Generalized Voronoi diagrams for a ladder: II. Efficient construction of the diagram

We present a collection of algorithms, all running in timeO(n2 logn α (n)o(α(n)3)) for some fixed integers(where α(n) is the inverse Ackermann's function), for constructing a skeleton representation of a suitably generalized “Voronoi diagram” for a ladder moving in a two-dimensional space bounded by polygonal barriers consisting ofn line segments. This diagram, which is a two-dimensional subcomplex of the dimensional configuration space of the ladder, is introduced and analyzed in a companion paper by the present authors. The construction of the diagram described in this paper yields a motion-planning algorithm for the ladder which runs within the same time bound given above.

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