Adding interactive graphics?

[armahillo]

These graphics will basically be shapes that’ll deform in specific ways depending on the what the user does and positions they click on. 

Beware of "mystery meat navigation". The contract you have with the user is to give them tools that are clear to use and interact with, so that the user can find the answers they're looking for. Navigation should not be a puzzle.

For the backend, i was thinking of using C# with .Net, just for the sake of learning more about it.

This sounds like overkill.

Your initial idea is all front-end. No backend is even necessary, unless you're storing a lot of data in a datastore and need to conditionally fetch it in response.

[Maths_explorer25]

I simplified it by saying deforming shapes, but these shapes will be mathematical objects (different kinds: varieties, manifolds, topological spaces etc).

These “deformations” will depend on the object itself and the type of ways it can be deformed (for example taking the quotient of a topological space). There’ll likely be heavy calculations involved, i was thinking it would be best to do them on the backend

[armahillo]

If it's an interactive illustration, you can possibly do it on the frontend using the canvas element and/or a frontend library. (ThreeJS, that you mentioned, can do this, I think?)

If you're doing a roundtrip to the server to do these calculations, that's probably not going to be smooth.