TOPOLOGICAL MODELS FOR BOUNDARY REPRESENTATION - A COMPARISON WITH N-DIMENSIONAL GENERALIZED MAPS
TOPOLOGICAL MODELS FOR BOUNDARY REPRESENTATION - A COMPARISON WITH N-DIMENSIONAL GENERALIZED MAPS
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DOI：
10.1016/0010-4485(91)90082-8
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发表时间：
1991-01-01
影响因子：
4.3
通讯作者：
LIENHARDT, P
中科院分区：
文献类型：
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作者：
LIENHARDT, P
在边界表示中，几何对象由“拓扑”模型和“嵌入”模型的联合来表示，其中“拓扑”模型描述了建模对象的拓扑，而“嵌入”模型描述了对象的嵌入，例如在三维欧几里得空间中。 近年来，许多拓扑模型已被开发用于边界表示，并且在维数和可定向性方面有了重要的发展。 大体上，可以区分两种类型的拓扑模型。 “关联图”是图或超图，其中节点通常表示建模细分的单元（顶点、边、面等），边表示这些单元之间的邻接和关联关系。 “有序”模型使用单一类型的基本元素（或多或少明确定义），“元素函数”作用于此;建模细分的单元在这种类型的模型中被隐式定义。 本文利用n维广义映射和n维映射的概念，比较了几种最有代表性的有序拓扑模型。 主要的结果是，有序拓扑模型（粗略地说）等价于可以建模的对象类（即关于尺寸和定向性）。
In boundary representation, a geometric object is represented by the union of a 'topological' model, which describes the topology of the modelled object, and an 'embedding' model, which describes the embedding of the object, for instance in three-dimensional Euclidean space. In recent years, numerous topological models have been developed for boundary representation, and there have been important developments with respect to dimension and orientability. In the main, two types of topological models can be distinguished. 'Incidence graphs' are graphs or hypergraphs, where the nodes generally represent the cells of the modelled subdivision (vertex, edge, face, etc.), and the edges represent the adjacency and incidence relations between these cells. 'Ordered' models use a single type of basic element (more or less explicitly defined), on which 'element functions' act; the cells of the modelled subdivision are implicitly defined in this type of model. In this paper some of the most representative ordered topological models are compared using the concepts of the n-dimensional generalized map and the n-dimensional map. The main result is that ordered topological models are (roughly speaking) equivalent with respect to the class of objects which can be modelled (i.e. with respect to dimension and orientability).