/// <summary>
/// The geometric center of a 3-dimensional, flat polygon.
/// WARNING: UNTESTED!
/// </summary>
public static V3d ComputeCentroid(this Polygon3d polygon)
{
var pc = polygon.PointCount;
if (pc < 3)
{
return(V3d.Zero);
}
V3d p0 = polygon[0], p1 = polygon[1];
V3d e0 = p1 - p0;
var p2 = polygon[2];
var e1 = p2 - p0;
var normal = e0.Cross(e1);
var area2 = normal.Length;
var centroid = area2 * (p0 + p1 + p2);
p1 = p2; e0 = e1;
for (int pi = 3; pi < pc; pi++)
{
p2 = polygon[pi]; e1 = p2 - p0;
var n = e0.Cross(e1);
var a2 = Fun.Sign(normal.Dot(n)) * n.Length;
area2 += a2;
centroid += a2 * (p0 + p1 + p2);
p1 = p2; e0 = e1;
}
if (area2 > Constant <double> .PositiveTinyValue)
{
return(centroid * (Constant.OneThird / area2));
}
else if (area2 < Constant <double> .NegativeTinyValue)
{
return(centroid * (-Constant.OneThird / area2));
}
else
{
return(V3d.Zero);
}
}
public static Trafo3d FromToRH(Axis from, Axis to)
{
var s = Fun.Sign(((int)to) - ((int)from)); // +/- sin(90°)
return(FromTo(from, to, s));
}