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

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 a...

• Type: Journal
• Year: 2007
• Where: CGF
• Authors: Jean-Philippe Pons, Jean-Daniel Boissonnat
• Keywords: CGF 2007, Efficient Lagrangian Approach, Topology Changes, Triangulation