@inproceedings{71b21d90a6464c11ab4bd9b84c76882b,
title = "Between Shapes, Using the Hausdorff Distance",
abstract = "Given two shapes A and B in the plane with Hausdorff distance 1, is there a shape S with Hausdorff distance 1/2 to and from A and B? The answer is always yes, and depending on convexity of A and/or B, S may be convex, connected, or disconnected. We show a generalization of this result on Hausdorff distances and middle shapes, and show some related properties. We also show that a generalization of such middle shapes implies a morph with a bounded rate of change. Finally, we explore a generalization of the concept of a Hausdorff middle to more than two sets and show how to approximate or compute it.",
keywords = "computational geometry, Hausdorff distance, shape interpolation",
author = "{van Kreveld}, M.J. and T. Miltzow and Tim Ophelders and Willem Sonke and Vermeulen, {Jordi L.}",
year = "2020",
doi = "10.4230/LIPIcs.ISAAC.2020.13",
language = "English",
isbn = "978-3-95977-173-3",
series = "Leibniz International Proceedings in Informatics (LIPIcs)",
publisher = "Schloss Dagstuhl – Leibniz-Zentrum f{\"u}r Informatik GmbH",
pages = "13:1--13:16",
editor = "Yixin Cao and Siu-Wing Cheng and Minming Li",
booktitle = "31st International Symposium on Algorithms and Computation (ISAAC 2020)",
}