Alternative sculpting hypotheses for terrain data compression

Digital Terrain Models (DTM~s) are large. Processes and data-structures employed to generate and represent them rarely capture the topographic complexity one finds in nature. The result is bulky, unwieldy data sets which need to be thinned to be useful. Many approaches to compressing terrain data resort to assumptions which compromise the complexity of the existing terrain; discontinuities are ignored, for example, surfaces are assumed to be ~2.5 D~; absent of elements such as overhangs, cliffs, or tunnels. Interpolation techniques over rough terrain, in the case of grids, often ignore topographic roughness where it exists. The tradeoffs between the traditional 3-dimensional terrain data structures - grids, TINs and contour line representations - are well-versed. What is called for are novel ways to describe and represent terrain that are compact but which also retain specific, subjectively selected complexity. This paper discusses five alternative notions of sculpting gleaned from a broad spectrum of domains, including CAD/CAM, computer graphics, and the traditional arts. The goal is to come up with novel computational alternatives for three-dimensional terrain surfaces, that may satisfy both the need for more compactness, and for complexity retention. The five notions are: * Carving (subtractive techniques) * ~Modeling~, in the traditional sculpting sense, where one adds material to form an object. * Assembly of sub-parts, or sub-regions * Bending, smoothing, or deforming * Dynamic sculpture or arrangements.