Dynamic Delaunay tetrahedralisation of a deforming surface

Abstract

Reconstruction algorithms make it possible to retrieve a surface from the Delaunay tetrahedralisation (DT) of a point sampling, whose density reflects the surface local geometry and thickness. Most of these algorithms are static and some work remains to be done to handle deforming surfaces. In such case, we defend the idea that each point of the sampling should move with the surface using the information given by the motion to allow fast reconstruction. In this article, we tackle the problem of producing a good evolving sampling of a deforming surface S, and maintaining its DT along the motion. The surface is known only through a projection operator (O 1):ℝ 3→S, and a normal operator (O 2) that returns the oriented normal at a point on the surface. On that basis, we offer some perspectives on how reconstruction algorithms can be extended to the tracking of deforming surfaces. © 2007 Springer-Verlag.