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|Title:||Shifting planes to follow a surface of revolution|
Inherently improper parametrizations
Surfaces of revolution
|Source:||Chionh, E.-W. (2008). Shifting planes to follow a surface of revolution. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 4975 LNCS : 398-409. ScholarBank@NUS Repository. https://doi.org/10.1007/978-3-540-79246-8-30|
|Abstract:||A degree n rational plane curve rotating about an axis in the plane creates a degree 2n rational surface. Two formulas are given to generate 2n moving planes that follow the surface. These 2n moving planes lead to a 2n×2n implicitization determinant that manifests the geometric revolution algebraically in two aspects. Firstly the moving planes are constructed by successively shifting terms of polynomials from one column to another of a spawning 3×3 determinant. Secondly the right half of the 2n×2n implicitization determinant is almost an n-row rotation of the left half. As an aside, it is observed that rational parametrizations of a surface of revolution due to a symmetric rational generatrix must be improper. © 2008 Springer-Verlag Berlin Heidelberg.|
|Source Title:||Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)|
|Appears in Collections:||Staff Publications|
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