On Compatible Star Decompositions of Simple Polygons

Michal Etzion; Ari Rappoport

doi:10.1109/2945.582388

Publication
1997
Issue No. 1 - January-March
Abstract - On Compatible Star Decompositions of Simple Polygons

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On Compatible Star Decompositions of Simple Polygons

January-March 1997 (vol. 3 no. 1)

pp. 87-95

	ASCII Text	x
	Michal Etzion, Ari Rappoport, "On Compatible Star Decompositions of Simple Polygons," IEEE Transactions on Visualization and Computer Graphics, vol. 3, no. 1, pp. 87-95, January-March, 1997.

	BibTex	x
	@article{ 10.1109/2945.582388, author = {Michal Etzion and Ari Rappoport}, title = {On Compatible Star Decompositions of Simple Polygons}, journal ={IEEE Transactions on Visualization and Computer Graphics}, volume = {3}, number = {1}, issn = {1077-2626}, year = {1997}, pages = {87-95}, doi = {http://doi.ieeecomputersociety.org/10.1109/2945.582388}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }

	RefWorks Procite/RefMan/Endnote	x
	TY - JOUR JO - IEEE Transactions on Visualization and Computer Graphics TI - On Compatible Star Decompositions of Simple Polygons IS - 1 SN - 1077-2626 SP87 EP95 EPD - 87-95 A1 - Michal Etzion, A1 - Ari Rappoport, PY - 1997 KW - Star decomposition KW - minimal star decomposition KW - compatible decompositions KW - compatible star decompositions. VL - 3 JA - IEEE Transactions on Visualization and Computer Graphics ER -

Michal Etzion

Ari Rappoport

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/2945.582388

Abstract—We introduce the notion of compatible star decompositions of simple polygons. In general, given two polygons with a correspondence between their vertices, two polygonal decompositions of the two polygons are said to be compatible if there exists a one-to-one mapping between them such that the corresponding pieces are defined by corresponding vertices. For compatible star decompositions, we also require correspondence between star points of the star pieces. Compatible star decompositions have applications in computer animation and shape representation and analysis.

We present two algorithms for constructing compatible star decompositions of two simple polygons. The first algorithm is optimal in the number of pieces in the decomposition, providing that such a decomposition exists without adding Steiner vertices. The second algorithm constructs compatible star decompositions with Steiner vertices, which are not minimal in the number of pieces but are asymptotically worst case optimal in this number and in the number of added Steiner vertices. We prove that some pairs of polygons require Ω(n2) pieces, and that the decompositions computed by the second algorithm possess no more than O(n2) pieces.

In addition to the contributions regarding compatible star decompositions, the paper also corrects an error in the only previously published polynomial algorithm for constructing a minimal star decomposition of a simple polygon, an error which might lead to a nonminimal decomposition.

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Index Terms:

Star decomposition, minimal star decomposition, compatible decompositions, compatible star decompositions.

Citation:

Michal Etzion, Ari Rappoport, "On Compatible Star Decompositions of Simple Polygons," IEEE Transactions on Visualization and Computer Graphics, vol. 3, no. 1, pp. 87-95, Jan.-March 1997, doi:10.1109/2945.582388

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