Skip to Main content Skip to Navigation
Journal articles

A Lagrangian Approach to Dynamic Interfaces through Kinetic Triangulation of the Ambient Space

Abstract : In this paper, we propose a robust and efficient Lagrangian approach for modeling dynamic interfaces between different materials undergoing large deformations and topology changes, in two dimensions. Our work brings an interesting alternative to popular techniques such as the level set method and the particle level set method, for two-dimensional and axisymmetric simulations. The principle of our approach is to maintain a two-dimensional triangulation which embeds the one-dimensional polygonal description of the interfaces. Topology changes can then be detected as inversions of the faces of this triangulation. Each triangular face is labeled with the type of material it contains. The connectivity of the triangulation and the labels of the faces are updated consistently during deformation, within a neat framework developed in computational geometry: kinetic data structures. Thanks to the exact computation paradigm, the reliability of our algorithm, even in difficult situations such as shocks and topology changes, can be certified. We demonstrate the applicability and the efficiency of our approach with a series of numerical experiments in two dimensions. Finally, we discuss the feasibility of an extension to three dimensions.
Document type :
Journal articles
Complete list of metadata

Cited literature [55 references]  Display  Hide  Download
Contributor : Jean-Daniel Boissonnat Connect in order to contact the contributor
Submitted on : Tuesday, June 1, 2010 - 8:16:52 AM
Last modification on : Thursday, October 21, 2021 - 3:06:15 PM
Long-term archiving on: : Friday, September 17, 2010 - 11:24:48 AM


Files produced by the author(s)


  • HAL Id : hal-00488039, version 1



Jean-Philippe Pons, Jean-Daniel Boissonnat. A Lagrangian Approach to Dynamic Interfaces through Kinetic Triangulation of the Ambient Space. Computer Graphics Forum, Wiley, 2007, 26 (2), pp.227-239. ⟨hal-00488039⟩



Record views


Files downloads