Delaunay Deformable Models: Topology-Adaptive Meshes Based on the Restricted Delaunay Triangulation

Abstract

International audienceIn this paper, we propose a robust and efficient La- grangian approach, which we call Delaunay Deformable Models, for modeling moving surfaces undergoing large de- formations and topology changes. Our work uses the con- cept of restricted Delaunay triangulation, borrowed from computational geometry. In our approach, the interface is represented by a triangular mesh embedded in the Delau- nay tetrahedralization of interface points. The mesh is it- eratively updated by computing the restricted Delaunay tri- angulation of the deformed objects. Our method has many advantages over popular Eulerian techniques such as the level set method and over hybrid Eulerian-Lagrangian tech- niques such as the particle level set method: localization accuracy, adaptive resolution, ability to track properties as- sociated to the interface, seamless handling of triple junc- tions. Our work brings a rigorous and efficient alternative to existing topology-adaptive mesh techniques such as T- snakes