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We present a simple algorithm to compute the straight skeleton and mitered offset surfaces of a polyhedral terrain in 3D, i.e., of a z-monotone piecewise-linear surface. Like its 2D pedant, the 3D straight skeleton is the result of a wavefront propagation process, which we simulate in order to construct the skeleton in (worst-case) time O(n 4 log n), where n is the number of vertices of the terrain. Any mitered offset surface can then be obtained from the skeleton in time linear in the combinatorial size of the skeleton.

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