Two Novel Surface Representation Techniques

We present two new surface representation techniques: scooping and overdetermined Laplacian PDE approximation. Scooping reveals the terrain by removing material with a set of operators that resembling a 3-axis drill. Each operator has a square cross section, perhaps 7×7 posts, and a surface that is a polynomial of degree ranging from 0 to 3. Scoops may either partition the whole data cell, or else may may applied hierarchically and adaptively as needed to reduce errors. The longterm goal is for scoops to model geologic formation mechanisms such as water erosion. The overdetermined PDE solves a overdetermined system of linear equations to produce a smooth surface approximation to a set of elevation posts. This representation has several advantages, such as the ability to infer local maxima inside nested rings of contours, and the ability to compute a best fit to an inconsistent set of inputs. The input data may be produced by an incremental Triangulated Irregular Network program, supplemented by an iterative insertion of the most inaccurately fitted points. Both representations are part of the GeoStar project to lossily compress large terrain elevation matrices while preserving their usefulness for applications such as visibility and mobility.