Terrain point cloud data are typically acquired through some form of Light Detection And Ranging sensing. They form a rich resource that is important in a variety of applications including navigation, line of sight, and terrain visualization. Processing terrain data has not received the attention of other forms of surface reconstruction or of image processing. The goal of terrain data processing is to convert the point cloud into a succinct representation system that is amenable to the various application demands. The present paper presents a platform for terrain processing built on the following principles: (i) measuring distortion in the Hausdorff metric, which we argue is a good match for the application demands, (ii) a multiscale representation based on tree approximation using local polynomial fitting. The basic elements held in the nodes of the tree can be efficiently encoded, transmitted, visualized, and utilized for the various target applications. Several challenges emerge because of the variable resolution of the data, missing data, occlusions, and noise. Techniques for identifying and handling these challenges are developed. © 2013 Society for Industrial and Applied Mathematics.