2026-07-22T07:15:45Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:13357 2024-03-06T10:51:46Z ddc:004 open_access

Between Shapes, Using the Hausdorff Distance van Kreveld, Marc Miltzow, Tillmann Ophelders, Tim Sonke, Willem Vermeulen, Jordi L. computational geometry Hausdorff distance shape interpolation 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Marc van Kreveld and Tillmann Miltzow and Tim Ophelders and Willem Sonke and Jordi L. Vermeulen 2020 Is Part Of LIPIcs, Volume 181, 31st International Symposium on Algorithms and Computation (ISAAC 2020) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ISAAC.2020.13 urn:nbn:de:0030-drops-133572 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2020.13 eng https://creativecommons.org/licenses/by/3.0/legalcode