线性复形数字模型拓扑表的构造与修改

IF 1.9 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS
Aleksandr N. Rozhkov, V. Galishnikova
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引用次数: 0

摘要

建筑信息系统使用拓扑表来实现从建筑几何形状的二维线形图到线性综合体的数字三维模型的转换。通过在拓扑表中排列元素名称来命名复数的拓扑元素,并描述复数的拓扑关系。研究了完整建筑拓扑表的有效构造和修改。用12个表描述了具有节点、边、面和单元的线性复合体的拓扑结构。一个综合体的三个表彼此独立,并构成其他表的构造基础。提出了一种复杂度为O(单元数)的高效构造算法,适用于每面边数和每单元面数近似不变的典型建筑。在实践中,建筑设计及其数字模型经常被修改。提出了一种修正算法,其复杂度与构造算法的复杂度相当。实例表明,有效的算法允许用对整个建筑的拓扑结构的关注来取代对建筑组件拓扑结构的传统关注。本文分析了原始拓扑表中没有明确描述的一组性质,例如曲面的方向和多重连通域。综述了拓扑表中不包含的拓扑属性的研究进展。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Construction and Modification of Topological Tables for Digital Models of Linear Complexes
Building information systems use topological tables to implement the transition from two-dimensional line drawings of the geometry of buildings to digital three-dimensional models of linear complexes. The topological elements of the complex are named and the topological relations of the complex are described by arranging the element names in topological tables. The efficient construction and modification of topological tables for complete buildings is investigated. The topology of a linear complex with nodes, edges, faces, and cells is described with 12 tables. Three of the tables of a complex are independent of each other and form a basis for the construction of the other tables. A highly efficient construction algorithm with complexity O (number of cells) for typical buildings with an approximately constant number of edges per face and faces per cell of is presented. In practice, building designs and their digital models are frequently modified. A modification algorithm is presented, whose complexity equals that of the construction algorithm. Examples illustrate that the efficient algorithms permit the replacement of the conventional focus on the topology of building components by a focus on the topology of the entire building. A set of properties of the original, which are not explicitly described by the topological tables, for example, the orientation of surfaces and multiply connected domains, are analyzed in the paper. An overview of the research dealing with the topological attributes that are not contained in topological tables concludes the paper.
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来源期刊
Mathematical & Computational Applications
Mathematical & Computational Applications MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-
自引率
10.50%
发文量
86
审稿时长
12 weeks
期刊介绍: Mathematical and Computational Applications (MCA) is devoted to original research in the field of engineering, natural sciences or social sciences where mathematical and/or computational techniques are necessary for solving specific problems. The aim of the journal is to provide a medium by which a wide range of experience can be exchanged among researchers from diverse fields such as engineering (electrical, mechanical, civil, industrial, aeronautical, nuclear etc.), natural sciences (physics, mathematics, chemistry, biology etc.) or social sciences (administrative sciences, economics, political sciences etc.). The papers may be theoretical where mathematics is used in a nontrivial way or computational or combination of both. Each paper submitted will be reviewed and only papers of highest quality that contain original ideas and research will be published. Papers containing only experimental techniques and abstract mathematics without any sign of application are discouraged.
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