Squares that Look Round: Transforming Spherical Images: Unterschied zwischen den Versionen
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== Used References == | == Used References == | ||
[1] Oscar S. Adams. Elliptic functions applied to conformal world maps. Department of Commerce | [1] Oscar S. Adams. Elliptic functions applied to conformal world maps. Department of Commerce | ||
| − | U.S. Coast and Geodetic Survey. Govt. Print. Off., 1925. http://docs.lib.noaa.gov/rescue/ | + | U.S. Coast and Geodetic Survey. Govt. Print. Off., 1925. http://docs.lib.noaa.gov/rescue/cgs_specpubs/QB275U35no1121925.pdf |
[2] Lars V. Ahlfors. Complex analysis: An introduction of the theory of analytic functions of one complex | [2] Lars V. Ahlfors. Complex analysis: An introduction of the theory of analytic functions of one complex | ||
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panoramas for practical and aesthetic purposes. In Computational Aesthetics’07 Proceedings of the | panoramas for practical and aesthetic purposes. In Computational Aesthetics’07 Proceedings of the | ||
Third Eurographics conference on Computational Aesthetics in Graphics, Visualization and Imaging, | Third Eurographics conference on Computational Aesthetics in Graphics, Visualization and Imaging, | ||
| − | pages 15–22, 2007. http://turingmachine.org/dmg/papers/ | + | pages 15–22, 2007. http://turingmachine.org/~dmg/papers/dmg2007_cae_panos.pdf |
[5] Jane M. McDougall, Lisbeth E. Schaubroeck, and James S. Rolf. Mappings to polygonal domains. | [5] Jane M. McDougall, Lisbeth E. Schaubroeck, and James S. Rolf. Mappings to polygonal domains. | ||
Aktuelle Version vom 27. Dezember 2016, 12:13 Uhr
Inhaltsverzeichnis
Reference
Saul Schleimer and Henry Segerman: Squares that Look Round: Transforming Spherical Images. In: Bridges 2016, Pages 15–24.
DOI
Abstract
We propose Möbius transformations as the natural rotation and scaling tools for editing spherical images. As an application we produce spherical Droste images. We obtain other self-similar visual effects using rational functions, elliptic functions, and Schwarz-Christoffel maps.
Extended Abstract
Bibtex
@inproceedings{bridges2016:15,
author = {Saul Schleimer and Henry Segerman},
title = {Squares that Look Round: Transforming Spherical Images},
pages = {15--24},
booktitle = {Proceedings of Bridges 2016: Mathematics, Music, Art, Architecture, Education, Culture},
year = {2016},
editor = {Eve Torrence, Bruce Torrence, Carlo S\'equin, Douglas McKenna, Krist\'of Fenyvesi and Reza Sarhangi},
isbn = {978-1-938664-19-9},
issn = {1099-6702},
publisher = {Tessellations Publishing},
address = {Phoenix, Arizona},
url = {http://de.evo-art.org/index.php?title=Squares_that_Look_Round:_Transforming_Spherical_Images },
note = {Available online at \url{http://archive.bridgesmathart.org/2016/bridges2016-15.html}}
}
Used References
[1] Oscar S. Adams. Elliptic functions applied to conformal world maps. Department of Commerce U.S. Coast and Geodetic Survey. Govt. Print. Off., 1925. http://docs.lib.noaa.gov/rescue/cgs_specpubs/QB275U35no1121925.pdf
[2] Lars V. Ahlfors. Complex analysis: An introduction of the theory of analytic functions of one complex variable. Second edition. McGraw-Hill Book Co., New York-Toronto-London, 1966.
[3] Bart de Smit and Hendrik W. Lenstra Jr. The mathematical structure of Escher’s Print Gallery. Journal of the American Mathematical Society, 50(4):446–451, 2003. http://www.ams.org/notices/200304/fea-escher.pdf.
[4] Daniel M. German, Pablo D’Angelo, Michael Gross, and Bruno Postle. New methods to project panoramas for practical and aesthetic purposes. In Computational Aesthetics’07 Proceedings of the Third Eurographics conference on Computational Aesthetics in Graphics, Visualization and Imaging, pages 15–22, 2007. http://turingmachine.org/~dmg/papers/dmg2007_cae_panos.pdf
[5] Jane M. McDougall, Lisbeth E. Schaubroeck, and James S. Rolf. Mappings to polygonal domains. In Explorations in complex analysis, Classr. Res. Mater. Ser., pages 271–315. Math. Assoc. America, Washington, DC, 2012. http://www.jimrolf.com/explorationsInComplexVariables/bookChapters/Ch5.pdf.
[6] Henry McKean and Victor Moll. Elliptic curves. Cambridge University Press, Cambridge, 1997. Function theory, geometry, arithmetic.
[7] John Milnor. Dynamics in One Complex Variable. Princeton University Press, 3rd edition, 2006.
[8] David Mumford, Caroline Series, and David Wright. Indra’s pearls. Cambridge University Press, New York, 2002. The vision of Felix Klein.
[9] Charles S. Peirce. A quincuncial projection of the sphere. Amer. J. Math., 2(4):394–396, 1879. https://www.jstor.org/stable/pdf/2369491.pdf.
[10] S´ebastien P´erez-Duarte and David Swart. The Mercator redemption. In Proceedings of Bridges 2013: Mathematics, Music, Art, Architecture, Culture, pages 217–224. Tessellations Publishing, 2013. http://archive.bridgesmathart.org/2013/bridges2013-217.html.
Links
Full Text
http://archive.bridgesmathart.org/2016/bridges2016-15.pdf
