Dynamic Progressive Triangle-Quadrilateral Meshes

Abstract

We present an extension of the original progressive mesh algorithm for large dynamic meshes that contain a mix of triangle and quadrilateral elements. The demand for this extension comes from the visualisation of dynamic finite element simulations, such as car crashes or metal sheet punch operations. These methods use meshes, which consist mainly of quadrilaterals, due to their increased numerical stability during the simulation. Furthermore, these meshes have a dynamic geometry with about 25 to 100 animation steps. Accordingly, we extend the original progressive mesh algorithm in two aspects: First, the edge collapse operation is extended for meshes with a mixture of triangle and quadrilateral elements. Second, we present an algorithm on how to extend quadric error metrics for the simplification of large dynamic meshes with many animation steps. The results are dynamic progressive triangle-quadrilateral meshes – a progressive multi-resolution mesh structure that has two interactive degrees of freedom: simulation time and mesh resolution. We show that our method works on meshes with up to one million vertices and 25 animation steps. We measure the approximation error and compare the results to other algorithms.