The problem of accurately modeling a level surface with polygons is cast in a distortion-rate framework and efficient tilings across a range of resolutions are found. A distinctive feature of this work is the quantification of surface approximation error. Existing algorithms for extracting polygonal isosurfaces from sampled 3-D scalar fields typically partition the samples into cubical cells and generate triangles for each cell. Adaptive schemes use variable-size cells to allocate more triangles in regions where the tilings do poorly, and vice versa. In this paper, an octree structure is imposed on the data and then selectively pruned according to local error. To guide the pruning, an ideal level surface is defined from the 3-D samples, and a distortion measure is introduced to quantify the error associated with any polygonal approximation to the ideal. Using the polygon count as the rate measure, the performance of tilings is then characterized by distortion-rate pairs. With this performance criterion, the pruning algorithm then finds good approximations at multiple resolutions. Results are presented for both simulated and experimental data sets. Lower resolution models are used for interactive viewing and editing while full resolution models are usually reserved for final analysis or presentation.© (1991) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.