Fast computation of weighted distance functions and geodesic on implicit hyper-surfaces
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| フォーマット: | article |
| 言語: | 英語 |
| 出版事項: |
2001
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| オンライン･アクセス: | https://hdl.handle.net/20.500.12008/21266 |
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| _version_ | 1868890216622718976 |
|---|---|
| author | Memoli, Facundo |
| author2 | Sapiro, Guillermo |
| author2_role | author |
| author_browse | Memoli, Facundo Sapiro, Guillermo |
| author_facet | Memoli, Facundo Sapiro, Guillermo |
| author_role | author |
| collection | COLIBRI |
| dc.creator.none.fl_str_mv | Memoli, Facundo Sapiro, Guillermo |
| dc.date.none.fl_str_mv | 2001 2019-07-03T16:36:16Z 2019-07-03T16:36:16Z 20190703 |
| dc.identifier.none.fl_str_mv | Memoli, F., Sapiro, G. Fast computation of weighted distance functions and geodesic on implicit hyper-surfaces [en línea]. Journal of Computational Physics, 2001 v. 173, no. 2. https://doi.org/10.1006/jcph.2001.6910 https://hdl.handle.net/20.500.12008/21266 |
| dc.language.none.fl_str_mv | en eng |
| dc.rights.none.fl_str_mv | info:eu-repo/semantics/openAccess Licencia Creative Commons Atribución – No Comercial – Sin Derivadas (CC - By-NC-ND) |
| dc.source.none.fl_str_mv | reponame:COLIBRI instname:Universidad de la República instacron:Universidad de la República |
| dc.subject.none.fl_str_mv | Implicit hyper-surfaces Distance functions Geodesics Hamilton–Jacobi equations Fast computations |
| dc.title.none.fl_str_mv | Fast computation of weighted distance functions and geodesic on implicit hyper-surfaces |
| dc.type.none.fl_str_mv | Artículo info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion |
| description | Postprint |
| eu_rights_str_mv | openAccess |
| format | article |
| id | anni_e2fdf9d13ccc5237a2843da1794e063f |
| identifier_str_mv | Memoli, F., Sapiro, G. Fast computation of weighted distance functions and geodesic on implicit hyper-surfaces [en línea]. Journal of Computational Physics, 2001 v. 173, no. 2. https://doi.org/10.1006/jcph.2001.6910 |
| instacron_str | Universidad de la República |
| institution | Universidad de la República |
| instname_str | Universidad de la República |
| language | eng |
| language_invalid_str_mv | en |
| network_acronym_str | anni |
| network_name_str | oai-lr-anni |
| oai_identifier_str | oai:colibri.udelar.edu.uy:20.500.12008/21266 |
| publishDate | 2001 |
| publishDateSort | 2001 |
| reponame_str | COLIBRI |
| repository.mail.fl_str_mv | |
| repository.name.fl_str_mv | |
| repository_id_str | |
| rights_invalid_str_mv | Licencia Creative Commons Atribución – No Comercial – Sin Derivadas (CC - By-NC-ND) |
| spelling | Fast computation of weighted distance functions and geodesic on implicit hyper-surfacesMemoli, FacundoSapiro, GuillermoImplicit hyper-surfacesDistance functionsGeodesicsHamilton–Jacobi equationsFast computationsPostprintAn algorithm for the computationally optimal construction of intrinsic weighted distance functions on implicit hyper-surfaces is introduced in this paper. The basic idea is to approximate the intrinsic weighted distance by the Euclidean weighted distance computed in a band surrounding the implicit hyper-surface in the embedding space, thereby performing all the computations in a Cartesian grid with classical and efficient numerics. Based on work on geodesics on Riemannian manifolds with boundaries, we bound the error between the two distance functions. We show that this error is of the same order as the theoretical numerical error in computationally optimal, Hamilton–Jacobi-based, algorithms for computing distance functions in Cartesian grids. Therefore, we can use these algorithms, modified to deal with spaces with boundaries, and obtain also for the case of intrinsic distance functions on implicit hyper-surfaces a computationally efficient technique. The approach can be extended to solve a more general class of Hamilton–Jacobi equations defined on the implicit surface, following the same idea of approximating their solutions by the solutions in the embedding Euclidean space. The framework here introduced thereby allows for the computations to be performed on a Cartesian grid with computationally optimal algorithms, in spite of the fact that the distance and Hamilton–Jacobi equations are intrinsic to the implicit hyper-surface. For other surface representation like triangulated or unorganized points one, the algorithm here introduced can be used after simple pre-processing of the data.2019-07-03T16:36:16Z2019-07-03T16:36:16Z200120190703Artículoinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionMemoli, F., Sapiro, G. Fast computation of weighted distance functions and geodesic on implicit hyper-surfaces [en línea]. Journal of Computational Physics, 2001 v. 173, no. 2. https://doi.org/10.1006/jcph.2001.6910https://hdl.handle.net/20.500.12008/21266reponame:COLIBRIinstname:Universidad de la Repúblicainstacron:Universidad de la RepúblicaenengLas obras depositadas en el Repositorio se rigen por la Ordenanza de los Derechos de la Propiedad Intelectual de la Universidad De La República. (Res. Nº 91 de C.D.C. de 8/III/1994 – D.O. 7/IV/1994) y por la Ordenanza del Repositorio Abierto de la Universidad de la República (Res. Nº 16 de C.D.C. de 07/10/2014)info:eu-repo/semantics/openAccessLicencia Creative Commons Atribución – No Comercial – Sin Derivadas (CC - By-NC-ND)oai:colibri.udelar.edu.uy:20.500.12008/212662026-04-14T10:15:07Z |
| spellingShingle | Fast computation of weighted distance functions and geodesic on implicit hyper-surfaces Memoli, Facundo Implicit hyper-surfaces Distance functions Geodesics Hamilton–Jacobi equations Fast computations |
| status_str | publishedVersion |
| title | Fast computation of weighted distance functions and geodesic on implicit hyper-surfaces |
| title_full | Fast computation of weighted distance functions and geodesic on implicit hyper-surfaces |
| title_fullStr | Fast computation of weighted distance functions and geodesic on implicit hyper-surfaces |
| title_full_unstemmed | Fast computation of weighted distance functions and geodesic on implicit hyper-surfaces |
| title_short | Fast computation of weighted distance functions and geodesic on implicit hyper-surfaces |
| title_sort | Fast computation of weighted distance functions and geodesic on implicit hyper-surfaces |
| topic | Implicit hyper-surfaces Distance functions Geodesics Hamilton–Jacobi equations Fast computations |
| url | https://hdl.handle.net/20.500.12008/21266 |