(arc.Evaluate(end));
Vector2 P = SpaceConverter.SphereToUV(arc.Evaluate(midpoint));
if (Point_Line_Distance(L1, L2, P) > 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, midpoint);
Subdivide(arc, midpoint, end);
}
else
{
AddLine(arc, begin, end);
}
}