An Improved Refinement and Decimation Method for Adaptive Terrain Surface Approximation

An improved method for adaptively constructing a terrain surface representation from a set of data points is presented. Refinement and decimation steps are repeatedly applied to triangular meshes, incrementally determining a better distribution of the data points, while a specified error tolerance is preserved. Even though not asymptotically optimal or monotonically convergent, it produces approximations that are, experimentally, significantly better than those generated by straightforward greedy insertion algorithms. A new local error metric is used to select points to be inserted into the triangulation, based on the maximum vertical error weighted by the standard deviation calculated in a neighborhood of the candidate point. Conversely, a measure of angle between surface normals is used to determine whether a vertex should be removed from the triangulation. The method has been implemented and tested on both synthetic test cases and real terrain data sets.