In N-Dimensional Rigid Body Dynamics, Bosch extends the geometric algebra-based formulate from 3D matrices to higher dimensional matrices to compute physical simulation and collision detection in 4D spaces. Using n-dimensional rotors to represent rotations as a replacement for quaternions in 3D spaces, using Gauss’ theorem[Dobrovolskis 1996] to simplify the inertia tensor in n-dimensional mesh generalization, and using sphere/convex-object collision detection, Bosch is able to achieve the underlying physics logic for game Miegakure and 4D Toys.
In Geometry Independent Game Encapsulation for Non-Euclidean Geometries, Guimaraes, Mello, and Velho explore the rendering of hyperbolic space on a 2D screen perspective. Taking the ideas inspired by the non-euclidean game HyperRogue, this project uses a hyperbolic octagon as the hyperbolic space representation and renders classical games like Asteroids in non-Euclidean geometric models, utilized in its screen representation.
In Illustrations of Non-Euclidean Geometry in Virtual Reality, Martin Skrodzki presents the virtual reality illustrations of hyperbolic geometry. Eliminating the coexistence between different geometrical setups by providing a fully immersive experience of the non-Euclidean space, virtual reality can provide interactive visualization through mapping hands and placing objects.