public static Double2[] CircleLineIntersection(Double2 c1, double r1, Double2 c, Double2 v)
{
// Firstly, rotate the second circle so it stands on the X-axis
var rot = v.Normalized;
// Get the displacement
var y = -(c - c1).Cross(rot);
var xs = r1 * r1 - y * y;
// No intersection if this is negative
if (xs < 0)
{
return(new Double2[0]);
}
else
{
var x = Math.Sqrt(xs);
var pos = new Double2[] { new Double2(x, y), new Double2(-x, y) };
// Project back to the new position
return(pos.Select(p => c1 + p.RotScale(rot)).ToArray());
}
}
public static Double2[] CircleIntersection(Double2 c1, double r1, Double2 c2, double r2)
{
// Firstly, rotate the second circle so it stands on the X-axis
var rot = (c2 - c1).Normalized;
// Get the displacement
var a = (c2 - c1).Dot(rot);
var x = (r1 * r1 + a * a - r2 * r2) / (2 * a);
var ys = r1 * r1 - x * x;
// No intersection if this is negative
if (ys < 0)
{
return(new Double2[0]);
}
else
{
var y = Math.Sqrt(ys);
var pos = new Double2[] { new Double2(x, y), new Double2(x, -y) };
// Project back to the new position
return(pos.Select(p => c1 + p.RotScale(rot)).ToArray());
}
}