I've always done those computations myself, having started out way before canned software was available.
Just in case you or others might want to try this as a sorta visualization ~exercise~ here's the technique that most old-school mechanical engineers use:
Imagine your scope and accessories spinning like a multi-axis, multi-dimensional propeller about all possible axes (e.g. RA, Dec, OTA, etc.) full 360 on all of them, all possible phase combinations That makes it clear that would generate a spherical envelope, centered on the point where the RA, Dec axes intersect. That places an upper bound on how big the interior of your dome wants to be, and where to place the pier. Now, take into account the actually-used phase combinations, discarding the rest. This allows you to pull sections of that spherical envelope inward... and that may be circumscribable by a sphere that is smaller than the original one, defining a least upper bound on the needed dome interior size, and a (possibly new) location for the pier (typically S or N of dome center).
My domes are geodesic, so I had to perform the additional step of visualizing rotations of the dome itself, and solving for the largest sphere entirely circumscribable by that.
Then, as a last step... add some comfortable margin... and build!
I carefully did all that, even for this latest scope, which very comfortably clears the dome by about ten inches, all around! Nice to know that it can never bump into anything, other than ladders, people... and maybe itself! Tom