public static Pnt2d FindEllipseCenterFromEndpoints(Pnt2d startPnt, Pnt2d endPnt, double rX, double rY, double angle, bool sense)
{
// https://www.w3.org/TR/SVG/implnote.html#ArcImplementationNotes
// F.6.5.1
var matRotation = new Mat2d();
matRotation.SetRotation(-angle);
var v1 = new XY(startPnt.X - endPnt.X, startPnt.Y - endPnt.Y)
.Multiplied(0.5)
.Multiplied(matRotation);
// F.6.5.2
var denom = rX.Sqr() * v1.Y.Sqr() + rY.Sqr() * v1.X.Sqr();
var numer = rX.Sqr() * rY.Sqr() - denom;
var root = Math.Sqrt(Math.Abs(numer / denom)) * (sense ? -1 : 1);
var c1 = new XY(rX * v1.Y / rY, -(rY * v1.X / rX)).Multiplied(root);
// F.6.5.3
matRotation.SetRotation(angle);
var c = new XY(startPnt.X + endPnt.X, startPnt.Y + endPnt.Y)
.Multiplied(0.5)
.Added(c1.Multiplied(matRotation));
return(c.ToPnt());
}
