Fast Triangular Approximation of Terrains and Height Fields

We present efficient algorithms for approximating a height field using a piecewise-linear triangulated surface. The algorithms attempt to minimize both the error and the number of triangles in the approximation. The methods we examine are variants of the greedy insertion algorithm. This method begins with a simple triangulation of the domain as an initial approximation. It then iteratively finds the input point with highest error in the current approximation and inserts it as a vertex in the triangulation. We describe optimized algorithms using both Delaunay and data-dependent triangulation criteria. The algorithms have typical costs of O((m + n) logm), where n is the number of points in the input height field and m is the number of vertices in the final approximation. We also present empirical comparisons of several variants of the algorithms on large digital elevation models. We have made a C++ implementation of our algorithms publicly available.

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