Rational function decomposition
ISSAC '91 Proceedings of the 1991 international symposium on Symbolic and algebraic computation
The moving line ideal basis of planar rational curves
Computer Aided Geometric Design
The mu-basis of a rational ruled surface
Computer Aided Geometric Design
The µ-basis of a planar rational curve: properties and computation
Graphical Models
The resultant of an unmixed bivariate system
Journal of Symbolic Computation - Special issue: International symposium on symbolic and algebraic computation (ISSAC 2002)
Revisiting the µ-basis of a rational ruled surface
Journal of Symbolic Computation
On the problem of proper reparametrization for rational curves and surfaces
Computer Aided Geometric Design
Implicitizing rational hypersurfaces using approximation complexes
Journal of Symbolic Computation
A computational study of ruled surfaces
Journal of Symbolic Computation
Set-theoretic generators of rational space curves
Journal of Symbolic Computation
Interval implicitization of parametric surfaces
ICICA'10 Proceedings of the First international conference on Information computing and applications
Proper real reparametrization of rational ruled surfaces
Computer Aided Geometric Design
Characterization of rational ruled surfaces
Journal of Symbolic Computation
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Chen, Sederberg, and Zheng introduced the notion of a ¼-basis for a rational ruled surface in Chen et al. [Chen, F., Zheng, J., Sederberg, T. W., 2001. The μ-basis of a rational ruled surface. Comput. Aided Geom. Design 18 (1), 6172] and showed that its resultant is the implicit equation of the surface, if the parametrization is generically injective. We generalize this result to the case of an arbitrary parametrization of a rational ruled surface. We also give a new proof for the corresponding theorem in the curve case and treat the reparametrization problem for curves and ruled surfaces. In particular, we propose a partial solution to the problem of computing a proper reparametrization for a rational ruled surface.