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Consider two (n−1)-dimensional manifolds, S and S′ in ℝ n . We say that they are normal-compatible when the closest projection of each one onto the other is a homeomorphism. We give a tight condition under which S and S′ are normal-compatible. It involves the minimum feature size of S and of S′ and the Hausdorff distance between them. Furthermore, when S and S′ are normal-compatible, their Frechet distance is equal to their Hausdorff distance. Our results hold for arbitrary dimension n.
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Chazal et al. (2007) studied this question.
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