{"title":"具有保证微分性质的隐函数","authors":"V. Shapiro, I. Tsukanov","doi":"10.1145/304012.304038","DOIUrl":null,"url":null,"abstract":"Theory of R-functions [12] provides the methodology for constructing exact implicit functions for any semianalytic set. This paper systematically explores and compares the known constructions in terms of their differential properties and explains how such functions may be constructed automatically from CSG and boundary representations of solids. The constructed functions may be automatically differentiated and integrated and have many important applications in meshfree engineering analysis, motion planning, and scientific visualization.","PeriodicalId":286112,"journal":{"name":"International Conference on Smart Media and Applications","volume":"41 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1999-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"101","resultStr":"{\"title\":\"Implicit functions with guaranteed differential properties\",\"authors\":\"V. Shapiro, I. Tsukanov\",\"doi\":\"10.1145/304012.304038\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Theory of R-functions [12] provides the methodology for constructing exact implicit functions for any semianalytic set. This paper systematically explores and compares the known constructions in terms of their differential properties and explains how such functions may be constructed automatically from CSG and boundary representations of solids. The constructed functions may be automatically differentiated and integrated and have many important applications in meshfree engineering analysis, motion planning, and scientific visualization.\",\"PeriodicalId\":286112,\"journal\":{\"name\":\"International Conference on Smart Media and Applications\",\"volume\":\"41 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1999-06-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"101\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Conference on Smart Media and Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/304012.304038\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Conference on Smart Media and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/304012.304038","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 101
摘要
r -函数理论[12]提供了构造任意半解析集的精确隐函数的方法。本文系统地探索和比较了已知的结构在它们的微分性质方面,并解释了如何从固体的CSG和边界表示自动构造这些函数。所构造的函数可以自动区分和集成,在无网格工程分析、运动规划和科学可视化等方面有着重要的应用。
Implicit functions with guaranteed differential properties
Theory of R-functions [12] provides the methodology for constructing exact implicit functions for any semianalytic set. This paper systematically explores and compares the known constructions in terms of their differential properties and explains how such functions may be constructed automatically from CSG and boundary representations of solids. The constructed functions may be automatically differentiated and integrated and have many important applications in meshfree engineering analysis, motion planning, and scientific visualization.