Abstract
We present a linear-time algorithm for computing a triangulation of n points in 2D whose positions are constrained to n disjoint disks of uniform size, after O ( n log n ) preprocessing applied to these disks. Our algorithm can be extended to any collection of convex sets of bounded areas and aspect ratios, assuming no point lies in more than some constant number of sets (bounded depth of overlap), and each set contains only a constant number of query points.
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