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Implicit Fairing of Irregular Meshes using Diffusion and Curvature Flow

Desbrun, Mathieu and Meyer, Mark and Schröder, Peter and Barr, Alan H. (1999) Implicit Fairing of Irregular Meshes using Diffusion and Curvature Flow. In: SIGGRAPH '99 Proceedings of the 26th annual conference on Computer graphics and interactive techniques. ACM Press/Addison-Wesley Publishing , New York, NY, pp. 317-324. ISBN 0-201-48560-5. https://resolver.caltech.edu/CaltechAUTHORS:20161006-145432340

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Abstract

In this paper, we develop methods to rapidly remove rough features from irregularly triangulated data intended to portray a smooth surface. The main task is to remove undesirable noise and uneven edges while retaining desirable geometric features. The problem arises mainly when creating high-fidelity computer graphics objects using imperfectly-measured data from the real world. Our approach contains three novel features: an implicit integration method to achieve efficiency, stability, and large time-steps; a scale-dependent Laplacian operator to improve the diffusion process; and finally, a robust curvature flow operator that achieves a smoothing of the shape itself, distinct from any parameterization. Additional features of the algorithm include automatic exact volume preservation, and hard and soft constraints on the positions of the points in the mesh. We compare our method to previous operators and related algorithms, and prove that our curvature and Laplacian operators have several mathematically-desirable qualities that improve the appearance of the resulting surface. In consequence, the user can easily select the appropriate operator according to the desired type of fairing. Finally, we provide a series of examples to graphically and numerically demonstrate the quality of our results.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1145/311535.311576DOIPaper
http://dl.acm.org/citation.cfm?doid=311535.311576PublisherPaper
ORCID:
AuthorORCID
Desbrun, Mathieu0000-0003-3424-6079
Schröder, Peter0000-0002-0323-7674
Additional Information:© 1999 ACM. The original 3D photography mesh was provided by Jean-Yves Bouguet, the mannequin head and spock dataset by Hugues Hoppe, the bunny and buddha models by Stanford University, and additional test meshes by Cyberware. The authors would like to thank John T. Reese for the initial implementation and the dragon mesh, and Konrad Polthier for interesting comments. This work was supported by the Academic Strategic Alliances Program of the Accelerated Strategic Computing Initiative (ASCI/ASAP) under subcontract B341492 of DOE contract W-7405-ENG-48. Additional support was provided by NSF (ACI-9624957, ACI-9721349, DMS-9874082, and ASC-89-20219 (STC for Computer Graphics and Scientific Visualization)), Alias|wavefront and through a Packard Fellowship.
Funders:
Funding AgencyGrant Number
Academic Strategic Alliances Program of the Accelerated Strategic Computing Initiative (ASCI/ASAP)B341492
Department of Energy (DOE)W-7405-ENG-48
NSFACI-9624957
NSFACI-9721349
NSFDMS-9874082
NSFASC-89-20219
Alias|wavefrontUNSPECIFIED
David and Lucile Packard FoundationUNSPECIFIED
DOI:10.1145/311535.311576
Record Number:CaltechAUTHORS:20161006-145432340
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20161006-145432340
Official Citation:Mathieu Desbrun, Mark Meyer, Peter Schröder, and Alan H. Barr. 1999. Implicit fairing of irregular meshes using diffusion and curvature flow. In Proceedings of the 26th annual conference on Computer graphics and interactive techniques (SIGGRAPH '99). ACM Press/Addison-Wesley Publishing Co., New York, NY, USA, 317-324. DOI=http://dx.doi.org/10.1145/311535.311576
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:70931
Collection:CaltechAUTHORS
Deposited By: Kristin Buxton
Deposited On:12 Oct 2016 23:09
Last Modified:11 Nov 2021 04:37

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