Geometric and solid modeling: an introduction
Geometric and solid modeling: an introduction
Singular points of algebraic curves
Journal of Symbolic Computation
Degree, multiplicity, and inversion formulas for rational surfaces using u-resultants
Computer Aided Geometric Design
Symbolic parametrization of curves
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
Implicitizing rational curves by the method of moving algebraic curves
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
Parametric generalized offsets to hypersurfaces
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
Normal parameterizations of algebraic plane curves
Journal of Symbolic Computation
Partial degree formulae for rational algebraic surfaces
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Degree formulae for offset curves
Journal of Pure And Applied Algebra
Using polynomial interpolation for implicitizing algebraic curves
Computer Aided Geometric Design
Computing singular points of plane rational curves
Journal of Symbolic Computation
Axial moving planes and singularities of rational space curves
Computer Aided Geometric Design
Detecting real singularities of a space curve from a real rational parametrization
Journal of Symbolic Computation
μ-Bases and singularities of rational planar curves
Computer Aided Geometric Design
On the different shapes arising in a family of plane rational curves depending on a parameter
Computer Aided Geometric Design
Topology of 2D and 3D rational curves
Computer Aided Geometric Design
Computing the singularities of rational space curves
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
Computing the shapes arising in a family of space rational curves depending on one parameter
Computer Aided Geometric Design
Using a bihomogeneous resultant to find the singularities of rational space curves
Journal of Symbolic Computation
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Given an algebraic plane curve C defined by a rational parametrization P(t), we present formulae for the computation of the degree of C, and the multiplicity of a point. Using the results presented in [Sendra, J.R., Winkler, F., 2001. Tracing index of rational curve parametrizations. Computer Aided Geometric Design 18 (8), 771-795], the formulae simply involve the computation of the degree of a rational function directly determined from P(t). Furthermore, we provide a method for computing the singularities of C and analyzing the non-ordinary ones without knowing its defining polynomial. This approach generalizes the results in [Abhyankar, S., 1990. Algebraic geometry for scientists and engineers. In: Mathematical Surveys and Monographs, vol. 35. American Mathematical Society; van den Essen, A., Yu, J.-T., 1997. The D-resultants, singularities and the degree of unfaithfulness. Proceedings of the American Mathematical Society 25, 689-695; Gutierrez, J., Rubio, R., Yu, J.-T., 2002. D-Resultant for rational functions. Proceedings of the American Mathematical Society 130 (8), 2237-2246] and [Park, H., 2002. Effective computation of singularities of parametric affine curves. Journal of Pure and Applied Algebra 173, 49-58].