My group has discussed a pill-capsule shape.
I think the last time the subject came up we decided it was not actually taking a shape; the circle affects the bodies/objects on the circle. A Ward Against Birds would not affect a bird flying by, but the bird cannot land on the circle or affect anything in it.
So, going with the disk idea...it wards the disk, and things on the disk are included. In your group's disk-ward, how would it affect a tree with extending branches?
So, you circle the tree with a ward; how does the ward affect the branches and roots?
One might wonder the same thing of a circle ward on the inner wall of a torus or the wall of a round room.
One might say, the effect affects everything in the circle, so extending beyond the circle is no problem. That seems odd, since it implies a ward on a finger-ring would protect someone wearing the ring.
Good question; will have to pose it.
My first thought is that it affects a whole Individual of that Form (although a Circle can affect more than one person or object, so that's odd), but that still leaves the finger-ring issue. Maybe that's not a big deal.
I can't imagine this is going to be anything other than a highly personalized answer. Just about everything proposed here is reasonable.
Were it my saga, I'd probably go with the following.
"The ring covers an area twice as tall as it's diameter. The upper half of that is a demisphere. It also covers about half that area beneath it.
If it's upperside collides with the underside of another ring, or if it's underside collides with the topside of another ring, the underside shall give way entirely to the upperside. If it's space collides with another Ring and the previous case does not apply, the coverage is divided proportionally.
In cases where an item extends out of these bounds, it shall still be fully affected provided the core of it is within (head and heart for humans, for example, or the trunk of a tree, so on so forth..) and no more than one part in (seven/ten at your discretion - ten is my default but other numbers are good if they hold significance to the character or to magic in the saga) is outside the circle. If it is not fully protected, then depending on the nature of the ward and the effects it is protecting against, either the whole of the object shall be unprotected, or only those parts outside the area of the ring shall be unprotected."
It's far from perfect and has a lot of leeway, though. It does cut down on some of the case by case arbitration, but a player can still drive a truck through it.
For entertainment, whenever these questions came up in game, I told players that they didn't know the answers, and should experiment in the lab to figure it out. <,< They hated that answer.
I like it, though I'd probably have gone with a magic theory check.
I admit it's not a GOOD answer. Though interetingly enough, now I'm wondering about experimentation changing the way Ring/Circle works as a side effect.
Yes, declare inside a boundary v. outside a boundary like a mathematician would! Make a little circle around yourself, declare yourself outside, affect the rest of the world...
Going full Zeno here, aren't you? I was more thinking of a spell with T: Circle that affects things in the circle-plane, so the branching tree can extend beyond...
Mathematically that is no less frustrating or useful than wondering how circles interact with regio boundaries the move within or the allowance of summoning something into them.
"Several centuries from now a man named Sir Isaac newton will invent a new mathematics called Calculus, after this has been accomplished there will be a better answer as to how the circle/ ring target and duration work, until then we simply have records of examples."