{"title":"Point-normal convexity preserving curve interpolation","authors":"Nikolaos C. Gabrielides , Nickolas S. Sapidis","doi":"10.1016/j.cad.2024.103836","DOIUrl":null,"url":null,"abstract":"<div><div>This paper studies the notion of convexity preservation in the context of point-normal interpolation in 2D. It is proved that <span><math><msup><mrow><mi>G</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-continuous piecewise <em>generalized cubic curves in tension</em> are always capable of preserving the convexity implied by the data with finite tension parameters. Focus is placed on the variable degree polynomials and it is proved that there always exist a <span><math><msup><mrow><mi>G</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-continuous cubic spline that interpolates the data and is also convexity preserving.</div></div>","PeriodicalId":50632,"journal":{"name":"Computer-Aided Design","volume":"180 ","pages":"Article 103836"},"PeriodicalIF":3.0000,"publicationDate":"2024-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computer-Aided Design","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0010448524001635","RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"COMPUTER SCIENCE, SOFTWARE ENGINEERING","Score":null,"Total":0}
引用次数: 0
Abstract
This paper studies the notion of convexity preservation in the context of point-normal interpolation in 2D. It is proved that -continuous piecewise generalized cubic curves in tension are always capable of preserving the convexity implied by the data with finite tension parameters. Focus is placed on the variable degree polynomials and it is proved that there always exist a -continuous cubic spline that interpolates the data and is also convexity preserving.
期刊介绍:
Computer-Aided Design is a leading international journal that provides academia and industry with key papers on research and developments in the application of computers to design.
Computer-Aided Design invites papers reporting new research, as well as novel or particularly significant applications, within a wide range of topics, spanning all stages of design process from concept creation to manufacture and beyond.