{"title":"使用移动曲线和曲面的隐式化","authors":"T. Sederberg, Falai Chen","doi":"10.1145/218380.218460","DOIUrl":null,"url":null,"abstract":"This paper presents a radically new approach to the century old problem of computing the implicit equation of a parametric surface. For surfaces without base points, the new method expresses the implicit equation in a determinant which is one fourth the size of the conventional expression based on Dixon’s resultant. If base points do exist, previous implicitization methods either fail or become much more complicated, while the new method actually simplifies.","PeriodicalId":447770,"journal":{"name":"Proceedings of the 22nd annual conference on Computer graphics and interactive techniques","volume":"3 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1995-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"214","resultStr":"{\"title\":\"Implicitization using moving curves and surfaces\",\"authors\":\"T. Sederberg, Falai Chen\",\"doi\":\"10.1145/218380.218460\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper presents a radically new approach to the century old problem of computing the implicit equation of a parametric surface. For surfaces without base points, the new method expresses the implicit equation in a determinant which is one fourth the size of the conventional expression based on Dixon’s resultant. If base points do exist, previous implicitization methods either fail or become much more complicated, while the new method actually simplifies.\",\"PeriodicalId\":447770,\"journal\":{\"name\":\"Proceedings of the 22nd annual conference on Computer graphics and interactive techniques\",\"volume\":\"3 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1995-09-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"214\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the 22nd annual conference on Computer graphics and interactive techniques\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/218380.218460\",\"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 of the 22nd annual conference on Computer graphics and interactive techniques","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/218380.218460","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
This paper presents a radically new approach to the century old problem of computing the implicit equation of a parametric surface. For surfaces without base points, the new method expresses the implicit equation in a determinant which is one fourth the size of the conventional expression based on Dixon’s resultant. If base points do exist, previous implicitization methods either fail or become much more complicated, while the new method actually simplifies.
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