• Corpus ID: 211010499

Non-Euclidean Virtual Reality IV: Sol

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

Virtual reality simulations of curved spaces

The present article presents a solution to the body coherence problem, as well as several other questions that arise in interactive VR simulations in curved space.

Illustrations of non-Euclidean geometry in virtual reality

In virtual reality, users have completely new opportunities to encounter geometric properties and effects that are not present in their surrounding Euclidean world.

Modeling and rendering non-euclidean spaces approximated with concatenated polytopes

The proof-of-concept implementation and experiments show that the proposed methods bring the virtual-world users unusual and fascinating experiences, which cannot be provided in Euclidean-space applications.

Visualization of Nil, Sol, and SL2(R)˜ geometries

Real-Time Visualization in Anisotropic Geometries

Novel methods for real-time native geodesic rendering of anisotropic geometries and similar geometry, Nil, twisted are presented and efficient methods for computing the inverse exponential mapping are used.

Real-Time Visualization in Non-Isotropic Geometries

Novel methods of computing real-time native geodesic rendering of non-isotropic geometries are presented and can be applied not only to visualization, but also are essential for potential applications in machine learning and video games.

Ray-Marching Thurston Geometries

Algorithms that produce accurate real-time interactive in-space views of the eight Thurston geometries using ray-marching are described and a theoretical framework for these algorithms is given, independent of the geometry involved.

How to see the eight Thurston geometries

This paper proposes a technique for immersive visualization of relevant three-dimensional manifolds in the context of the Geometrization conjecture that generalizes traditional computer graphics ray tracing.



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