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DOI: 10.4230/LIPIcs.SoCG.2020.41

Combinatorial Properties of Self-Overlapping Curves and Interior Boundaries

Authors: Parker Evans, Brittany Terese Fasy, and Carola Wenk

Published in: LIPIcs, Volume 164, 36th International Symposium on Computational Geometry (SoCG 2020)

Abstract

We study the interplay between the recently-defined concept of minimum homotopy area and the classical topic of self-overlapping curves. The latter are plane curves that are the image of the boundary of an immersed disk. Our first contribution is to prove new sufficient combinatorial conditions for a curve to be self-overlapping. We show that a curve γ with Whitney index 1 and without any self-overlapping subcurves is self-overlapping. As a corollary, we obtain sufficient conditions for self-overlapping ness solely in terms of the Whitney index of the curve and its subcurves. These results follow from our second contribution, which shows that any plane curve γ, modulo a basepoint condition, is transformed into an interior boundary by wrapping around γ with Jordan curves. In fact, we show that n+1 wraps suffice, where γ has n vertices. Our third contribution is to prove the equivalence of various definitions of self-overlapping curves and interior boundaries, often implicit in the literature. We also introduce and characterize zero-obstinance curves, a further generalization of interior boundaries defined by optimality in minimum homotopy area.

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Parker Evans, Brittany Terese Fasy, and Carola Wenk. Combinatorial Properties of Self-Overlapping Curves and Interior Boundaries. In 36th International Symposium on Computational Geometry (SoCG 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 164, pp. 41:1-41:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{evans_et_al:LIPIcs.SoCG.2020.41,
  author =	{Evans, Parker and Fasy, Brittany Terese and Wenk, Carola},
  title =	{{Combinatorial Properties of Self-Overlapping Curves and Interior Boundaries}},
  booktitle =	{36th International Symposium on Computational Geometry (SoCG 2020)},
  pages =	{41:1--41:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-143-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{164},
  editor =	{Cabello, Sergio and Chen, Danny Z.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2020.41},
  URN =		{urn:nbn:de:0030-drops-121993},
  doi =		{10.4230/LIPIcs.SoCG.2020.41},
  annote =	{Keywords: Self-overlapping curves, interior boundaries, minimum homotopy area, immersion}
}

Document

DOI: 10.4230/DagRep.7.7.54

From Observations to Prediction of Movement (Dagstuhl Seminar 17282)

Authors: Mark Birkin, Somayeh Dodge, Brittany Terese Fasy, and Richard Philip Mann

Published in: Dagstuhl Reports, Volume 7, Issue 7 (2018)

Abstract

This report documents the program and the outcomes of Dagstuhl Seminar 17282 "From Observations to Prediction of Movement". This seminar brought together researchers from Animal Behaviour, GIS, Computational Geometry, Data Science and other fields to exchange insights from these diverse fields. Presentations focused both on outstanding practical questions, as well as on fundamental mathematical and computational tools.

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Mark Birkin, Somayeh Dodge, Brittany Terese Fasy, and Richard Philip Mann. From Observations to Prediction of Movement (Dagstuhl Seminar 17282). In Dagstuhl Reports, Volume 7, Issue 7, pp. 54-71, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@Article{birkin_et_al:DagRep.7.7.54,
  author =	{Birkin, Mark and Dodge, Somayeh and Fasy, Brittany Terese and Mann, Richard Philip},
  title =	{{From Observations to Prediction of Movement (Dagstuhl Seminar 17282)}},
  pages =	{54--71},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2018},
  volume =	{7},
  number =	{7},
  editor =	{Birkin, Mark and Dodge, Somayeh and Fasy, Brittany Terese and Mann, Richard Philip},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.7.7.54},
  URN =		{urn:nbn:de:0030-drops-84235},
  doi =		{10.4230/DagRep.7.7.54},
  annote =	{Keywords: trajectory analysis, computational geometry and topology, GIS, animal movement, prediction, home range}
}

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Documents authored by Fasy, Brittany Terese

Combinatorial Properties of Self-Overlapping Curves and Interior Boundaries

Abstract

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From Observations to Prediction of Movement (Dagstuhl Seminar 17282)

Abstract

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