Isotopic Reconstruction of Surfaces with Boundaries

We present an algorithm for the reconstruction of a surface with boundaries (including a non‐orientable one) in three dimensions from a sufficiently dense sample. It is guaranteed that the output is isotopic to the unknown sampled surface. No previously known algorithm guarantees isotopic or homeomo...

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Bibliographic Details
Published inComputer graphics forum Vol. 28; no. 5; pp. 1371 - 1382
Main Authors Dey, Tamal K., Li, Kuiyu, Ramos, Edgar A., Wenger, Rephael
Format Journal Article
LanguageEnglish
Published Oxford, UK Blackwell Publishing Ltd 01.07.2009
Subjects
Algorithms
Computer graphics
Computer programming
I.3.3 [Computer Graphics]: Surface Reconstruction
Sampling
Studies
Online AccessGet full text
ISSN0167-7055
1467-8659
DOI10.1111/j.1467-8659.2009.01514.x

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Summary:We present an algorithm for the reconstruction of a surface with boundaries (including a non‐orientable one) in three dimensions from a sufficiently dense sample. It is guaranteed that the output is isotopic to the unknown sampled surface. No previously known algorithm guarantees isotopic or homeomorphic reconstruction of surfaces with boundaries. Our algorithm is surprisingly simple. It ‘peels’ slivers greedily from an α‐complex of a sample of the surface. No other post‐processing is necessary. We provide several experimental results from an implementation of our basic algorithm and also a modified version of it.
Bibliography:istex:071B6D39A0F39FA4994E14DD08FF346B9E17B8E0
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ArticleID:CGF1514
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ISSN:0167-7055
1467-8659
DOI:10.1111/j.1467-8659.2009.01514.x