{"title":"圆锥曲线点-线枚举问题的闭式解法","authors":"Yang Guo","doi":"10.1007/s00373-024-02793-6","DOIUrl":null,"url":null,"abstract":"<p>We use the reciprocal transformation to propose the closed-form solutions to the conics through <i>m</i> points and tangent to <i>n</i> lines satisfying <span>\\(m+n=5\\)</span> in general position. We also derive the algebraic and geometric necessary and sufficient conditions for the non-degenerate real conics.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Closed-Form Solution of Conic in Point-Line Enumerative Problem of Conic\",\"authors\":\"Yang Guo\",\"doi\":\"10.1007/s00373-024-02793-6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We use the reciprocal transformation to propose the closed-form solutions to the conics through <i>m</i> points and tangent to <i>n</i> lines satisfying <span>\\\\(m+n=5\\\\)</span> in general position. We also derive the algebraic and geometric necessary and sufficient conditions for the non-degenerate real conics.</p>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-05-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s00373-024-02793-6\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00373-024-02793-6","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
我们利用倒易变换提出了通过 m 个点、与 n 条直线相切、满足 \(m+n=5\) 的圆锥在一般位置上的闭式解。我们还推导出了非退化实圆锥的代数和几何必要条件和充分条件。
Closed-Form Solution of Conic in Point-Line Enumerative Problem of Conic
We use the reciprocal transformation to propose the closed-form solutions to the conics through m points and tangent to n lines satisfying \(m+n=5\) in general position. We also derive the algebraic and geometric necessary and sufficient conditions for the non-degenerate real conics.
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