Extensible spherical Fibonacci grids

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  • dc.contributor.author Marques, Ricardo
  • dc.contributor.author Bouville, Christian
  • dc.contributor.author Bouatouch, Kadi
  • dc.contributor.author Blat, Josep
  • dc.date.accessioned 2023-03-03T07:42:49Z
  • dc.date.available 2023-03-03T07:42:49Z
  • dc.date.issued 2021
  • dc.description.abstract 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.
  • dc.description.sponsorship Ricardo Marques was supported by the European Union’s Horizon 2020 research programme through a Marie Sklodowska-Curie Individual Fellowship (Grant number 707027).
  • dc.format.mimetype application/pdf
  • dc.identifier.citation Marques R, Bouville C, Bouatouch K, Blat J. Extensible spherical Fibonacci grids. IEEE Trans Vis Comput Graph. 2021;27(4):2341-54. DOI: 10.1109/TVCG.2019.2952131
  • dc.identifier.doi http://dx.doi.org/10.1109/TVCG.2019.2952131
  • dc.identifier.issn 1077-2626
  • dc.identifier.uri http://hdl.handle.net/10230/56016
  • dc.language.iso eng
  • dc.publisher Institute of Electrical and Electronics Engineers (IEEE)
  • dc.relation.ispartof IEEE Transactions on Visualization and Computer Graphics. 2021;27(4):2341-54.
  • dc.relation.projectID info:eu-repo/grantAgreement/EC/H2020/707027
  • dc.rights © 2021 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. http://dx.doi.org/10.1109/TVCG.2019.2952131
  • dc.rights.accessRights info:eu-repo/semantics/openAccess
  • dc.subject.keyword spherical quasi-Monte Carlo
  • dc.subject.keyword low discrepancy spherical point sets
  • dc.subject.keyword adaptive sampling
  • dc.subject.keyword rendering equation
  • dc.title Extensible spherical Fibonacci grids
  • dc.type info:eu-repo/semantics/article
  • dc.type.version info:eu-repo/semantics/acceptedVersion

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