Surface point of collision of two spheres?

[rachmann]

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!)

 

[LightHero]

The angles you'll need are the polar coordinates of the vector from sphere 1 to sphere 2. You can get them by taking the arctangent of the ratio of the components of the vector. For example, if the vector is (x,y,z) then the angles would be theta = arctan(z/y) and psi = arctan(x/y).