Implicitization using moving curves and surfaces
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Rectangular corner cutting and Dixon A -resultants
Journal of Symbolic Computation
Corner edge cutting and Dixon A-resultant quotients
Journal of Symbolic Computation
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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.