public static Circle2d[] CirclePointPoint(Circle2d ci, Point2d pt1, Point2d pt2)
{
// Solution by Robert.P. 2013-02-10
// solved by intersecting the line which has equal distance to pt1 and pt2 at every point,
// with the hyperbola that has equal distance to ci and pt1 at every point.
List <Circle2d> res = null;
//get squared constants of hyperbola
double c2 = ci.Center.SquaredDistance(pt1) / 4.0; //center->focus distance squared
double a = 0.5 * ci.Radius;
double b = Math.Sqrt(c2 - a * a);
if (double.IsNaN(b))
{
return(null); //negative square root, no such hyperbola
}
// this hyperbola has equal distance to ci and pt1 at every point.
// it also has focus at ci.Center and pt1
Hyperbola2d hyper = new Hyperbola2d(new Point2d((ci.X + pt1.X) * 0.5, (ci.Y + pt1.Y) * 0.5), a, b, ci.Center.Angle(pt1));
//get constants of line dx+ey+f=0, which is equal distance from p1,p2 on every point
double dx = pt2.X - pt1.X, dy = pt2.Y - pt1.Y;
double mx = pt1.X + dx * 0.5;
double my = pt1.Y + dy * 0.5;
Line2d perp = new Line2d(mx, my, mx - dy, my + dx); //starts from mipoint pt1-pt2 and is perpendicular to that line
var intpts = Intersect2d.HyperbolaLine(hyper, perp);
if (intpts == null)
{
return(null);
}
foreach (Point2d intpt in intpts)
{
AddResult(ref res, intpt.X, intpt.Y, intpt.Distance(pt1));
}
return(MakeResult(res));
}
