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Building your own DEC at home

Elcott, Sharif and Schröder, Peter (2005) Building your own DEC at home. In: SIGGRAPH '05 ACM SIGGRAPH 2005 Courses. ACM , New York, NY, Art. No. 8. https://resolver.caltech.edu/CaltechAUTHORS:20161011-163903630

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Abstract

The methods of Discrete Exterior Calculus (DEC) have given birth to many new algorithms applicable to areas such as fluid simulation, deformable body simulation, and others. Despite the (possibly intimidating) mathematical theory that went into deriving these algorithms, in the end they lead to simple, elegant, and straightforward implementations. However, readers interested in implementing them should note that the algorithms presume the existence of a suitable simplicial complex data structure. Such a data structure needs to support local traversal of elements, adjacency information for all dimensions of simplices, a notion of a dual mesh, and all simplices must be oriented. Unfortunately, most publicly available tetrahedral mesh libraries provide only unoriented representations with little more than vertex-tet adjacency information (while we need vertex-edge, edge-triangle, edge-tet, etc.). For those eager to implement and build on the algorithms presented in this course without having to worry about these details, we provide an implementation of a DEC-friendly tetrahedral mesh data structure in C++. This chapter documents the ideas behind the implementation.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1145/1198555.1198667DOIPaper
http://dl.acm.org/citation.cfm?doid=1198555.1198667PublisherPaper
ORCID:
AuthorORCID
Schröder, Peter0000-0002-0323-7674
Additional Information:© 2005 ACM. This work was supported in part through a James Irvine Fellowship to the first author, NSF (DMS-0220905, DMS-0138458, ACI-0219979), DOE (W-7405-ENG-48/B341492), nVidia, the Center for Integrated Multiscale Modeling and Simulation, Alias, and Pixar.
Funders:
Funding AgencyGrant Number
James Irvine FellowshipUNSPECIFIED
NSFDMS-0220905
NSFDMS-0138458
NSFACI-0219979
Department of Energy (DOE)ENG-48/B341492
nVidiaUNSPECIFIED
Center for Integrated Multiscale Modeling and SimulationUNSPECIFIED
AliasUNSPECIFIED
PixarUNSPECIFIED
DOI:10.1145/1198555.1198667
Record Number:CaltechAUTHORS:20161011-163903630
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20161011-163903630
Official Citation:Sharif Elcott and Peter Schröder. 2005. Building your own DEC at home. In ACM SIGGRAPH 2005 Courses (SIGGRAPH '05), John Fujii (Ed.). ACM, New York, NY, USA, , Article 8 . DOI=http://dx.doi.org/10.1145/1198555.1198667
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:71004
Collection:CaltechAUTHORS
Deposited By: Kristin Buxton
Deposited On:12 Oct 2016 16:32
Last Modified:11 Nov 2021 04:38

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