Representing Terrain with Mathematical Operators

Abstract

This work describes a mathematical representation of terrain data consisting of a novel operation, the “drill”. It facilitates the representation of legal terrains, capturing the richness of the physics of the terrain’s generation by digging channels in the surface. Given our current reliance on digital map data, hand-held devices, and GPS navigation systems, the accuracy and compactness of terrain data representations are becoming increasingly important. Representing a terrain as a series of operations that can procedurally regenerate the terrains allows for compact representation that retains more information than height fields, TINs, and other popular representations. Our model relies on the hydrography information extracted from the terrain, and so drainage information is retained during encoding. To determine the shape of the drill along each channel in the channel network, a cross section of the channel is extracted, and a quadratic polynomial is fit to it. We extract the drill representation from a mountainous dataset, using a series of parameters (including size and area of influence of the drill, as well as the density of the hydrography data), and present the accuracy calculated using a series of metrics. We demonstrate that the drill operator provides a viable and accurate terrain representation that captures both the terrain shape and the richness of its generation.