/// <summary>
/// Interpolate a Bezier segment with a given precision
/// </summary>
/// <param name="i">Index first point of Bezier segment</param>
/// <param name="precision">precision</param>
/// <param name="points">List of points where to add new points for the segment</param>
private void InterpolateSegment(int i, double precision, List <PointD> points)
{
PointD P0, P1, P2, P3;
double maxMedianLengthSqr = Math.Max(
ControlPoints[i + 1].Median(ControlPoints[i], ControlPoints[i + 2]).LengthSqr(),
ControlPoints[i + 2].Median(ControlPoints[i + 1], ControlPoints[i + 3]).LengthSqr()
);
if (maxMedianLengthSqr <= 0.25 * precision * precision)
{
points.Add(ControlPoints[i + 3]);
return;
}
double cnt = Math.Min((int)Math.Sqrt(Math.Sqrt(maxMedianLengthSqr) / precision) + 3, 1500);
double d = 1 / cnt;
P0 = ControlPoints[i];
P1 = DeCasteljau(i, d);
points.Add(P1);
P2 = DeCasteljau(i, 2 * d);
points.Add(P2);
P3 = DeCasteljau(i, 3 * d);
points.Add(P3);
P0 = P1.Substract(P0);
P1 = P2.Substract(P1);
P2 = P3.Substract(P2);
//
P0 = P1.Substract(P0);
P1 = P2.Substract(P1);
//
P0 = P1.Substract(P0);
for (int j = 4; j <= (int)cnt; j++)
{
P1 = P1.Addition(P0);
P2 = P2.Addition(P1);
P3 = P3.Addition(P2);
points.Add(P3);
}
}
