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Title: 0/0 Simplifies implicitization
Authors: Chionh, E.-W. 
Keywords: Base points
Corner cutting
Dixon resultants
Exposed points
Quotient resultants
Issue Date: 2008
Citation: Chionh, E.-W. (2008). 0/0 Simplifies implicitization. Journal of Symbolic Computation 43 (6-7) : 475-489. ScholarBank@NUS Repository.
Abstract: A base point of a surface rational parametrization maps to an indeterminate surface point (0/0,0/0,0/0). A quotient resultant becomes indeterminate when it specializes to 0/0. These double anomalies seem hazardous to implicitization. But surprisingly, when they do happen simultaneously, the implicitization result may become simpler. This desirable situation arises when base points are due to a corner-cut parametric monomial support and the corresponding quotient resultant is indeterminate due to the collinearity of corner control vertices. The simplification effect is quite substantial: the implicit polynomial is an a priori known maximal minor from the numerator determinant of the quotient resultant, consequently not only the implicitization determinant is shrunk but division is avoided altogether. © 2007 Elsevier Ltd. All rights reserved.
Source Title: Journal of Symbolic Computation
ISSN: 07477171
DOI: 10.1016/j.jsc.2007.07.011
Appears in Collections:Staff Publications

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