Extensible Spherical Fibonacci Grids
| Autor: | Josep Blat, Ricardo Marques, Christian Bouville, Kadi Bouatouch |
|---|---|
| Přispěvatelé: | Universitat Pompeu Fabra [Barcelona] (UPF), Computational Visual Perception and Applications ( PERCEPT), MEDIA ET INTERACTIONS (IRISA-D6), Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Université de Bretagne Sud (UBS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National de Recherche en Informatique et en Automatique (Inria)-École normale supérieure - Rennes (ENS Rennes)-Centre National de la Recherche Scientifique (CNRS)-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-CentraleSupélec-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Université de Bretagne Sud (UBS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT), Computational Visual Perception and Applications (PERCEPT), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes) |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Fibonacci number
Mean squared error Computer science Vector quantization Spherical cap adaptive sampling 020207 software engineering spherical quasi-Monte Carlo low discrepancy spherical point sets 02 engineering and technology Computer Graphics and Computer-Aided Design Rendering (computer graphics) Numerical integration rendering equation [SPI]Engineering Sciences [physics] Signal Processing 0202 electrical engineering electronic engineering information engineering Computer Vision and Pattern Recognition Algorithm [SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing Software ComputingMilieux_MISCELLANEOUS |
| Zdroj: | IEEE Transactions on Visualization and Computer Graphics IEEE Transactions on Visualization and Computer Graphics, Institute of Electrical and Electronics Engineers, In press, pp.1-1. ⟨10.1109/TVCG.2019.2952131⟩ IEEE Transactions on Visualization and Computer Graphics, In press, pp.1-1. ⟨10.1109/TVCG.2019.2952131⟩ |
| ISSN: | 1077-2626 |
| Popis: | Spherical Fibonacci grids (SFG) yield extremely uniform point set distributions on the sphere. This feature makes SFGs particularly well-suited to a wide range of computer graphics applications, from numerical integration, to vector quantization, among others. However, the application of SFGs to problems in which further refinement of an initial point set is required is currently not possible. This is because there is currently no solution to the problem of adding new points to an existing SFG while maintaining the point set properties. In this work, we fill this gap by proposing the extensible spherical Fibonacci grids (E-SFG). We start by carrying out a formal analysis of SFGs to identify the properties which make these point sets exhibit a nearly-optimal uniform spherical distribution. Then, we propose an algorithm (E-SFG) to extend the original point set while preserving these properties. Finally, we compare the E-SFG with a other extensible spherical point sets. Our results show that the E-SFG outperforms spherical point sets based on a low discrepancy sequence both in terms of spherical cap discrepancy and in terms of root mean squared error for evaluating the rendering integral. Ricardo Marques was supported by the European Union’s Horizon 2020 research programme through a Marie Sklodowska-Curie Individual Fellowship (Grant number 707027). |
| Databáze: | OpenAIRE |
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