/// <summary>Returns closest T value to point by binary search</summary>
internal static float FindNearestApproachToPoint(PointF test, PointF[] P, float maximumError = 0.001f)
{
float lowT = 0;
float hiT = 1;
float lowDistance = Geometry.DistanceBetween(test, P[0]);
float hiDistance = Geometry.DistanceBetween(test, P[3]);
float half = 0;
while (hiT - lowT > maximumError)
{
half = (lowT + hiT) / 2;
PointF newPoint = Bezier.GetPoint(P, half);
float testDistance = Geometry.DistanceBetween(test, newPoint);
if (lowDistance > hiDistance)
{
lowDistance = testDistance;
lowT = half;
}
else
{
hiDistance = testDistance;
hiT = half;
}
}
return(half);
}
private float CalculateError(PointF[] P, PointF[] points)
{
// calculates the sum of the squares of the distances from the points to the line
float error = 0;
// the first and last points in points should be the endpoints of the curve itself, so we don't need to check how far these are from the line!
Debug.Assert(P[0] == points[0] && P[3] == points[points.Length - 1]);
for (int index = 1; index <= points.Length - 1 - 1; index++)
{
PointF pt = points[index];
float T = Bezier.FindNearestApproachToPoint(pt, P);
PointF curve = Bezier.GetPoint(P, T);
error += (pt.X - curve.X) * (pt.X - curve.X) + (pt.Y - curve.Y) * (pt.Y - curve.Y);
}
return(error);
}
private PointF GetPoint(int vertex, float T)
{
// Like the above function, but using a given arc from this object
return(Bezier.GetPoint(Vertices[vertex], Vertices[vertex + 1], m_ControlPoints[vertex * 2], m_ControlPoints[vertex * 2 + 1], T));
}
