Matches in SemOpenAlex for { <https://semopenalex.org/work/W4247827992> ?p ?o ?g. }
Showing items 1 to 60 of
60
with 100 items per page.
- W4247827992 endingPage "187" @default.
- W4247827992 startingPage "187" @default.
- W4247827992 abstract "We prove the following criterion: a compact connected piecewise-linear hypersurface (without boundary) in Rn (n⩾3) is the boundary of a convex body if and only if every point in the relative interior of each (n−3)-face has a neighborhood that lies on the boundary of some convex body. This criterion is derived from our theorem that any connected complete locally convex hypersurface in Sn (n⩾3) is the boundary of a convex body in Sn. We give an easy-to-implement convexity testing algorithm based on our criterion. This algorithm does not require any assumptions about the global topology of the input hypersurface. For R3 the number of arithmetic operations used by our algorithm is at most linear in the number of vertices, while in general it is at most linear in the number of incidences between (n−2)-faces and (n−3)-faces. The algorithm still remains polynomial even when the dimension n is a variable and the bit complexity model for (exact) arithmetic operations is used. The suggested method works in more general situations than the convexity verification algorithms developed by [K. Mehlhorn, S. Näher, M. Seel, R. Seidel, T. Schilz, S. Schirra, U. Stefan, C. Uhrig, Checking geometric properties or verification of geometric structures, in: Proc. of 12th Annual ACM Sympos. Comput. Geom., Computational Geom., 1996, pp. 159–165] and [O. Devillers, G. Liotta, F. Preparata, R. Tamassia, Checking the convexity of polytopes and the planarity of subdivisions, Comput. Geom. 11 (1998) 187–208]—for example, our method does not require the input surface to be homeomorphic to the sphere, nor does it require the input data to include normal vectors to the facets that are oriented “in a coherent way”. For R3 the complexity of our algorithm is the same as that of previously known algorithms; for higher dimensions there seems to be no clear winner, but our approach is the only one that easily treats surfaces of arbitrary topology without a preliminary topological computation aimed at verifying that the input is a topological sphere. Furthermore, our method can be easily extended to piecewise-polynomial surfaces of degree 2 and 3." @default.
- W4247827992 created "2022-05-12" @default.
- W4247827992 date "1976-01-01" @default.
- W4247827992 modified "2023-10-17" @default.
- W4247827992 title "Comparative investigation of thick-film and thin-film components and MIC's up to 16 GHz" @default.
- W4247827992 doi "https://doi.org/10.1016/0026-2714(76)90729-0" @default.
- W4247827992 hasPublicationYear "1976" @default.
- W4247827992 type Work @default.
- W4247827992 citedByCount "0" @default.
- W4247827992 crossrefType "journal-article" @default.
- W4247827992 hasConcept C106159729 @default.
- W4247827992 hasConcept C112680207 @default.
- W4247827992 hasConcept C114410712 @default.
- W4247827992 hasConcept C114614502 @default.
- W4247827992 hasConcept C118615104 @default.
- W4247827992 hasConcept C134306372 @default.
- W4247827992 hasConcept C145691206 @default.
- W4247827992 hasConcept C162324750 @default.
- W4247827992 hasConcept C184720557 @default.
- W4247827992 hasConcept C202444582 @default.
- W4247827992 hasConcept C2524010 @default.
- W4247827992 hasConcept C33923547 @default.
- W4247827992 hasConcept C62354387 @default.
- W4247827992 hasConcept C72134830 @default.
- W4247827992 hasConcept C90119067 @default.
- W4247827992 hasConceptScore W4247827992C106159729 @default.
- W4247827992 hasConceptScore W4247827992C112680207 @default.
- W4247827992 hasConceptScore W4247827992C114410712 @default.
- W4247827992 hasConceptScore W4247827992C114614502 @default.
- W4247827992 hasConceptScore W4247827992C118615104 @default.
- W4247827992 hasConceptScore W4247827992C134306372 @default.
- W4247827992 hasConceptScore W4247827992C145691206 @default.
- W4247827992 hasConceptScore W4247827992C162324750 @default.
- W4247827992 hasConceptScore W4247827992C184720557 @default.
- W4247827992 hasConceptScore W4247827992C202444582 @default.
- W4247827992 hasConceptScore W4247827992C2524010 @default.
- W4247827992 hasConceptScore W4247827992C33923547 @default.
- W4247827992 hasConceptScore W4247827992C62354387 @default.
- W4247827992 hasConceptScore W4247827992C72134830 @default.
- W4247827992 hasConceptScore W4247827992C90119067 @default.
- W4247827992 hasIssue "3" @default.
- W4247827992 hasLocation W42478279921 @default.
- W4247827992 hasOpenAccess W4247827992 @default.
- W4247827992 hasPrimaryLocation W42478279921 @default.
- W4247827992 hasRelatedWork W1998973221 @default.
- W4247827992 hasRelatedWork W2009773457 @default.
- W4247827992 hasRelatedWork W2123195153 @default.
- W4247827992 hasRelatedWork W2171108458 @default.
- W4247827992 hasRelatedWork W2494974567 @default.
- W4247827992 hasRelatedWork W2951049512 @default.
- W4247827992 hasRelatedWork W2951603011 @default.
- W4247827992 hasRelatedWork W2953085781 @default.
- W4247827992 hasRelatedWork W2993215509 @default.
- W4247827992 hasRelatedWork W940482830 @default.
- W4247827992 hasVolume "15" @default.
- W4247827992 isParatext "false" @default.
- W4247827992 isRetracted "false" @default.
- W4247827992 workType "article" @default.