广义bsamzier Patch参数的优化

Q3 Computer Science

计算机辅助设计与图形学学报 Pub Date : 2021-09-01 DOI:10.3724/sp.j.1089.2021.18684

Huibiao Wen, Yajuan Li, Chongyang Deng

{"title":"广义bsamzier Patch参数的优化","authors":"Huibiao Wen, Yajuan Li, Chongyang Deng","doi":"10.3724/sp.j.1089.2021.18684","DOIUrl":null,"url":null,"abstract":": In 2016, Várady, et al. introduced the generalized Bézier patch (GB-patch) using generalized barycentric coordinates and bivariate Bernstein functions. GB-patch has a simple control structure and wonderful geometric properties, but the parameters of Bernstein basis functions are rational polynomial of generalized barycentric coordinates. The linear form of generalized barycentric coordinates is used as parameters of the GB-patch. So, it is convenient to analyze the geometric properties of the patch. Furthermore, it is proved that the new GB-patch has the same blending condition as the original GB-patch between the shared boundary of adjacent patches. Next, the time complexity of the new GB-patch is compared to original GB-patch, which shows that the calculating time is reduced. Finally, several geometric examples are pre-sented to show that the geometric characteristics of the patch are almost the same as those of the original ones.","PeriodicalId":52442,"journal":{"name":"计算机辅助设计与图形学学报","volume":" ","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Optimization for Parameters of Generalized Bézier Patch\",\"authors\":\"Huibiao Wen, Yajuan Li, Chongyang Deng\",\"doi\":\"10.3724/sp.j.1089.2021.18684\",\"DOIUrl\":null,\"url\":null,\"abstract\":\": In 2016, Várady, et al. introduced the generalized Bézier patch (GB-patch) using generalized barycentric coordinates and bivariate Bernstein functions. GB-patch has a simple control structure and wonderful geometric properties, but the parameters of Bernstein basis functions are rational polynomial of generalized barycentric coordinates. The linear form of generalized barycentric coordinates is used as parameters of the GB-patch. So, it is convenient to analyze the geometric properties of the patch. Furthermore, it is proved that the new GB-patch has the same blending condition as the original GB-patch between the shared boundary of adjacent patches. Next, the time complexity of the new GB-patch is compared to original GB-patch, which shows that the calculating time is reduced. Finally, several geometric examples are pre-sented to show that the geometric characteristics of the patch are almost the same as those of the original ones.\",\"PeriodicalId\":52442,\"journal\":{\"name\":\"计算机辅助设计与图形学学报\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-09-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"计算机辅助设计与图形学学报\",\"FirstCategoryId\":\"1093\",\"ListUrlMain\":\"https://doi.org/10.3724/sp.j.1089.2021.18684\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"Computer Science\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"计算机辅助设计与图形学学报","FirstCategoryId":"1093","ListUrlMain":"https://doi.org/10.3724/sp.j.1089.2021.18684","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Computer Science","Score":null,"Total":0}

引用次数: 0

摘要

: 2016年Várady等人利用广义质心坐标和二元Bernstein函数引入了广义bsamzier patch (GB-patch)。GB-patch具有简单的控制结构和优良的几何特性，但Bernstein基函数的参数是广义质心坐标的有理多项式。采用广义质心坐标的线性形式作为GB-patch的参数。这样便于对贴片的几何特性进行分析。进一步证明了新GB-patch在相邻patch的共享边界之间具有与原GB-patch相同的混合条件。然后，将新GB-patch与原GB-patch的时间复杂度进行比较，结果表明计算时间减少。最后，给出了几个几何算例，表明该补丁的几何特征与原始补丁的几何特征基本相同。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Optimization for Parameters of Generalized Bézier Patch

: In 2016, Várady, et al. introduced the generalized Bézier patch (GB-patch) using generalized barycentric coordinates and bivariate Bernstein functions. GB-patch has a simple control structure and wonderful geometric properties, but the parameters of Bernstein basis functions are rational polynomial of generalized barycentric coordinates. The linear form of generalized barycentric coordinates is used as parameters of the GB-patch. So, it is convenient to analyze the geometric properties of the patch. Furthermore, it is proved that the new GB-patch has the same blending condition as the original GB-patch between the shared boundary of adjacent patches. Next, the time complexity of the new GB-patch is compared to original GB-patch, which shows that the calculating time is reduced. Finally, several geometric examples are pre-sented to show that the geometric characteristics of the patch are almost the same as those of the original ones.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

计算机辅助设计与图形学学报 Computer Science-Computer Graphics and Computer-Aided Design

CiteScore

1.20

自引率

0.00%

发文量

6833

期刊介绍：