DC Field | Value | Language |
---|---|---|
dc.contributor.author | Ahn, HK | ko |
dc.contributor.author | Bae, S | ko |
dc.contributor.author | Cheong, Otfried | ko |
dc.contributor.author | Gudmundsson, J | ko |
dc.date.accessioned | 2008-10-30T08:44:14Z | - |
dc.date.available | 2008-10-30T08:44:14Z | - |
dc.date.created | 2012-02-06 | - |
dc.date.created | 2012-02-06 | - |
dc.date.issued | 2008-10 | - |
dc.identifier.citation | DISCRETE & COMPUTATIONAL GEOMETRY, v.40, no.3, pp.414 - 429 | - |
dc.identifier.issn | 0179-5376 | - |
dc.identifier.uri | http://hdl.handle.net/10203/7708 | - |
dc.description.abstract | The aperture angle alpha(x, Q) of a point x is not an element of Q in the plane with respect to a convex polygon Q is the angle of the smallest cone with apex x that contains Q. The aperture angle approximation error of a compact convex set C in the plane with respect to an inscribed convex polygon Q. C is the minimum aperture angle of any x is an element of C \ Q with respect to Q. We show that for any compact convex set C in the plane and any k > 2, there is an inscribed convex k-gon Q subset of C with aperture angle approximation error (1 - 2/k+1)pi. This bound is optimal, and settles a conjecture by Fekete from the early 1990s. The same proof technique can be used to prove a conjecture by Brass: If a polygon P admits no approximation by a sub-k-gon (the convex hull of k vertices of P) with Hausdorff distance sigma, but all subpolygons of P (the convex hull of some vertices of P) admit such an approximation, then P is a (k + 1)-gon. This implies the following result: For any k > 2 and any convex polygon P of perimeter at most 1 there is a sub-k-gon Q of P such that the Hausdorff-distance of P and Q is at most 1/k+1 sin pi/k+1. | - |
dc.description.sponsorship | This research was supported by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD) (KRF-2006-311-D00763). | en |
dc.language | English | - |
dc.language.iso | en_US | en |
dc.publisher | SPRINGER | - |
dc.title | Aperture-angle and Hausdorff-approximation of convex figures | - |
dc.type | Article | - |
dc.identifier.wosid | 000259563600008 | - |
dc.identifier.scopusid | 2-s2.0-52949129795 | - |
dc.type.rims | ART | - |
dc.citation.volume | 40 | - |
dc.citation.issue | 3 | - |
dc.citation.beginningpage | 414 | - |
dc.citation.endingpage | 429 | - |
dc.citation.publicationname | DISCRETE & COMPUTATIONAL GEOMETRY | - |
dc.identifier.doi | 10.1007/s00454-007-9039-5 | - |
dc.contributor.localauthor | Cheong, Otfried | - |
dc.contributor.nonIdAuthor | Ahn, HK | - |
dc.contributor.nonIdAuthor | Bae, S | - |
dc.contributor.nonIdAuthor | Gudmundsson, J | - |
dc.type.journalArticle | Article | - |
dc.subject.keywordAuthor | Hausdorff approximation | - |
dc.subject.keywordAuthor | aperture angle | - |
dc.subject.keywordAuthor | convex figure | - |
dc.subject.keywordAuthor | subpolygon | - |
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