/***************************************************/
private static double IntegrateRegion(Arc arc, int powX, double tol = Tolerance.Distance)
{
Point centre = arc.CoordinateSystem.Origin;
double r = arc.Radius;
Point start = arc.StartPoint();
Point end = arc.EndPoint();
double a = Vector.XAxis.Angle(start - centre, Plane.XY);
double k = Math.Abs(arc.Angle());
if ((start - centre).CrossProduct(arc.StartDir()).Z < 0)
{
k *= -1;
}
switch (powX)
{
case 0:
return(
centre.X * r * (-Math.Sin(a) + Math.Sin(a + k)) +
(r * r * (2 * k - Math.Sin(2 * a) + Math.Sin(2 * (a + k)))
) / 4);
/********************/
case 1:
return((r * (
(Math.Sin(3 * (k + a)) + 9 * Math.Sin(k + a) -
Math.Sin(3 * a) - 9 * Math.Sin(a)) * r * r +
6 * (Math.Sin(2 * (k + a)) + 2 * k - Math.Sin(2 * a)) * centre.X * r +
12 * (Math.Sin(k + a) - Math.Sin(a)) * centre.X * centre.X
)) / 24);
/********************/
case 2:
return((r * (
(Math.Sin(4 * (k + a)) + 8 * Math.Sin(2 * (k + a)) + 12 * k - Math.Sin(4 * a) -
8 * Math.Sin(2 * a)) * r * r * r -
32 * (Math.Sin(k + a) * (Math.Sin(k + a) * Math.Sin(k + a) - 3) +
(Math.Cos(a) * Math.Cos(a) + 2) * Math.Sin(a)) * centre.X * r * r +
24 * (Math.Sin(2 * (k + a)) + 2 * k - Math.Sin(2 * a)) * centre.X * centre.X * r +
32 * (Math.Sin(k + a) - Math.Sin(a)) * centre.X * centre.X * centre.X
)) / 96);
/********************/
default:
return(IntegrateRegion(arc.CollapseToPolyline(0.01), powX, tol)); //TODO is this good value??
}
}
/***************************************************/
private static Polyline Divide(this Arc arc, double angleTolerance, double baseTolerance, int maxDivisionsPerSegment = 200)
{
return(arc.CollapseToPolyline(Soften(arc.Radius, angleTolerance, baseTolerance), maxDivisionsPerSegment));
}
