Curvature based surface mesh simplification

Abstract

In numerical simulations in science and engineering, e.g., biomechanics and electrical engineering, the representation of the investigated objects or devices is a key aspect regarding both simulation accuracy and performance. Commonly, two different types of representation are used: an implicit or an explicit form. The first can be obtained using, for example, so called level-sets, whereas the latter can be represented using an explicit surface mesh. In some cases an explicit representation extracted from an implicit one is beneficial, e.g., flux calculation. However, the extraction algorithms often yield a too high number of explicit elements potentially jeopardizing the performance of subsequent computation steps. Hence, mesh simplification algorithms are usually applied. However, these algorithms consider the surface mesh as a whole and keep the number of elements higher than necessary in areas with very simple geometry (e.g., flat planes). In this work an algorithm is proposed that analyzes the geometric properties of surface meshes, and adapts the simplification process accordingly. This is achieved by utilizing the curvature of the vertices in the mesh. Depending on the curvature of these vertices the surface is partitioned into different regions. These regions are simplified using different strategies depending on their geometric properties. To maintain a high element quality, which is of utmost importance for the numerical stability of potential subsequent simulation steps, a so called transition region is introduced. This region solves the issue of the highly different element sizes in the initial regions. Compared to the algorithm of Lindstrom and Turk, the distance to the original geometry is smaller, when the same number of vertices is removed. While the calculation time differs on average only by one second, and the element quality is comparable to the element quality when using the Lindstrom and Turk simplification algorithm.