Removing Degeneracies by Perturbing the Problem or Perturbing the World*

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We describe two problem-specific approaches to remove geometric degeneracies that we call perturbing the problem and perturbing the world. Using as our primary examples 2-d and 3-d Delaunay triangulation with Euclidean and polygonal metrics, we show that these approaches lead to relatively simple and efficient perturbations of the points that do not depend on a fixed ordering or index. Thus, they produce canonical output, which is important for producing test suites and verifiers for randomized or dynamic geometric algorithms.

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