Surface point of collision of two spheres?

  1. Hi!

    I need to calculate the point (or average point) of actual collision between any two spheres of any size and mass in any orientation in space.

    I understand that I can zero things out a bit by assuming that one sphere is centered at (0,0,0).


    OK, I know how to calculate collision detection, I've seen many examples:

    calculate distance from centres and subtract sum of radiuses (radii?? lol)

    public static bool Collision(Sphere A, Sphere B)
    {
    bool results = false;
    Vector3 centerA = new Vector3(A.x, A.y, A.z);
    Vector3 centerB = new Vector3(B.x, B.y, B.z);

    if (centerA.Distance(centerB) < (A.radius + B.radius))
    {
    results = true;
    }
    return results;
    }



    and I know how to caculate point on sphere:

    public static Vector3 GetPointOnSphere(Vector3 sphereOrigin, double radius, double theta, double psi)
    {
    Vector3 results = new Vector3();

    if ((psi >= 0 && psi <= (2 * Math.PI)) && (theta >= 0 && theta <= Math.PI))
    {
    // x = x0 + r * Sin theta * cos psi
    // y = y0 + r * sin theta * sin psi
    // z = z0 + r * cos theta
    results.X = sphereOrigin.X + radius * Math.Sin(theta) * Math.Cos(psi);
    results.Y = sphereOrigin.Y + radius * Math.Sin(theta) * Math.Sin(psi);
    results.X = sphereOrigin.X + radius * Math.Cos(theta);
    }
    return results;
    }

    so, I guess I want to find psi and theta from the theoretical new line that stretches between the centres of both spheres. If sphere 2 is at 0,0,0, then what are the 2 angles that describes the direction to the centre of sphere 1?

    Help!

    (ps - yes I use Richard Potter's Vector3 class from CodeProject.com - thanks!!)
     
  2. jcsd
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