Article

Ambient isotopic approximations for surface reconstruction and interval solids

Authors:

Takis Sakkalis,

Thomas J. PetersAuthors Info & Claims

SM '03: Proceedings of the eighth ACM symposium on Solid modeling and applications

Pages 176 - 184

https://doi.org/10.1145/781606.781634

Published: 16 June 2003 Publication History

Abstract

Given a nonsingular compact 2-manifold F without boundary, we present methods for establishing a family of surfaces which can approximate F so that each approximant is ambient isotopic to F. The current state of the art in surface reconstruction is that both theory and practice are limited to generating a piecewise linear (PL) approximation. The methods presented here offer broader theoretical guidance for a rich class of ambient isotopic approximations. They are also used to establish sufficient conditions for an interval solid to be ambient isotopic to the solid it is approximating.The methods are based on global theoretical considerations and are compared to existing local methods. Practical implications of these methods are also presented. For the global case, a differential surface analysis is performed to find a positive number ρ so that the offsets F_o(± ρ) of F at distances ± ρ are nonsingular. In doing so, a normal tubular neighborhood, F(ρ), of F is constructed. Then, each approximant of F lies inside F(ρ). Comparisons between these global and local constraints are given.

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Cited By

Jordan KMiller LMoore EPeters TRussell A(2008)Modeling time and topology for animation and visualization with examples on parametric geometryTheoretical Computer Science10.1016/j.tcs.2008.06.023405:1-2(41-49)Online publication date: 1-Oct-2008
https://dl.acm.org/doi/10.1016/j.tcs.2008.06.023
Rossignac J(2007)Solid and Physical ModelingWiley Encyclopedia of Electrical and Electronics Engineering10.1002/047134608X.W7526.pub2Online publication date: 15-Jun-2007
https://doi.org/10.1002/047134608X.W7526.pub2
Abe KBisceglio JPeters TRussell ASakkalis T(2005)Computational Topology for Reconstruction of Surfaces with BoundaryProceedings of the International Conference on Shape Modeling and Applications 200510.1109/SMI.2005.8(290-299)Online publication date: 13-Jun-2005
https://dl.acm.org/doi/10.1109/SMI.2005.8
Show More Cited By

Index Terms

Ambient isotopic approximations for surface reconstruction and interval solids
1. Computing methodologies
  1. Computer graphics
    1. Shape modeling
      1. Parametric curve and surface models
      2. Volumetric models

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cover image ACM Conferences

SM '03: Proceedings of the eighth ACM symposium on Solid modeling and applications

June 2003

362 pages

ISBN:1581137060

DOI:10.1145/781606

Conference Chairs:
George Turkiyyah
University of Washington, USA
,
Pere Brunet
Polytechnical University of Catalonia, Barcelona, Spain
,
Program Chairs:
Gershon Elber
Technion, Israel
,
Vadim Shapiro
University of Wisconsin, USA

Copyright © 2003 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Publication History

Published: 16 June 2003

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SM03: 8th ACM Symposium on Solid Modeling and Applications

June 16 - 20, 2003

Washington, Seattle, USA

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SM '03 Paper Acceptance Rate 43 of 80 submissions, 54%;

Overall Acceptance Rate 86 of 173 submissions, 50%

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Cited By

Jordan KMiller LMoore EPeters TRussell A(2008)Modeling time and topology for animation and visualization with examples on parametric geometryTheoretical Computer Science10.1016/j.tcs.2008.06.023405:1-2(41-49)Online publication date: 1-Oct-2008
https://dl.acm.org/doi/10.1016/j.tcs.2008.06.023
Rossignac J(2007)Solid and Physical ModelingWiley Encyclopedia of Electrical and Electronics Engineering10.1002/047134608X.W7526.pub2Online publication date: 15-Jun-2007
https://doi.org/10.1002/047134608X.W7526.pub2
Abe KBisceglio JPeters TRussell ASakkalis T(2005)Computational Topology for Reconstruction of Surfaces with BoundaryProceedings of the International Conference on Shape Modeling and Applications 200510.1109/SMI.2005.8(290-299)Online publication date: 13-Jun-2005
https://dl.acm.org/doi/10.1109/SMI.2005.8
Chazal FCohen-Steiner D(2005)A condition for isotopic approximationGraphical Models10.1016/j.gmod.2005.01.00567:5(390-404)Online publication date: 1-Sep-2005
https://dl.acm.org/doi/10.1016/j.gmod.2005.01.005
Chazal FCohen-Steiner DElber GPatrikalakis NBrunet P(2004)A condition for isotopic approximationProceedings of the ninth ACM symposium on Solid modeling and applications10.5555/1217875.1217890(93-99)Online publication date: 9-Jun-2004
https://dl.acm.org/doi/10.5555/1217875.1217890

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