{"title":"利用偏微分方程的曲面建模:综述","authors":"L. You, Xiaogang Jin, X. You, J. Zhang","doi":"10.1109/IV.2013.62","DOIUrl":null,"url":null,"abstract":"Partial differential equation-based surface modelling is a new approach of creating and manipulating three-dimensional geometric models. It uses the solution to a vector-valued partial differential equation subjected to suitably defined boundary constraints to carry out surface modeling. This paper provides a survey on this approach which summarizes various mathematical models of partial differential equation-based surface modelling, accurate and approximate analytical solutions as well as numerical solutions of the mathematical models, and the applications of partial differential equation-based surface modelling. It also discusses some future research directions of partial differential equation-based surface modelling.","PeriodicalId":354135,"journal":{"name":"2013 17th International Conference on Information Visualisation","volume":"22 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2013-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Surface Modeling Using Partial Differential Equations: A Survey\",\"authors\":\"L. You, Xiaogang Jin, X. You, J. Zhang\",\"doi\":\"10.1109/IV.2013.62\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Partial differential equation-based surface modelling is a new approach of creating and manipulating three-dimensional geometric models. It uses the solution to a vector-valued partial differential equation subjected to suitably defined boundary constraints to carry out surface modeling. This paper provides a survey on this approach which summarizes various mathematical models of partial differential equation-based surface modelling, accurate and approximate analytical solutions as well as numerical solutions of the mathematical models, and the applications of partial differential equation-based surface modelling. It also discusses some future research directions of partial differential equation-based surface modelling.\",\"PeriodicalId\":354135,\"journal\":{\"name\":\"2013 17th International Conference on Information Visualisation\",\"volume\":\"22 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2013-07-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2013 17th International Conference on Information Visualisation\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/IV.2013.62\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2013 17th International Conference on Information Visualisation","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/IV.2013.62","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Surface Modeling Using Partial Differential Equations: A Survey
Partial differential equation-based surface modelling is a new approach of creating and manipulating three-dimensional geometric models. It uses the solution to a vector-valued partial differential equation subjected to suitably defined boundary constraints to carry out surface modeling. This paper provides a survey on this approach which summarizes various mathematical models of partial differential equation-based surface modelling, accurate and approximate analytical solutions as well as numerical solutions of the mathematical models, and the applications of partial differential equation-based surface modelling. It also discusses some future research directions of partial differential equation-based surface modelling.
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