Article

A simple manifold-based construction of surfaces of arbitrary smoothness

Authors:

Denis ZorinAuthors Info & Claims

SIGGRAPH '04: ACM SIGGRAPH 2004 Papers

Pages 271 - 275

https://doi.org/10.1145/1186562.1015714

Published: 01 August 2004 Publication History

Abstract

We present a smooth surface construction based on the manifold approach of Grimm and Hughes. We demonstrate how this approach can relatively easily produce a number of desirable properties which are hard to achieve simultaneously with polynomial patches, subdivision or variational surfaces. Our surfaces are C^∞-continuous with explicit nonsingular C^∞ parameterizations, high-order flexible at control vertices, depend linearly on control points, have fixed-size local support for basis functions, and have good visual quality.

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https://doi.org/10.1109/TVCG.2021.3110658
Lingg MHughey SShanker BAktulga H(2022)High Performance Evaluation of Helmholtz Potentials Using the Multi-Level Fast Multipole AlgorithmIEEE Transactions on Parallel and Distributed Systems10.1109/TPDS.2022.316564933:12(3651-3666)Online publication date: 1-Dec-2022
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Index Terms

A simple manifold-based construction of surfaces of arbitrary smoothness
1. Computing methodologies
  1. Computer graphics
    1. Shape modeling
2. Theory of computation
  1. Randomness, geometry and discrete structures
    1. Computational geometry

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cover image ACM Conferences

SIGGRAPH '04: ACM SIGGRAPH 2004 Papers

August 2004

684 pages

ISBN:9781450378239

DOI:10.1145/1186562

Editor:
Joe Marks
Mitsubishi Electric Research Laboratories (MERL)

Copyright © 2004 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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Published: 01 August 2004

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SIGGRAPH04: Special Interest Group on Computer Graphics and Interactive Techniques

August 8 - 12, 2004

California, Los Angeles

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SIGGRAPH '04 Paper Acceptance Rate 83 of 478 submissions, 17%;

Overall Acceptance Rate 1,822 of 8,601 submissions, 21%

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Cited By

Feng WZhang JZhou YXin S(2022)GDR-Net: A Geometric Detail Recovering Network for 3D Scanned ObjectsIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2021.311065828:12(3959-3973)Online publication date: 1-Dec-2022
https://doi.org/10.1109/TVCG.2021.3110658
Lingg MHughey SShanker BAktulga H(2022)High Performance Evaluation of Helmholtz Potentials Using the Multi-Level Fast Multipole AlgorithmIEEE Transactions on Parallel and Distributed Systems10.1109/TPDS.2022.316564933:12(3651-3666)Online publication date: 1-Dec-2022
https://doi.org/10.1109/TPDS.2022.3165649
Blidia AMourrain BXu G(2020)Geometrically smooth spline bases for data fitting and simulationComputer Aided Geometric Design10.1016/j.cagd.2020.101814(101814)Online publication date: Jan-2020
https://doi.org/10.1016/j.cagd.2020.101814
Zhang QSabin MCirak F(2018)Subdivision surfaces with isogeometric analysis adapted refinement weightsComputer-Aided Design10.1016/j.cad.2018.04.020102(104-114)Online publication date: Sep-2018
https://doi.org/10.1016/j.cad.2018.04.020
Majeed MCirak F(2017)Isogeometric analysis using manifold-based smooth basis functionsComputer Methods in Applied Mechanics and Engineering10.1016/j.cma.2016.08.013316(547-567)Online publication date: Apr-2017
https://doi.org/10.1016/j.cma.2016.08.013
Runions ASamavati F(2011)Partition of unity parametrics: a framework for meta-modelingThe Visual Computer: International Journal of Computer Graphics10.1007/s00371-011-0567-x27:6-8(495-505)Online publication date: 1-Jun-2011
https://dl.acm.org/doi/10.1007/s00371-011-0567-x
Haviv DYomdin Y(2008)Uniform approximation of near-singular surfacesTheoretical Computer Science10.1016/j.tcs.2007.10.005392:1-3(92-100)Online publication date: 20-Feb-2008
https://dl.acm.org/doi/10.1016/j.tcs.2007.10.005
Joshi PSéquin C(2007)Energy Minimizers for Curvature-Based Surface FunctionalsComputer-Aided Design and Applications10.1080/16864360.2007.107384954:5(607-617)Online publication date: Jan-2007
https://doi.org/10.1080/16864360.2007.10738495
Ray NLi WLévy BSheffer AAlliez P(2006)Periodic global parameterizationACM Transactions on Graphics10.1145/1183287.118329725:4(1460-1485)Online publication date: 1-Oct-2006
https://dl.acm.org/doi/10.1145/1183287.1183297
Yoon S(2006)A surface displaced from a manifoldProceedings of the 4th international conference on Geometric Modeling and Processing10.1007/11802914_56(677-686)Online publication date: 26-Jul-2006
https://dl.acm.org/doi/10.1007/11802914_56

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