Polygonization of Multi-Component Non-Manifold Implicit Surfaces through A Symbolic-Numerical Continuation Algorithm
Autor(a) principal: | |
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Data de Publicação: | 2006 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10400.6/614 |
Resumo: | In computer graphics, most algorithms for sampling implicit surfaces use a 2-points numerical method. If the surface-describing function evaluates positive at the first point and negative at the second one, we can say that the surface is located somewhere between them. Surfaces detected this way are called sign-variant implicit surfaces. However, 2-points numerical methods may fail to detect and sample the surface because the functions of many implicit surfaces evaluate either positive or negative everywhere around them. These surfaces are here called sign-invariant implicit surfaces. In this paper, instead of using a 2-points numerical method, we use a 1-point numerical method to guarantee that our algorithm detects and samples both sign-variant and sign-invariant surface components or branches correctly. This algorithm follows a continuation approach to tessellate implicit surfaces, so that it applies symbolic factorization to decompose the function expression into symbolic components, sampling then each symbolic function component separately. This ensures that our algorithm detects, samples, and triangulates most components of implicit surfaces. |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository_id_str |
7160 |
spelling |
Polygonization of Multi-Component Non-Manifold Implicit Surfaces through A Symbolic-Numerical Continuation AlgorithmImplicit surfacesPolygonizationSymbolic factorizationNumerical methods.In computer graphics, most algorithms for sampling implicit surfaces use a 2-points numerical method. If the surface-describing function evaluates positive at the first point and negative at the second one, we can say that the surface is located somewhere between them. Surfaces detected this way are called sign-variant implicit surfaces. However, 2-points numerical methods may fail to detect and sample the surface because the functions of many implicit surfaces evaluate either positive or negative everywhere around them. These surfaces are here called sign-invariant implicit surfaces. In this paper, instead of using a 2-points numerical method, we use a 1-point numerical method to guarantee that our algorithm detects and samples both sign-variant and sign-invariant surface components or branches correctly. This algorithm follows a continuation approach to tessellate implicit surfaces, so that it applies symbolic factorization to decompose the function expression into symbolic components, sampling then each symbolic function component separately. This ensures that our algorithm detects, samples, and triangulates most components of implicit surfaces.uBibliorumRaposo, AdrianoGomes, Abel J.P.2010-04-28T10:07:23Z20062006-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.6/614enginfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-12-15T09:35:54Zoai:ubibliorum.ubi.pt:10400.6/614Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T00:42:38.692743Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
Polygonization of Multi-Component Non-Manifold Implicit Surfaces through A Symbolic-Numerical Continuation Algorithm |
title |
Polygonization of Multi-Component Non-Manifold Implicit Surfaces through A Symbolic-Numerical Continuation Algorithm |
spellingShingle |
Polygonization of Multi-Component Non-Manifold Implicit Surfaces through A Symbolic-Numerical Continuation Algorithm Raposo, Adriano Implicit surfaces Polygonization Symbolic factorization Numerical methods. |
title_short |
Polygonization of Multi-Component Non-Manifold Implicit Surfaces through A Symbolic-Numerical Continuation Algorithm |
title_full |
Polygonization of Multi-Component Non-Manifold Implicit Surfaces through A Symbolic-Numerical Continuation Algorithm |
title_fullStr |
Polygonization of Multi-Component Non-Manifold Implicit Surfaces through A Symbolic-Numerical Continuation Algorithm |
title_full_unstemmed |
Polygonization of Multi-Component Non-Manifold Implicit Surfaces through A Symbolic-Numerical Continuation Algorithm |
title_sort |
Polygonization of Multi-Component Non-Manifold Implicit Surfaces through A Symbolic-Numerical Continuation Algorithm |
author |
Raposo, Adriano |
author_facet |
Raposo, Adriano Gomes, Abel J.P. |
author_role |
author |
author2 |
Gomes, Abel J.P. |
author2_role |
author |
dc.contributor.none.fl_str_mv |
uBibliorum |
dc.contributor.author.fl_str_mv |
Raposo, Adriano Gomes, Abel J.P. |
dc.subject.por.fl_str_mv |
Implicit surfaces Polygonization Symbolic factorization Numerical methods. |
topic |
Implicit surfaces Polygonization Symbolic factorization Numerical methods. |
description |
In computer graphics, most algorithms for sampling implicit surfaces use a 2-points numerical method. If the surface-describing function evaluates positive at the first point and negative at the second one, we can say that the surface is located somewhere between them. Surfaces detected this way are called sign-variant implicit surfaces. However, 2-points numerical methods may fail to detect and sample the surface because the functions of many implicit surfaces evaluate either positive or negative everywhere around them. These surfaces are here called sign-invariant implicit surfaces. In this paper, instead of using a 2-points numerical method, we use a 1-point numerical method to guarantee that our algorithm detects and samples both sign-variant and sign-invariant surface components or branches correctly. This algorithm follows a continuation approach to tessellate implicit surfaces, so that it applies symbolic factorization to decompose the function expression into symbolic components, sampling then each symbolic function component separately. This ensures that our algorithm detects, samples, and triangulates most components of implicit surfaces. |
publishDate |
2006 |
dc.date.none.fl_str_mv |
2006 2006-01-01T00:00:00Z 2010-04-28T10:07:23Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10400.6/614 |
url |
http://hdl.handle.net/10400.6/614 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
repository.mail.fl_str_mv |
|
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1799136326859096064 |