Intersection position of 2 spheres

[Skybar]

I'm trying to find the position where 2 spheres intersect eachother. Just a location in the middle. If they both have the same radius it's pretty straightforward, I put both centroids into a Mix VOP with bias at 0.5. But if they're NOT the same radius I just can't figure it out. I suppose I need some sort of bias towards the smaller sphere, but I don't know where to get that from. I'm sure it's possible to calculate somehow from the centroids and radii, at least I think so but I can't get it right. Dialling it in manually doesn't really work when the spheres move. Does anyone have a clue?

[dimovfx]

I'm sure it's all wrong, but for a quickie should work

someone better at math should help

middle_point.hip

[Skybar]

@sasho78 Hey thanks! Yeah that's about how far I've gotten as well. See picture what I mean. For same size spheres it works perfectly, but when they're not it's a little bit off.

[vtrvtr]

Sorry if this kind of answer isn't allowed, but this link explains it fairly straight forwardly 

 

 

[konstantin magnus]

You can point a normal from one sphere's center to the other and multiply that by its own radius plus half the overlap of the spheres radii.

float rad_1 = ch("../sphere1/scale");
float rad_2 = ch("../sphere2/scale");

@N = normalize(@opinput1_P - @P);
@dist = distance(@P, @opinput1_P);
@diff = @dist - (rad_1 + rad_2);
@ibtw = rad_1 + ( @diff / 2 );

vector pos = @P + (@N * @ibtw );
addpoint(0, pos);

intersect_spheres.hipnc

Edited January 31, 2017 by konstantin magnus
added hip file

[f1480187]

Another way:

vector sphere_x_sphere_pos(vector a, b; float rada, radb)
{
    vector delta = b - a;
    float dist = length(delta);
    float x_dist = (rada*rada - radb*radb + dist*dist) / (2 * dist);
    vector x_pos = a + normalize(delta) * x_dist;
    return x_pos;
}

Check this thread for hips.

[Skybar]

@vtrvtr @konstantin magnus @f1480187 This looks great! I'll look into it a bit later tonight, thanks a lot!