{"title":"Constraints Matrices and Convergence Proof of TPMS2STEP","authors":"Yaonaiming Zhao, Qiang Zou","doi":"arxiv-2407.03352","DOIUrl":null,"url":null,"abstract":"TPMS is consistently described in the functional representation (F-rep)\nformat, while modern CAD/CAM/CAE tools are built upon the boundary\nrepresentation (B-rep) format. To solve this issue, translating TPMS to STEP is\nneeded, called TPMS2STEP. This paper provides constraint matrices and\nconvergence proof of TPMS2STEP so that $C^2$ continuity and an error bound of\n$2\\epsilon$ on the deviation can be ensured during the translation.","PeriodicalId":501570,"journal":{"name":"arXiv - CS - Computational Geometry","volume":"66 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - CS - Computational Geometry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2407.03352","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
TPMS is consistently described in the functional representation (F-rep)
format, while modern CAD/CAM/CAE tools are built upon the boundary
representation (B-rep) format. To solve this issue, translating TPMS to STEP is
needed, called TPMS2STEP. This paper provides constraint matrices and
convergence proof of TPMS2STEP so that $C^2$ continuity and an error bound of
$2\epsilon$ on the deviation can be ensured during the translation.
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