{"title":"线性复形数字模型拓扑表的构造与修改","authors":"Aleksandr N. Rozhkov, V. Galishnikova","doi":"10.3390/mca28020037","DOIUrl":null,"url":null,"abstract":"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.","PeriodicalId":53224,"journal":{"name":"Mathematical & Computational Applications","volume":" ","pages":""},"PeriodicalIF":1.9000,"publicationDate":"2023-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Construction and Modification of Topological Tables for Digital Models of Linear Complexes\",\"authors\":\"Aleksandr N. Rozhkov, V. Galishnikova\",\"doi\":\"10.3390/mca28020037\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"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. 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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.
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.