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

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Vi Hart, Andrea Hawksley, Elisabetta Matsumoto and Henry Segerman: Non-euclidean Virtual Reality II: Explorations of H² ✕ E. In: Bridges 2017, Pages 41–48.

DOI

Abstract

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 is available at http://h2xe.hypernom.com.

Extended Abstract

Bibtex

@inproceedings{bridges2017:41,
 author      = {Vi Hart, Andrea Hawksley, Elisabetta Matsumoto and Henry Segerman},
 title       = {Non-euclidean Virtual Reality II: Explorations of H\ensuremathVorlage:^2 \ding{53} E},
 pages       = {41--48},
 booktitle   = {Proceedings of Bridges 2017: Mathematics, Art, Music, Architecture, Education, Culture},
 year        = {2017},
 editor      = {David Swart, Carlo H. S\'equin, and Krist\'of Fenyvesi},
 isbn        = {978-1-938664-22-9},
 issn        = {1099-6702},
 publisher   = {Tessellations Publishing},
 address     = {Phoenix, Arizona},
 note        = {Available online at \url{http://archive.bridgesmathart.org/2017/bridges2017-41.pdf}}
}

Used References

[1] Vi Hart, Andrea Hawksley, Elisabetta A. Matsumoto, and Henry Segerman. Non-euclidean virtual reality I: explorations of H3. In Proc. Bridges 2017. Tessellations Publishing, 2017.

[2] Emil Moln´ar. The projective interpretation of the eight 3-dimensional homogeneous geometries. Beitrage zur Algebra und Geometrie (Contributions to Algebra and Geometry), 38(2):261–288, 1997.

[3] Grisha Perelman. The entropy formula for the Ricci flow and its geometric applications. arXiv:0211159.

[4] William P. Thurston. Three-Dimensional Geometry and Topology. Princeton Univ. Press, 1997.

[5] Jeff Weeks. Curved Spaces. a flight simulator for multiconnected universes, available from http://www.geometrygames.org/CurvedSpaces/.

[6] Jeff Weeks. Real-time rendering in curved spaces. IEEE Computer Graphics and Applications, 22(6):90– 99, 2002.


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http://archive.bridgesmathart.org/2017/bridges2017-41.pdf

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