Preserving Topology and Elasticity for Embedded Deformable Models
ACM Transaction on Graphics (Proceedings of SIGGRAPH 2009), to appear
Matthieu Nesme1,2,3,4 Paul G. Kry1 Lenka Jeřábková3,4 François Faure2,3,4
1McGill University 2Grenoble Universités 3INRIA 4LJK-CNRS


In this paper we introduce a new approach for the embedding of linear elastic deformable models. Our technique results in significant improvements in the efficient physically based simulation of highly detailed objects. First, our embedding takes into account topological details, that is, disconnected parts that fall into the same coarse element are simulated independently. Second, we account for the varying material properties by computing stiffness and interpolation functions for coarse elements which accurately approximate the behavior of the embedded material. Finally, we also take into account empty space in the coarse embeddings, which provides a better simulation of the boundary. The result is a straightforward approach to simulating complex deformable models with the ease and speed associated with a coarse regular embedding, and with a quality of detail that would only be possible at much finer resolution.

A model of a liver with attached vascular system simulated with coarse resolution hexahedra. Our technique models the behavior of the soft liver tissue, stiffer veins, and much stiffer tumors by taking into account a distribution of materials and the presence of empty regions in the embedding. The complex topological branching of the vascular system is preserved by superimposing elements.



M. Nesme, P. G. Kry, L. Jeřábková, F. Faure, Preserving Topology and Elasticity for Embedded Deformable Models, In ACM Transactions on Graphics (SIGGRAPH 2009 Conference Proceedings), 9 pages.

author = "Matthieu Nesme and Paul G. Kry and Lenka Je\v{r}\'abkov\'a and Fran\c{c}ois Faure",
title = "Preserving Topology and Elasticity for Embedded Deformable Models",
booktitle = "ACM Transactions on Graphics (Proc. of SIGGRAPH)",
month = "august",
year = "2009",
organization = "ACM",
note = "to appear",
keywords = "simulation, animation, embedded deformation, finite element method, heterogeneous materials",
url = ""


This probject was created with the help of SOFA. Our implementation will be freely available for download at in an upcoming release of SOFA.

iPhone Demonstration

Use your fingers to squish a 3D model, and let gravity make the model tumble against the walls of its environment. C-FEM is an interactive demonstration that runs on the iPhone and iPod touch. The application is a proof of concept which includes examples demonstrating piecewise interpolation and non homogeneous elastic properties. Version 1.0 will be available as a free application in late July 2009. A future release of this application will include examples exported from the SOFA implementation.

This application was created by Mattiew Williams and Paul Kry at McGill University. Thanks go to Matthieu Nesme for examples (coming soon) from the SOFA implementation, Adrian Secord for helping us get us started with IB, Christopher Harvey for triangle stripification glue, and Joseph Wain / Glyphish for the free icons.