Triangulation-based L 1-tting of Terrain Surfaces

Given a planar triangulation, the goal is to select elevations at its vertices so that resulting piecewise-linear triangulated surface approximates speci ed elevations using the L 1 -norm as the primary measure-oft. 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 lter and thus provides advantages for \bare earth" representation. For added exibility, a \sign-oriented scaling" scheme has been developed, which generalizes standard norm-based measures-oft. L 1 -approximation is either tackled directly or by iterating suitably weighted L 2 approximations. Numerical experiments are reported.