A Hierarchical Model for Multiresolution Surface Reconstruction

Abstract

The approximation of topographical surfaces is required in a variety of disciplines, for example, computer graphics and geographic information systems (GIS). The constrained Delaunay pyramid is a hierarchical model for approximating 2$\text{1}\text{2}$-dimensional surfaces at a variety of predefined resolutions. Basically, the topographical data are given by a set of three-dimensional points, but an additional set of nonintersecting line segments describing linear surface features like valleys, ridges, and coast lines is required to constrain the representation. The approximation is obtained by computing a constrained Delaunay triangulation for each resolution. The model generalizes the constraints at coarse resolutions. Due to its structure, the constrained Delaunay pyramid efficiently supports browsing and zooming in large data sets stored in database systems underlying the GIS. For very large data sets, a divide-and-conquer approach allows the computation of the constrained Delaunay pyramid on secondary storage.