Abstract
There are a lot of transformations that can turn one raster image into a derived one in a mathematically interesting way. This article describes a collection of such filters, implemented in OpenGL in order to use the high degree of parallelism modern GPUs provide, thereby providing performance required to process e.g. live camera images in real-time. The filters contained in this library include wallpaper groups, conformal maps described by meromorphic functions, as well as hyperbolic symmetry groups. Using examples of increasing complexity, several key implementation techniques are explained, including texture wrap configurations, user-configurable control points, and custom fragment shader programs. This work might exhibit aesthetic aspects of mathematics to the masses and provide useful building blocks for scientists as well as artists.
Keywords
- Transformation
- tiling
- wallpaper group
- conformal map
- meromorphic function
- hyperbolic geometry
- GPU
- parallelism
- webcam
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References
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von Gagern, M., Richter-Gebert, J.: Hyperbolization of Euclidean Ornaments. Electronic Journal of Combinatorics 16(2), R12 (2009)
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© 2010 Springer-Verlag Berlin Heidelberg
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von Gagern, M., Mercat, C. (2010). A Library of OpenGL-Based Mathematical Image Filters. In: Fukuda, K., Hoeven, J.v.d., Joswig, M., Takayama, N. (eds) Mathematical Software – ICMS 2010. ICMS 2010. Lecture Notes in Computer Science, vol 6327. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15582-6_33
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DOI: https://doi.org/10.1007/978-3-642-15582-6_33
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-15581-9
Online ISBN: 978-3-642-15582-6
eBook Packages: Computer ScienceComputer Science (R0)
