Feels more organic to me if the original metaball gets smaller as the other one moves out (like its stealing material). Haven't worked out the correct math but a quick PoC is here:
Keeping 100% accurate constant area would require a pretty insane closed form equation. Even ignoring the amount of area added by the stretched portions.
Yes, in this case a numeric approach would probably be the way to go:
- Assume that R1, R2 are the radii of the discs and A_ORIG is the original area (eg. R1^2 PI)
- Calculate the area A for a given R1, R2
- Multiply R1 and R2 with SQRT(A_ORIG / A)
- Repeat
If this doesn't converge after a few iterations, you can use the Newton method, or even a simple binary search to find he correct radii very quickly. A(k R1, k R2) should be monotonic for k, so solving it numerically for a given value should be trivial.
https://codepen.io/femto113/pen/MEZava