The Mercator Redemption
Inhaltsverzeichnis
Reference
Sébastien Pérez-Duarte and David Swart: The Mercator Redemption. In: Bridges 2013. Pages 217–224
DOI
Abstract
The Mercator projection is arguably the most famous projection in cartography and it has a long and useful history, especially as a navigation tool. In the last century, the Mercator projection’s reputation has suffered a setback. This paper hopes to restore some of the projection’s former glory by applying the Mercator projection to spherical content and the related complex logarithm function to planar content. We take advantage of its cylindrical and conformal properties and we showcase the projection’s ability to zoom through many orders of scale. Finally, we show some related image manipulations such as the Droste effect, and a new Conformal Spherical Stretching operation by the first author that allows for a new degree of freedom when composing spherical panoramas.
Extended Abstract
Bibtex
Used References
[1] American Cartographic Association. Geographers and cartographers urge end to popular use of rectangular maps. The American Cartographer. 16(3):222–223. 1989.
[2] Nikolaus Baumgarten et al. Zoomquilt. http://zoomquilt.org/. Accessed 03/01/2013.
[3] Nikolaus Baumgarten et al. Zoomquilt II. http://zoomquilt2.madmindworx.com/. Accessed 03/01/2013.
[4] Daniel M. Germán, Lloyd Burchill, Alexandre Duret-Lutz, Sébastien Pérez-Duarte, Emmanuel Pérez-Duarte, Josh Sommers. Flattening the Viewable Sphere. Computational Aesthetics 2007:23–28. 2007.
[5] Sébastien Pérez-Duarte. Notre Dame de Reims by night, centered and stretched. http://fieldofview.com/flickr/?page=photos/sbprzd/666952257/. Accessed 03/01/2013.
[6] Bart de Smit and Hendrik W. Lenstra Jr. The Mathematical Structure of Escher’s Print Gallery. In Notices of the AMS. 50(4):446–451, 2003.
[7] David Swart and Bruce Torrence. Mathematics Meets Photography. Math Horizons, 19(1):14–17 and 19(2):24–27, 2011.
Links
Full Text
http://archive.bridgesmathart.org/2013/bridges2013-217.pdf
