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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Combinatorial map ： ウィキペディア英語版 Combinatorial map A combinatorial map is a combinatorial object modelling topological structures with subdivided objects. Historically, the concept was introduced informally by J. Edmonds for polyhedral surfaces 〔Edmonds J., A Combinatorial Representation for Polyhedral Surfaces, Notices Amer. Math. Soc., vol. 7, 1960〕 which are planar graphs. It was given its first definite formal expression under the name "Constellations" by A. Jacques 〔Jacques A., Constellations et Graphes Topologiques, Colloque Math. Soc. János Bolyai, p. 657-672, 1970〕 but the concept was already extensively used under the name "rotation" by Gerhard Ringel〔Ringel G., Map Color Theorem, Springer-Verlag, Berlin 1974〕 and J.W.T. Youngs in their famous solution of the Heawood map-coloring problem. The term "constellation" was not retained and instead "combinatorial map" was favored. The concept was later extended to represent higher-dimensional orientable subdivided objects. Combinatorial maps are used as efficient data structures in image representation and processing, in geometrical modeling. This model is related to simplicial complexes and to combinatorial topology. Note that combinatorial maps were extended to generalized maps that allow also to represent non-orientable objects like the Möbius strip and the Klein bottle. A combinatorial map is a boundary representation model; it represents object by its boundaries. ==Motivation== Several applications require a data structure to represent the subdivision of an object. For example, a 2D object can be decomposed into vertices (0-cells), edges (1-cells), and faces (2-cells). More generally, an n-dimensional object is composed with cells of dimension 0 to n. Moreover, it is also often necessary to represent neighboring relations between these cells. Thus, we want to describe all the cells of the subdivision, plus all the incidence and adjacency relations between these cells. When all the represented cells are simplexes, a simplicial complex can be used, but when we want to represent any type of cells, we need to use cellular topological model, like combinatorial maps or generalized maps. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Combinatorial map」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.