Keinert B, Innmann M, Sänger M, Stamminger M (2015)
Publication Status: Published
Publication Type: Journal article, Original article
Publication year: 2015
Publisher: Association for Computing Machinery
Book Volume: 34
Article Number: 193
Journal Issue: 6
Spherical Fibonacci point sets yield nearly uniform point distributions on the unit sphere S ⊂ ℝ. The forward generation of these point sets has been widely researched and is easy to implement, such that they have been used in various applications. Unfortunately, the lack of an efficient mapping from points on the unit sphere to their closest spherical Fibonacci point set neighbors rendered them impractical for a wide range of applications, especially in computer graphics. Therefore, we introduce an inverse mapping from points on the unit sphere which yields the nearest neighbor in an arbitrarily sized spherical Fibonacci point set in constant time, without requiring any precomputations or table lookups. We show how to implement this inverse mapping on GPUs while addressing arising floating point precision problems. Further, we demonstrate the use of this mapping and its variants, and show how to apply it to fast unit vector quantization. Finally, we illustrate the means by which to modify this inverse mapping for texture mapping with smooth filter kernels and showcase its use in the field of procedural modeling.
APA:
Keinert, B., Innmann, M., Sänger, M., & Stamminger, M. (2015). Spherical Fibonacci mapping. Acm Transactions on Graphics, 34(6). https://doi.org/10.1145/2816795.2818131
MLA:
Keinert, Benjamin, et al. "Spherical Fibonacci mapping." Acm Transactions on Graphics 34.6 (2015).
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