Improperly parametrized rational curves
Computer Aided Geometric Design
Automatic parameterization of rational curves and surfaces III: algebraic plane curves
Computer Aided Geometric Design
Symbolic parametrization of curves
Journal of Symbolic Computation
Using multivariate resultants to find the implicit equation of a rational surface
The Visual Computer: International Journal of Computer Graphics
Computing parameterizations of rational algebraic curves
ISSAC '94 Proceedings of the international symposium on Symbolic and algebraic computation
A rational function decomposition algorithm by near-separated polynomials
Journal of Symbolic 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
Parametric generalized offsets to hypersurfaces
Journal of Symbolic Computation - Special issue: parametric algebraic curves and applications
Rational parametrization of surfaces
Journal of Symbolic Computation
The moving line ideal basis of planar rational curves
Computer Aided Geometric Design
Tracing index of rational curve parametrizations
Computer Aided Geometric Design
Polynomial Algorithms in Computer Algebra
Polynomial Algorithms in Computer Algebra
On multivariate rational function decomposition
Journal of Symbolic Computation - Computer algebra: Selected papers from ISSAC 2001
Partial degree formulae for rational algebraic surfaces
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
A univariate resultant-based implicitization algorithm for surfaces
Journal of Symbolic Computation
Rational Algebraic Curves: A Computer Algebra Approach
Rational Algebraic Curves: A Computer Algebra Approach
On the problem of proper reparametrization for rational curves and surfaces
Computer Aided Geometric Design
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Given an algebraically closed field K, and a rational parametrization P of an algebraic surface V@?K^3, we consider the problem of computing a proper rational parametrization Q from P (reparametrization problem). More precisely, we present an algorithm that computes a rational parametrization Q of V such that the degree of the rational map induced by Q is less than the degree induced by P. The properness of the output parametrization Q is analyzed. In particular, if the degree of the map induced by Q is one, then Q is proper and the reparametrization problem is solved. The algorithm works if at least one of two auxiliary parametrizations defined from P is not proper.