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4d and n-dimensional physics engine

Was somebody trying to implement 4d or n-dimension physics realtime (or not) engine?

What difficulties in this implementation, compare to 3d and 2d physics engines? Of course, one of which is presentation problem. Is's an interesting to look at and to find out more about 4d hyperspheres, hypercubes, springs, joints, liquids and other objects.

I am just curious, and not have a real application using it.

Generalization of my idea is physics in lobachevskian or riemann geometries, distortion spaces (you can go through the needle's eye), looped spaces (returning to the same place), physics paradoxes and other amazing things.

Solution

  • An example of a 4D physics engine is 4D Toys, created by Marc ten Bosch.

    enter image description here

    The author goes into more detail about how it works on their blog (see this post about geometric algebra, for instance).

    Their technical paper, N-Dimensional Rigid Body Dynamics, was also accepted to SIGGRAPH 2020.

    I also explained a bit how angular velocity works in higher dimensions here.