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0/0 Simplifies implicitization

Chionh, Eng-Wee

Journal of symbolic computation, 2008-06, Vol.43 (6), p.475-489 [Periódico revisado por pares]

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Título:
0/0 Simplifies implicitization
Autor: Chionh, Eng-Wee
Assuntos: Base points ; Corner cutting ; Dixon resultants ; Exposed points ; Implicitization ; Quotient resultants
É parte de: Journal of symbolic computation, 2008-06, Vol.43 (6), p.475-489
Descrição: 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.
Editor: Elsevier Ltd
Idioma: Inglês

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