Fakultät Informatik

A Multigrid Framework for Real-Time Simulation of Deformable Volumes

 Joachim Georgii, Rüdiger Westermann

Computer Graphics and Visualization Group, Technische Universität München, Germany


In this paper, we present a multigrid framework for constructing implicit, yet interactive solvers for the governing equations of motion of deformable volumetric bodies. We have integrated linearized, corotational linearized and non-linear Green strain into this framework. Based on a 3D finite element hierarchy, this approach enables realistic simulation of objects exhibiting an elastic modulus with a dynamic range of several orders of magnitude. Using the linearized strain measure, we can simulate 50 thousand tetrahedral elements with 20 fps on a single processor CPU. By using corotational linearized and non-linear Green strain, we can still simulate five thousand and two thousand elements, respectively, at the same rates.

Iso-surface visualization from a deformed CT data set. A tetrahedral simulation mesh was adaptively refined along the surface and bone structures in the 3D medical data set. This mesh consists of 1.1M tetrahedra, and it was deformed using the linear strain measure at 0.5 fps.

Associated publications

A Multigrid Framework for Real-Time Simulation of Deformable Volumes
J. Georgii, R.Westermann, VRIPHYS Workshop in Virtual Reality Interactions and Physical Simulations 2005 [Bibtex]


Accompanying video of the paper [30 MB AVI]



- In collaboration with partners from industry, we have a number of thesis topics available in the area of point-based rendering, geo-localization using public data, scene fusion from different viewpoints. If you are interested, please contact  westermann(at)tum.de


- Game Devel. Lab Practical for SS'18: kick off meeting on April 3rd,  details here. No matching system sign-up needed!


- One PhD position on   Turbulence Visualization is available at the Computer Graphics & Visualization group.