Related Academic Research

N-Dimensional Rigid Body Dynamics

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.

Geometry Independent Game Encapsulation for Non-Euclidean Geometries

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.

Illustrations of Non-Euclidean Geometry in Virtual Reality

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.

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1. N-Dimensional Rigid Body Dynamics

2. Geometry Independent Game Encapsulation for Non-Euclidean Geometries

3. Illustrations of Non-Euclidean Geometry in Virtual Reality

4. Real-Time Non-Euclidean Ray Tracer Illusions

5. The Foundations of Geometry and the Non-Euclidean Plane

6. Rendering Non-Euclidean Space in Real-Time Using Spherical and Hyperbolic Trigonometry

7. Incorporation of Non-euclidean Distance Metrics into Fuzzy Clustering on Graphics Processing Units

8. Non-Euclidean Billiards in VR

9. Immersive Visualization of the Classical Non-Euclidean Spaces using Real-Time Ray Tracing

10. Discrete Geometric Mechanics for Variational Time Integrators

11. A Survey of the Use of Non-Euclidean Geometry in Electrical Engineering

12. Non-Euclidean Virtual Reality III: Nil

13. Artistic Patterns in Hyperbolic Geometry

14. Non-Euclidean Geometry in the Modeling of Contemporary Architectural Forms

15. Non-Euclidean Virtual Reality I: Explorations of ℍ3

16. Understanding Curved Spacetime

17. Elementary Mathematics from an Advanced Standpoint: Geometry

18. Euclid’s Elements

19. Trigonometry in the Hyperbolic Plane

20. Rendering non-Euclidean space in realtime using spherical and hyperbolic trigonometry

Image used: https://store.steampowered.com/app/619210/4D_Toys/