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arXiv · 2309.02588

Distances between realizations of order types

Boris Bukh·R. Amzi Jeffs
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Abstract

Any $n$-tuple of points in the plane can be moved to any other $n$-tuple by a continuous motion with at most $\binom{n}{3}$ intermediate changes of the order type. Even for tuples with the same order type, the cubic bound is sharp: there exist pairs of $n$-tuples of the same order type requiring $c\binom{n}{3}$ intermediate changes.

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Boris Bukh, R. Amzi Jeffs. 2023-09-05. Distances between realizations of order types. https://arxiv.org/abs/2309.02588

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