{"title":"基于压缩自映射的数字地图自动归纳算法","authors":"Piotr Banasik, T. Chrobak, Bartosz Biegun","doi":"10.2478/pcr-2022-0001","DOIUrl":null,"url":null,"abstract":"Abstract The research of modern cartography in the field of digital generalisation focuses on the development of such methods that would be fully automatic and give an unambiguously objective result. Devising them requires specific standards as well as unique and verifiable algorithms. In metric space, a proposal for such a method, based on contractive mapping, the Lipschitz and Cauchy conditions and the Banach theorem, using the Salishchev metric, was presented in the publication (Barańska et al., 2021). The method formulated there is dedicated to linear objects (polylines). The current work is a practical supplement to it. It presents the practical implementation of the algorithm for automatic and objective generalisation. The article describes an operational diagram of the subsequent stages of the proposed generalisation method. In the test example, a binary tree structure of an ordered polyline was created. It was simplified in two selected scales and its shape after generalisation was illustrated. The resulting polyline obtained by the fully automatic method was verified in terms of accuracy.","PeriodicalId":30929,"journal":{"name":"Polish Cartographical Review","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Algorithm of automatic digital cartographic generalisation with the use of contractive self-mapping\",\"authors\":\"Piotr Banasik, T. Chrobak, Bartosz Biegun\",\"doi\":\"10.2478/pcr-2022-0001\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract The research of modern cartography in the field of digital generalisation focuses on the development of such methods that would be fully automatic and give an unambiguously objective result. Devising them requires specific standards as well as unique and verifiable algorithms. In metric space, a proposal for such a method, based on contractive mapping, the Lipschitz and Cauchy conditions and the Banach theorem, using the Salishchev metric, was presented in the publication (Barańska et al., 2021). The method formulated there is dedicated to linear objects (polylines). The current work is a practical supplement to it. It presents the practical implementation of the algorithm for automatic and objective generalisation. The article describes an operational diagram of the subsequent stages of the proposed generalisation method. In the test example, a binary tree structure of an ordered polyline was created. It was simplified in two selected scales and its shape after generalisation was illustrated. The resulting polyline obtained by the fully automatic method was verified in terms of accuracy.\",\"PeriodicalId\":30929,\"journal\":{\"name\":\"Polish Cartographical Review\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Polish Cartographical Review\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2478/pcr-2022-0001\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Polish Cartographical Review","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2478/pcr-2022-0001","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
摘要
现代地图学在数字概括领域的研究重点是开发这种完全自动化并给出明确客观结果的方法。设计它们需要特定的标准以及独特和可验证的算法。在度量空间中,基于压缩映射,Lipschitz和Cauchy条件以及Banach定理,使用Salishchev度量的方法的建议在出版物中提出(Barańska et al., 2021)。该方法专门用于线性对象(折线)。目前的工作是对它的实际补充。给出了自动客观泛化算法的具体实现。本文描述了所提出的泛化方法的后续阶段的操作图。在测试示例中,创建了有序折线的二叉树结构。将其简化为两个选择的尺度,并说明了其推广后的形状。对全自动法得到的折线进行了精度验证。
Algorithm of automatic digital cartographic generalisation with the use of contractive self-mapping
Abstract The research of modern cartography in the field of digital generalisation focuses on the development of such methods that would be fully automatic and give an unambiguously objective result. Devising them requires specific standards as well as unique and verifiable algorithms. In metric space, a proposal for such a method, based on contractive mapping, the Lipschitz and Cauchy conditions and the Banach theorem, using the Salishchev metric, was presented in the publication (Barańska et al., 2021). The method formulated there is dedicated to linear objects (polylines). The current work is a practical supplement to it. It presents the practical implementation of the algorithm for automatic and objective generalisation. The article describes an operational diagram of the subsequent stages of the proposed generalisation method. In the test example, a binary tree structure of an ordered polyline was created. It was simplified in two selected scales and its shape after generalisation was illustrated. The resulting polyline obtained by the fully automatic method was verified in terms of accuracy.