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Decomposing a polygon into its convex parts

Authors:

Bernard Chazelle,

David DobkinAuthors Info & Claims

STOC '79: Proceedings of the eleventh annual ACM symposium on Theory of computing

Pages 38 - 48

https://doi.org/10.1145/800135.804396

Published: 30 April 1979 Publication History

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Abstract

A common operation in geometric computing is the decomposition of complex structures into more basic structures. Since it is easier to apply most algorithms to triangles or arbitrary convex polygons, there is considerable interest in finding fast algorithms for such decompositions. We consider the problem of decomposing a simple (non-convex) polygon into the union of a minimal number of convex polygons. Although the structure of the problem led to the conjecture that it was NP-complete, we have been able to reach polynomial time bounded algorithms for exact solution as well as low degree polynomial time bounded algorithm/or approximation methods.

References

[1]

Dobkin,D., Keyword structures in a language for computer geometry, Bell Laboratories Technical Memorandum, TM 78-1271-9, June 29,1978.

Google Scholar

[2]

Dobkin,D. and Lipton,R., Multidimensional searching problems, SIAM Journal on Computing, Vol. 5, No. 2, June 1976, pp. 181-186.

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Google Scholar

[3]

Dobkin,D. and Snyder,L., On a general method of maximizing and minimizing among certain geometric problems, in preparation.

Google Scholar

[4]

Dobkin,D. and Tomlin,D., Cartographic modelling techniques in environmental planning: an efficient system design, submitted for publication.

Google Scholar

[5]

Feng,H. and Pavlidis,T., Decomposition of polygons into simpler components: feature generation for syntactic pattern recognition, IEEE Transactions on Computers, Vo. C-24, No. 6, June 1975, pp. 636-650.

Google Scholar

[6]

Garey,M., Johnson,D., Preparata,F., and Tarjan,R., Triangulating a simple polygon, Information Processing Letters, Vol. 7, No. 4, June 1978, pp. 175-180.

Google Scholar

[7]

Lloyd,E., On triangulations of a set of points in the plane, 18th Annual IEEE FOCS Conference Proceedings, Providence, R.I., October 1977, pp. 228-240.

Digital Library

Google Scholar

[8]

Pavlidis,T., Analysis of set patterns, Pattern Recognition, Vol. 1, 1968, pp. 165-178.

Google Scholar

[9]

Shamos,M., Geometric Complexity, PhD Thesis, Yale University, May 1978.

Google Scholar

[10]

Volecker,H. private communication to D. Dobkin, November 14, 1977.

Google Scholar

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Decomposing a polygon into its convex parts

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Published In

STOC '79: Proceedings of the eleventh annual ACM symposium on Theory of computing

April 1979

364 pages

ISBN:9781450374385

DOI:10.1145/800135

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: 30 April 1979

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STOC '79 Paper Acceptance Rate 37 of 111 submissions, 33%;

Overall Acceptance Rate 1,469 of 4,586 submissions, 32%

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Gupta PGuo YBoddeti NKrishnamoorthy B(2022)SFCDecomp: Multicriteria Optimized Tool Path Planning in 3D Printing using Space-Filling Curve Based Domain DecompositionInternational Journal of Computational Geometry & Applications10.1142/S021819592150009631:04(193-220)Online publication date: 4-Jun-2022
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