• Corpus ID: 211010499

Non-Euclidean Virtual Reality IV: Sol

@article{Coulon2020NonEuclideanVR,
  title={Non-Euclidean Virtual Reality IV: Sol},
  author={R{\'e}mi Coulon and Elisabetta A. Matsumoto and Henry Segerman and Steve J. Trettel},
  journal={ArXiv},
  year={2020},
  volume={abs/2002.00369}
}
This article presents virtual reality software designed to explore the Sol geometry. The simulation is available on 3-dimensional.space/sol.html 

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References

SHOWING 1-10 OF 14 REFERENCES

Non-euclidean virtual reality I: explorations of $\mathbb{H}^3$

We describe our initial explorations in simulating non-euclidean geometries in virtual reality. Our simulations of three-dimensional hyperbolic space are available at this http URL.

Non-euclidean virtual reality II: explorations of $\mathbb{H}^2\times\mathbb{E}$

We describe our initial explorations in simulating non-euclidean geometries in virtual reality. Our simulation of the product of two-dimensional hyperbolic space with one-dimensional euclidean space

Non-euclidean Virtual Reality II: Explorations of H² ✕ E

The goal is to make three-dimensional non-euclidean spaces feel more natural by giving people experiences inside those spaces, including the ability to move through those spaces with their bodies, particularly for users who are not familiar with moving through space using “computer game” controls.

The spheres of Sol

Let Sol be the three-dimensional solvable Lie group equipped with its standard left-invariant Riemannian metric. We give a precise description of the cut locus of the identity, and a maximal domain

L'horizon de SOL

The goal of this paper is to give an explicit analysis of the geodesic flow on the three dimensional Lie group SOL. In particular we describe its horizon. (The horizon of a riemannian manifold is a

Visualizing hyperbolic space: unusual uses of 4x4 matrices

Formulas for computing reflections, translations, and rotations in hyperbolic space are presented, which emphasizes the need for graphics libraries which allow completely arbitrary 4 X 4 transformations.

Non - euclidean virtual reality II : explorations of H 2 × E Visualizing Hyperbolic Space : Unusual Uses of 4 x 4 Matrices Troyanov . “ L ’ horizon de SOL . ” Exposition

    HyperRogue: Thurston Geometries.

    • 2019

    Curved Spaces

      Espaces Imaginaires.

      • http://espaces-imaginaires.fr
      • 2015