/// <summary>
/// Calculates the points of intersection between 2 CircleF objects</summary>
/// <param name="c1">First CircleF</param>
/// <param name="c2">Second CircleF</param>
/// <param name="p1">First intersection point</param>
/// <param name="p2">Second intersection point</param>
/// <returns>True iff there are 1 or 2 intersection points; false if there are none or an infinite number</returns>
public static bool Intersect(CircleF c1, CircleF c2, ref Vec2F p1, ref Vec2F p2)
{
Vec2F v1 = c2.Center - c1.Center;
double d = v1.Length;
const double EPS = 1.0e-6;
if (d < EPS ||
d > c1.Radius + c2.Radius)
{
return(false);
}
v1 *= (float)(1 / d);
Vec2F v2 = v1.Perp;
double cos = (d * d + c1.Radius * c1.Radius - c2.Radius * c2.Radius) / (2 * c1.Radius * d);
double sin = Math.Sqrt(1 - cos * cos);
Vec2F t1 = Vec2F.Mul(v1, (float)(c1.Radius * cos));
Vec2F t2 = Vec2F.Mul(v2, (float)(c1.Radius * sin));
p1 = c1.Center + t1 + t2;
p2 = c1.Center + t1 - t2;
return(true);
// From http://mathforum.org/library/drmath/view/51710.html
// First, let C1 and C2 be the centers of the Circlefs with radii r1 and
// r2, and let d be the distance between C1 and C2.
//
// Now let V1 be the unit vector from C1 to C2, and let V2 be the unit
// vector perpendicular to V1.
//
// Also let V3 be the vector from C1 to one of the intersection points.
//
// Finally, let A be the angle between V1 and V3.
//
// From the law of cosines we know that
//
// r2^2 = r1^2 + d^2 - 2*r1*d*cos(A)
//
// With this equation we can solve for 'A'.
//
// The intersection points will be
//
// C1 + [r1*cos(A)]*V1 + [r1*sin(A)]*V2
//
// C1 + [r1*cos(A)]*V1 - [r1*sin(A)]*V2
// a simple unit test
// CircleF test1 = new CircleF(new Vec2F(-0.5f, 0), 1);
// CircleF test2 = new CircleF(new Vec2F(0.5f, 0), 1);
// Vec2F result1 = new Vec2F();
// Vec2F result2 = new Vec2F();
// CircleF.Intersect(test1, test2, ref result1, ref result2);
}
/// <summary>
/// Projects a point onto a circle</summary>
/// <param name="p">Point to project</param>
/// <param name="c">Circle to project onto</param>
/// <param name="projection">Projected point</param>
/// <returns>True iff projection is well defined</returns>
public static bool Project(Vec2F p, CircleF c, ref Vec2F projection)
{
Vec2F d = Vec2F.Sub(p, c.Center);
float length = d.Length;
bool wellDefined = false;
if (length > 0.000001f * c.Radius)
{
wellDefined = true;
float scale = c.Radius / length;
projection = Vec2F.Add(c.Center, Vec2F.Mul(d, scale));
}
return(wellDefined);
}
