Improperly parametrized rational curves
Computer Aided Geometric Design
Automatic parameterization of rational curves and surfaces III: algebraic plane curves
Computer Aided Geometric Design
On the choice of pencils in the parametrization of curves
Journal of Symbolic Computation
Computing parameterizations of rational algebraic curves
ISSAC '94 Proceedings of the international symposium on Symbolic and algebraic computation
Implicitization of parametric curves and surfaces by using multidimensional Newton formulae
Journal of Symbolic Computation - Special issue: parametric algebraic curves and applications
Parametrization of algebraic curves over optimal field extensions
Journal of Symbolic Computation - Special issue: parametric algebraic curves and applications
Rational parametrizations of algebraic curves using a canonical divisor
Journal of Symbolic Computation - Special issue: parametric algebraic curves and applications
The moving line ideal basis of planar rational curves
Computer Aided Geometric Design
Tracing index of rational curve parametrizations
Computer Aided Geometric Design
Efficient topology determination of implicitly defined algebraic plane curves
Computer Aided Geometric Design
Inversion of parameterized hypersurfaces by means of subresultants
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
A note on implicitization and normal parametrization of rational curves
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
On the problem of proper reparametrization for rational curves and surfaces
Computer Aided Geometric Design
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
On the simplification of the coefficients of a parametrization
Journal of Symbolic Computation
Resultant-based methods for plane curves intersection problems
CASC'05 Proceedings of the 8th international conference on Computer Algebra in Scientific Computing
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From the rational functions defining a rational plane curve it is possible to construct two bivariate polynomials that can be seen as univariate polynomials in the parameter value. In this paper several relevant properties of the subresultant sequence of these two polynomials are introduced which are used to solve simultaneously the implicitization, inversion, properness and reparametrization problems. It is also shown that these methods can be suitably transformed in order to deal with curves in the three-dimensional space presented by a polynomial parametrization.