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Animation of Deformable Bodies with Quadratic Bézier Finite Elements

Published: 02 June 2014 Publication History

Abstract

In this article, we investigate the use of quadratic finite elements for graphical animation of deformable bodies. We consider both integrating quadratic elements with conventional linear elements to achieve a computationally efficient adaptive-degree simulation framework as well as wholly quadratic elements for the simulation of nonlinear rest shapes. In both cases, we adopt the Bézier basis functions and employ a co-rotational linear strain formulation. As with linear elements, the co-rotational formulation allows us to precompute per-element stiffness matrices, resulting in substantial computational savings. We present several examples that demonstrate the advantages of quadratic elements in general and our adaptive-degree system in particular. Furthermore, we demonstrate, for the first time in computer graphics, animations of volumetric deformable bodies with nonlinear rest shapes.

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bargteil (bargteil.zip)
Supplemental movie, appendix, image and software files for, Animation of Deformable Bodies with Quadratic Bézier Finite Elements
MP4 File (a27-sidebyside.mp4)

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Published In

cover image ACM Transactions on Graphics
ACM Transactions on Graphics  Volume 33, Issue 3
May 2014
145 pages
ISSN:0730-0301
EISSN:1557-7368
DOI:10.1145/2631978
Issue’s Table of Contents
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 the author(s) 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: 02 June 2014
Accepted: 01 January 2014
Revised: 01 October 2013
Received: 01 December 2012
Published in TOG Volume 33, Issue 3

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Author Tags

  1. Finite-element methods
  2. adaptive simulation
  3. deformable bodies
  4. natural phenomena
  5. physics-based animation

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