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

Abstract

Terrain simplification generates multi-resolution models, from which - traditionally - irregular or semi-regular triangulations are extracted to render a terrain at a suitable level of detail. Recent terrain simplification techniques, in contrast, rely on GPU-friendly regular grids and generate multiple resolutions by applying the filtering and sub-sampling paradigm. However, due to the smoothing and uniform sampling, these techniques sparsely approximate the terrain surface. Consequently, in order to guarantee a certain error threshold, considerably more triangles need to be rendered. 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 while recomputing the vertex positions by taking a specific error metric into account, namely the quadric error metric (QEM). Compared to previous approaches, we apply the paradigm to the grid of vertex-associated quadrics. From these we extract vertices of the new resolution by relying on quadric error minimization. We, thus, maintain the regular grid structure while preserving terrain features. Compared to methods, which are solely based on vertex-filtering and sub-sampling, our approach reduces the approximation error. As a consequence, we require fewer triangles, which improves the rendering performance.