Triangulation-Based L1-fitting of Terrain Surfaces
Javier Bernal, Christoph Witzgall · 1999
. Given a planar triangulation, the goal is to select elevations at its vertices so that resulting piecewise-linear triangulated surface approximates specified elevations using the L 1 -norm as the primary measure-of-fit. Several suboptimal algorithms relating to that problem have been devised and implemented, and are described here, as part of TIN prototype software for terrain modeling in the context of distributed simulation as well as elevation data editing. L 1 -approximation acts as a median filter and thus provides advantages for "bare earth" representation. For added flexibility, a "sign-oriented scaling" scheme has been developed, which generalizes standard norm-based measures-of-fit. L 1 -approximation is either tackled directly or by iterating suitably weighted L 2 - approximations. Numerical experiments are reported. Key words. bare earth, distributed simulation, L 1 -approximation, L 2 -approximation, linear programming, median filter, terrain surface modeling, TIN, triang...