Non-euclidean Virtual Reality II: Explorations of H² ✕ E
Inhaltsverzeichnis
Referenz
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.
Links
Full Text
http://archive.bridgesmathart.org/2017/bridges2017-41.pdf
