research-article

Unified simulation of elastic rods, shells, and solids

Authors:

Sebastian Martin,

Peter Kaufmann,

Eitan Grinspun,

Markus GrossAuthors Info & Claims

ACM Transactions on Graphics (TOG), Volume 29, Issue 4

Article No.: 39, Pages 1 - 10

https://doi.org/10.1145/1778765.1778776

Published: 26 July 2010 Publication History

Abstract

We develop an accurate, unified treatment of elastica. Following the method of resultant-based formulation to its logical extreme, we derive a higher-order integration rule, or elaston, measuring stretching, shearing, bending, and twisting along any axis. The theory and accompanying implementation do not distinguish between forms of different dimension (solids, shells, rods), nor between manifold regions and non-manifold junctions. Consequently, a single code accurately models a diverse range of elastoplastic behaviors, including buckling, writhing, cutting and merging. Emphasis on convergence to the continuum sets us apart from early unification efforts.

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* elastons.mov - Video demonstrating the method's performance on various examples. * elastonsSupplementary.pdf - Implementation notes. Description of plasticity, cutting and meshless virtual node. * elastonsSupplementary.mov - Video sequence showing dynamic resampling for a swinging bar.

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Index Terms

Unified simulation of elastic rods, shells, and solids
1. Computing methodologies
  1. Computer graphics
    1. Shape modeling
  2. Modeling and simulation
2. Theory of computation
  1. Randomness, geometry and discrete structures
    1. Computational geometry

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Published In

cover image ACM Transactions on Graphics

ACM Transactions on Graphics Volume 29, Issue 4

July 2010

942 pages

ISSN:0730-0301

EISSN:1557-7368

DOI:10.1145/1778765

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Copyright © 2010 ACM.

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Publication History

Published: 26 July 2010

Published in TOG Volume 29, Issue 4

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Darke AOlander IKim TBurbano AWest R(2024)More Than Killmonger Locs: A Style Guide for Black Hair (in Computer Graphics)ACM SIGGRAPH 2024 Courses10.1145/3664475.3664535(1-251)Online publication date: 27-Jul-2024
https://dl.acm.org/doi/10.1145/3664475.3664535
Modi VSharp NPerel OSueda SLevin D(2024)Simplicits: Mesh-Free, Geometry-Agnostic Elastic SimulationACM Transactions on Graphics10.1145/365818443:4(1-11)Online publication date: 19-Jul-2024
https://dl.acm.org/doi/10.1145/3658184
Chen ALiu ZYang YYuksel C(2024)Vertex Block DescentACM Transactions on Graphics10.1145/365817943:4(1-16)Online publication date: 19-Jul-2024
https://dl.acm.org/doi/10.1145/3658179
Feng YShang YLi XShao TJiang CYang Y(2024)PIE-NeRF: Physics-Based Interactive Elastodynamics with NeRF2024 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)10.1109/CVPR52733.2024.00426(4450-4461)Online publication date: 16-Jun-2024
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Mercier-Aubin AKry P(2023)Adaptive Rigidification of Discrete ShellsProceedings of the ACM on Computer Graphics and Interactive Techniques10.1145/36069326:3(1-17)Online publication date: 24-Aug-2023
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