Please use this identifier to cite or link to this item:
|Title:||Shifting planes always implicitize a surface of revolution|
Inherently improper parametrizations
Surfaces of revolution
|Citation:||Chionh, E.-W. (2009). Shifting planes always implicitize a surface of revolution. Computer Aided Geometric Design 26 (4) : 369-377. ScholarBank@NUS Repository. https://doi.org/10.1016/j.cagd.2008.12.005|
|Abstract:||A degree n rational plane curve revolving in space around an axis in its plane yields a degree 2n rational surface. Two formulas are presented to generate 2n moving planes that follow the surface. These 2n moving planes give a 2 n × 2 n implicitization determinant that manifests conspicuously the geometric action of revolution in two algebraic 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 an n-row rotation of the left half with some sign flipping. Additionally, it is observed that rational parametrizations for a surface obtained as a surface of revolution with a symmetric generatrix must be improper. © 2009 Elsevier B.V. All rights reserved.|
|Source Title:||Computer Aided Geometric Design|
|Appears in Collections:||Staff Publications|
Show full item record
Files in This Item:
There are no files associated with this item.
checked on Sep 19, 2018
WEB OF SCIENCETM
checked on Sep 3, 2018
checked on Sep 7, 2018
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.