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Erschienen in:
2008 | OriginalPaper | Buchkapitel
Shifting Planes to Follow a Surface of Revolution
verfasst von : Eng-Wee Chionh
Erschienen in: Advances in Geometric Modeling and Processing
Verlag: Springer Berlin Heidelberg
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A degree
n
rational plane curve rotating about an axis in the plane creates a degree 2
n
rational surface. Two formulas are given to generate 2
n
moving planes that follow the surface. These 2
n
moving planes lead to a 2
n
×2
n
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 2
n
×2
n
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.