HyperRogue: Playing with Hyperbolic Geometry
Inhaltsverzeichnis
Referenz
Eryk Kopczyński, Dorota Celińska and Marek Čtrnáct: HyperRogue: Playing with Hyperbolic Geometry. In: Bridges 2017, Pages 9–16.
DOI
Abstract
HyperRogue is a computer game whose action takes place in the hyperbolic plane. We discuss how HyperRogue is relevant for mathematicians, artists, teachers, and game designers interested in hyperbolic geometry.
Extended Abstract
Bibtex
@inproceedings{bridges2017:9,
author = {Eryk Kopczy\'{n}ski, Dorota Celi\'{n}ska and Marek \v{C}trn\'{a}ct},
title = {HyperRogue: Playing with Hyperbolic Geometry},
pages = {9--16},
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/bridges2017-9.pdf}}
}
Used References
[1] Thomas Bl¨asius, Tobias Friedrich, Anton Krohmer, and S¨oren Laue. Efficient embedding of scale-free graphs in the hyperbolic plane. In European Symposium on Algorithms (ESA), pages 16:1–16:18, 2016.
[2] Vladimir Bulatov. Conformal models of the hyperbolic geometry, 2010. Available online at http: //bulatov.org/math/1001/index.html (as of Jan 20, 2017).
[3] Dorota Celi´nska and Eryk Kopczy´nski. Programming languages in GitHub: a visualization in hyperbolic plane. In Proceedings of ICWSM 2017, Montreal, Canada, May 16-18, 2017. To appear.
[4] H. S. M. Coxeter. The non-Euclidean symmetry of Escher’s picture Circle Limit III. Leonardo, 12:19– 25, 1979.
[5] David L. Craddock. Dungeon Hacks: How NetHack, Angband, and Other Roguelikes Changed the Course of Video Games. Press Start Press, 1st edition, 2015.
[6] Chamberlain Fong. The conformal hyperbolic square and its ilk. In Proceedings of Bridges 2016: Mathematics, Music, Art, Architecture, Education, Culture, pages 179–186. Tessellations Publishing.
[7] Alain Fournier, Don Fussell, and Loren Carpenter. Computer rendering of stochastic models. Commun. ACM, 25(6):371–384, June 1982.
[8] Vi Hart, Andrea Hawksley, Elisabetta A. Matsumoto, and Henry Segerman. Non-euclidean virtual reality I: explorations of H3. In Proceedings of Bridges 2017: Mathematics, Music, Art, Architecture, Culture. Tessellations Publishing, 2017.
[9] D. W. Henderson and Daina Tamina. Crocheting the hyperbolic plane. Mathematical Intelligencer, 23(2):17–28, 2001.
[10] Douglas R. Hofstadter. Godel, Escher, Bach: An Eternal Golden Braid. Basic Books, Inc., 1979.
[11] T. Hughes, Y. Hyun, and D. Liberles. Visualising very large phylogenetic trees in three dimensional hyperbolic space. BMC Bioinformatics, 5:48, Apr 2004. http://www.caida.org/tools/visualization/walrus/gallery1/.
[12] John Lamping, Ramana Rao, and Peter Pirolli. A focus+context technique based on hyperbolic geometry for visualizing large hierarchies. In Proceedings of the SIGCHI Conference on Human Factors in Computing Systems, CHI ’95, pages 401–408, New York, NY, USA, 1995. ACM Press/Addison-Wesley Publishing Co.
[13] David Madore, 2013. http://www.madore.org/~david/math/hyperbolic-maze.html (Jan 27, 2017).
[14] Tamara Munzner. Exploring large graphs in 3d hyperbolic space. IEEE Computer Graphics and Applications, 18(4):18–23, 1998.
[15] Fragkiskos Papadopoulos, Maksim Kitsak, M. Angeles Serrano, Marian Bogu˜n´a, and Dmitri Krioukov. Popularity versus Similarity in Growing Networks. Nature, 489:537–540, Sep 2012.
[16] Radmila Sazdanovic. Fisheye view of tessellations. In Proceedings of Bridges 2012: Mathematics, Music, Art, Architecture, Culture, pages 361–364, Phoenix, Arizona, USA, 2012. Tessellations Publishing.
[17] Jeff Weeks, 2009. http://www.geometrygames.org/HyperbolicGames/ (as of Jan 27, 2017).
[18] HyperRogue website. http://www.roguetemple.com/z/hyper/ (as of Jan 27, 2017).
[19] HyperRogue: programming. http://www.roguetemple.com/z/hyper/dev.php (as of Jan 27, 2017).
Links
Full Text
http://archive.bridgesmathart.org/2017/bridges2017-9.pdf
