{"title":"环面形状","authors":"R. Krasauskas","doi":"10.1109/SCCG.2001.945337","DOIUrl":null,"url":null,"abstract":"We present an informal introduction to the theory of toric surfaces from the viewpoint of geometric modeling. Bezier surfaces and many well-known low-degree rational surfaces are found to be toric. Bezier-like control point schemes for toric surfaces are defined via mixed trigonometric-polynomial parametrizations. Many examples are considered: quadrics, cubic Mobius strip, quartic 'pillow', 'crosscap' and Dupin cyclides. A 'pear' shape modeling is presented.","PeriodicalId":331436,"journal":{"name":"Proceedings Spring Conference on Computer Graphics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2001-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"15","resultStr":"{\"title\":\"Shape of toric surfaces\",\"authors\":\"R. Krasauskas\",\"doi\":\"10.1109/SCCG.2001.945337\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We present an informal introduction to the theory of toric surfaces from the viewpoint of geometric modeling. Bezier surfaces and many well-known low-degree rational surfaces are found to be toric. Bezier-like control point schemes for toric surfaces are defined via mixed trigonometric-polynomial parametrizations. Many examples are considered: quadrics, cubic Mobius strip, quartic 'pillow', 'crosscap' and Dupin cyclides. A 'pear' shape modeling is presented.\",\"PeriodicalId\":331436,\"journal\":{\"name\":\"Proceedings Spring Conference on Computer Graphics\",\"volume\":\"1 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2001-04-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"15\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings Spring Conference on Computer Graphics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/SCCG.2001.945337\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings Spring Conference on Computer Graphics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/SCCG.2001.945337","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We present an informal introduction to the theory of toric surfaces from the viewpoint of geometric modeling. Bezier surfaces and many well-known low-degree rational surfaces are found to be toric. Bezier-like control point schemes for toric surfaces are defined via mixed trigonometric-polynomial parametrizations. Many examples are considered: quadrics, cubic Mobius strip, quartic 'pillow', 'crosscap' and Dupin cyclides. A 'pear' shape modeling is presented.
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