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Detecting and decomposing self-overlapping curves

Authors:

P. W. Shor,

C. J. van WykAuthors Info & Claims

SCG '89: Proceedings of the fifth annual symposium on Computational geometry

Pages 44 - 50

https://doi.org/10.1145/73833.73838

Published: 05 June 1989 Publication History

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Abstract

Paint one side of a rubber disk black and the other side white; stretch the disk any way you wish in three-dimensional space, subject to the condition that from any point in space, if you look down you see either the white side of the disk or nothing at all. Now make the stretched disk transparent but color its boundary black; project its boundary into a plane that lies below the disk. The resulting curve is self-overlapping. We show how to test whether a given curve is self-overlapping, and how to count how many essentially different stretchings of the disk could give rise to the same curve.

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Cited By

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Li YBarbič J(2018)Immersion of self-intersecting solids and surfacesACM Transactions on Graphics10.1145/3197517.320132737:4(1-14)Online publication date: 30-Jul-2018
https://dl.acm.org/doi/10.1145/3197517.3201327
Sacht LJacobson APanozzo DSchüller CSorkine-Hornung OFalcidieno BSpagnuolo MLipman YZhang H(2013)Consistent volumetric discretizations inside self-intersecting surfacesProceedings of the Eleventh Eurographics/ACMSIGGRAPH Symposium on Geometry Processing10.1111/cgf.12181(147-156)Online publication date: 3-Jul-2013
https://dl.acm.org/doi/10.1111/cgf.12181

Index Terms

Detecting and decomposing self-overlapping curves
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
      1. Graph algorithms

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Published In

SCG '89: Proceedings of the fifth annual symposium on Computational geometry

June 1989

401 pages

ISBN:0897913183

DOI:10.1145/73833

Chairman:
Kurt Mehlhorn

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 05 June 1989

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Li YBarbič J(2018)Immersion of self-intersecting solids and surfacesACM Transactions on Graphics10.1145/3197517.320132737:4(1-14)Online publication date: 30-Jul-2018
https://dl.acm.org/doi/10.1145/3197517.3201327
Sacht LJacobson APanozzo DSchüller CSorkine-Hornung OFalcidieno BSpagnuolo MLipman YZhang H(2013)Consistent volumetric discretizations inside self-intersecting surfacesProceedings of the Eleventh Eurographics/ACMSIGGRAPH Symposium on Geometry Processing10.1111/cgf.12181(147-156)Online publication date: 3-Jul-2013
https://dl.acm.org/doi/10.1111/cgf.12181

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