hi rogerlette

i would go that way:

we have 3 points A, B, C with spheres around them with radiuses r_a, r_b and r_c. a point P has to be on all 3 sphere surfaces to be an intersection point.

so how can we formulate that mathematically?

lets start with a try of describing the relationship of a point P on the surface of a sphere to the center A and radius r_a.

one solution would be to state that the radius r_a is just the distance from A to P (the point on the surface):

length (P - A) = r_a

the same is true for the other spheres (with same point P)

length (P - B) = r_b

length (P - C) = r_c

so we have 3 equations and 3 open variables P.x, P.y and P.z.

so it should be solvable that way.

length(d) = sqrt( d.x*d.x + d.y*d.y + d.z*d.z )

if we know that the radius r_a is positive we can skip the sqrt by sqr-ing the equation

d_a.x*d_a.x + d_a.y*d_a.y + d_a.z*d_a.z = r_a*r_a

with d_a = P - A

…

now it would be good to use a math program to solve the equations for P.x, P.y and P.z.