{"title":"On the Curve of Minimal Length between Two Points On a Bézier Surface","authors":"A. Carriazo, M. C. Márquez, H. Ugail","doi":"10.1109/SKIMA47702.2019.8982434","DOIUrl":null,"url":null,"abstract":"In this paper, we present a method to obtain the distance between two fixed points of a Bézier surface by minimizing the length of curves on the surface linking the two points. We use a discretization of the classical orthogonal variations method for a regular planar curve. We provide interesting examples of Bézier surfaces which approximate the cylinder, the sphere and the hyperbolic paraboloid.","PeriodicalId":245523,"journal":{"name":"2019 13th International Conference on Software, Knowledge, Information Management and Applications (SKIMA)","volume":"117 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2019-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2019 13th International Conference on Software, Knowledge, Information Management and Applications (SKIMA)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/SKIMA47702.2019.8982434","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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Abstract
In this paper, we present a method to obtain the distance between two fixed points of a Bézier surface by minimizing the length of curves on the surface linking the two points. We use a discretization of the classical orthogonal variations method for a regular planar curve. We provide interesting examples of Bézier surfaces which approximate the cylinder, the sphere and the hyperbolic paraboloid.
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