QEM-Filtering: A New Technique for Feature-Sensitive Terrain Mesh Simplification

Traditionally, terrain simplification is time consuming and generates multi-resolution models, from which irregular or semi-regular triangulations are extracted to render a terrain at a suitable level of detail. Recent terrain simplification techniques use GPU-friendly regular grids and apply the filtering and sub-sampling paradigm to generate multiple resolutions. However, such approximations only sparsely adapt the terrain surface due to the smoothing and uniform sampling. Consequently, considerably more triangles have to be rendered in order to guarantee a certain error threshold. In this paper we present a novel feature-sensitive simplification technique. Our approach follows the aforementioned paradigm. The key idea is to maintain the regularity and, at the same time, to recompute the vertex positions regarding a specific metric, the quadric error metric (QEM). Compared to previous methods we apply the paradigm to the grid of vertex-associated quadrics, from which the vertices for the new resolution are extracted by quadric error minimization. The benefit is, maintaining the regularity while taking the terrain features into account. As an overall consequence, the approximation error is decreased compared to methods based solely on vertex-filtering and sub-sampling. Hence, our method requires fewer triangles resulting in an improved rendering performance as reported in our results.