{"title":"确定参数化曲面何时为旋转曲面","authors":"Haohao Wang, Jerzy Wojdylo","doi":"10.36890/iejg.1064089","DOIUrl":null,"url":null,"abstract":"A surface of revolution is a surface that can be generated by rotating a planar curve (the directrix)\naround a straight line (the axis) in the same plane. Using the mathematics of quaternions, we provide a parametric\nequation of a surface of revolution generated by rotating a directrix about an axis by quaternion multiplication\nof the parametric representations of the directrix curve and the line of axis. Then, we describe an algorithm\nto determine whether a parametric surface is a surface of revolution, and identify the axis and the directrix.\nExamples are provided to illustrate our algorithm.","PeriodicalId":43768,"journal":{"name":"International Electronic Journal of Geometry","volume":" ","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2022-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"DETERMINE WHEN A PARAMETRIC SURFACE IS A SURFACE OF REVOLUTION\",\"authors\":\"Haohao Wang, Jerzy Wojdylo\",\"doi\":\"10.36890/iejg.1064089\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A surface of revolution is a surface that can be generated by rotating a planar curve (the directrix)\\naround a straight line (the axis) in the same plane. Using the mathematics of quaternions, we provide a parametric\\nequation of a surface of revolution generated by rotating a directrix about an axis by quaternion multiplication\\nof the parametric representations of the directrix curve and the line of axis. Then, we describe an algorithm\\nto determine whether a parametric surface is a surface of revolution, and identify the axis and the directrix.\\nExamples are provided to illustrate our algorithm.\",\"PeriodicalId\":43768,\"journal\":{\"name\":\"International Electronic Journal of Geometry\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2022-10-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Electronic Journal of Geometry\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.36890/iejg.1064089\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Electronic Journal of Geometry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.36890/iejg.1064089","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
DETERMINE WHEN A PARAMETRIC SURFACE IS A SURFACE OF REVOLUTION
A surface of revolution is a surface that can be generated by rotating a planar curve (the directrix)
around a straight line (the axis) in the same plane. Using the mathematics of quaternions, we provide a parametric
equation of a surface of revolution generated by rotating a directrix about an axis by quaternion multiplication
of the parametric representations of the directrix curve and the line of axis. Then, we describe an algorithm
to determine whether a parametric surface is a surface of revolution, and identify the axis and the directrix.
Examples are provided to illustrate our algorithm.
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