Improperly parametrized rational curves
Computer Aided Geometric Design
Applications of Gro¨bner bases in non-linear computational geometry
Mathematical aspects of scientific software
Computations with parametric equations
ISSAC '91 Proceedings of the 1991 international symposium on Symbolic and algebraic computation
Degree, multiplicity, and inversion formulas for rational surfaces using u-resultants
Computer Aided Geometric Design
Implicitization of rational parametric equations
Journal of Symbolic Computation
Algorithmic algebra
Irreducible decomposition of algebraic varieties via characteristic sets and Gro¨bner bases
Computer Aided Geometric Design
Curve implicitization using moving lines
Computer Aided Geometric Design
Implicitization using moving curves and surfaces
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
A rational function decomposition algorithm by near-separated polynomials
Journal of Symbolic Computation
Matrix computations (3rd ed.)
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
Applied numerical linear algebra
Applied numerical linear algebra
The moving line ideal basis of planar rational curves
Computer Aided Geometric Design
A direct approach to computing the &mgr;-basis of planar rational curves
Journal of Symbolic Computation
Tracing index of rational curve parametrizations
Computer Aided Geometric Design
A new implicit representation of a planar rational curve with high order singularity
Computer Aided Geometric Design
Normal parameterizations of algebraic plane curves
Journal of Symbolic Computation
On multivariate rational function decomposition
Journal of Symbolic Computation - Computer algebra: Selected papers from ISSAC 2001
Elimination and Resultants - Part 1: Elimination and Bivariate Resultants
IEEE Computer Graphics and Applications
Implicitization of Rational Parametric Curves and Surfaces
AAECC-8 Proceedings of the 8th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
The µ-basis of a planar rational curve: properties and computation
Graphical Models
Implicit and parametric curves and surfaces for computer aided geometric design
Implicit and parametric curves and surfaces for computer aided geometric design
Various New Expressions for Subresultants and Their Applications
Applicable Algebra in Engineering, Communication and Computing
Computing μ-bases of rational curves and surfaces using polynomial matrix factorization
Proceedings of the 2005 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)
A matrix-based approach to properness and inversion problems for rational surfaces
Applicable Algebra in Engineering, Communication and Computing
Structured matrices in the application of bivariate interpolation to curve implicitization
Mathematics and Computers in Simulation
Plotting missing points and branches of real parametric curves
Applicable Algebra in Engineering, Communication and Computing
Implicit polynomial support optimized for sparseness
ICCSA'03 Proceedings of the 2003 international conference on Computational science and its applications: PartIII
Using polynomial interpolation for implicitizing algebraic curves
Computer Aided Geometric Design
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Real implicitization of parametric curves has important applications in computer aided geometric design. Implicitization of parametric curves by resultant computations may lead to super uous isolated points. Hence, an exact implicit description should consist of equations and further conditions excluding these geometric extraneous components. Although a real implicit description of this kind can be obtained by real quantifier elimination, we give a direct way to find the conditions to add for an exact description. This results in a more effective algorithm and nicer formulas.