Analytic properties of plane offset curves
Computer Aided Geometric Design
Rational curves and surfaces with rational offsets
Computer Aided Geometric Design
Offset-rational parametric plane curves
Computer Aided Geometric Design
An improved upper complexity bound for the topology computation of a real algebraic plane curve
Journal of Complexity - Special issue for the Foundations of Computational Mathematics conference, Rio de Janeiro, Brazil, Jan. 1997
An efficient method for analyzing the topology of plane real algebraic curves
Selected papers presented at the international IMACS symposium on Symbolic computation, new trends and developments
Parametric generalized offsets to hypersurfaces
Journal of Symbolic Computation - Special issue: parametric algebraic curves and applications
A Laguerre geometric approach to rational offsets
Computer Aided Geometric Design
Polynomial Algorithms in Computer Algebra
Polynomial Algorithms in Computer Algebra
Normal parameterizations of algebraic plane curves
Journal of Symbolic Computation
Efficient topology determination of implicitly defined algebraic plane curves
Computer Aided Geometric Design
Plotting missing points and branches of real parametric curves
Applicable Algebra in Engineering, Communication and Computing
A delineability-based method for computing critical sets of algebraic surfaces
Journal of Symbolic Computation
Fast and exact geometric analysis of real algebraic plane curves
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Computation of the singularities of parametric plane curves
Journal of Symbolic Computation
Topology of families of implicit algebraic surfaces depending on a parameter
CASC'11 Proceedings of the 13th international conference on Computer algebra in scientific computing
Computing the shapes arising in a family of space rational curves depending on one parameter
Computer Aided Geometric Design
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Given a family of plane rational curves depending on a real parameter, defined by its parametric equations, we provide an algorithm to compute a finite partition of the parameter space (R, in general) so that the shape of the family stays invariant along each element of the partition. So, from this partition the topology types in the family can be determined. The algorithm is based on a geometric interpretation of previous work (Alcazar et al., 2007) for the implicit case. However, in our case the algorithm works directly with the parametrization of the family, and the implicit equation does not need to be computed. Timings comparing the algorithm in the implicit and the parametric cases are given; these timings show that the parametric algorithm developed here provides in general better results than the known algorithm for the implicit case.