Representing geometric structures in d dimensions: topology and order
Representing geometric structures in d dimensions: topology and order
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DOI：
10.1145/73833.73858
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发表时间：
1989-06
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影响因子：
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通讯作者：
Erik Brisson
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文献类型：
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作者：
Erik Brisson
我们开发了维数d≥1的细分流形（有边界和无边界）拓扑结构的表示，它允许直接访问可用的顺序信息。证明了细分流形中存在大量的有序信息：给定一个(k-2)-单元在一个(k+1)-单元的边界上，1≤k≤d，它们之间的所有k-和(k-1)-单元都可以“围绕”(k-2)-单元有序。这包括在二维和三维对象中通常的排序。我们引入了“单元元组结构”，这是一种在细分流形中表示关联和排序信息的简单、统一的表示。它包括gu和Stolfi [GS 85]的四边数据结构和Dobkin和Laszlo [DL 87]的面边数据结构，分别作为2维和3维的特例。
We develop a representation for the topological structure of subdivided manifolds (with and without boundary) of dimension d ≥ 1 which allows straightforward access of the available order information. It is shown that there exists a large amount of ordering information in subdivided manifolds: given a (k-2)-cell in the boundary of a (k+1)-cell, 1 ≤ k ≤ d, all of the k- and (k-1)-cells 'between them' can be ordered 'around' the (k-2)-cell. This includes the usual orderings in 2- and 3-dimensional objects. We introduce the 'cell-tuple structure', a simple, uniform representation of the incidence and ordering information in a subdivided manifold. It includes the quad-edge data structure of Guibas and Stolfi [GS 85] and the facet-edge data structure of Dobkin and Laszlo [DL 87] as special cases in dimensions 2 and 3, respectively.