Please use this identifier to cite or link to this item: `https://doi.org/10.1016/j.cagd.2008.12.005`
DC FieldValue
dc.titleShifting planes always implicitize a surface of revolution
dc.contributor.authorChionh, E.-W.
dc.date.accessioned2013-07-04T07:49:23Z
dc.date.available2013-07-04T07:49:23Z
dc.date.issued2009
dc.identifier.citationChionh, 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
dc.identifier.issn01678396
dc.identifier.urihttp://scholarbank.nus.edu.sg/handle/10635/39780
dc.description.abstractA 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.
dc.sourceScopus
dc.subjectImplicitization determinants
dc.subjectInherently improper parametrizations
dc.subjectMoving planes
dc.subjectSurfaces of revolution
dc.typeArticle
dc.contributor.departmentCOMPUTER SCIENCE
dc.description.doi10.1016/j.cagd.2008.12.005
dc.description.sourcetitleComputer Aided Geometric Design
dc.description.volume26
dc.description.issue4
dc.description.page369-377
dc.description.codenCAGDE
dc.identifier.isiut000265813300002
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