On the numerical condition of polynomials in Berstein form
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
Implicitizing rational curves by the method of moving algebraic curves
Journal of Symbolic Computation - Special issue: parametric algebraic curves and applications
The moving line ideal basis of planar rational curves
Computer Aided Geometric Design
The mu-basis of a rational ruled surface
Computer Aided Geometric Design
A direct approach to computing the &mgr;-basis of planar rational curves
Journal of Symbolic Computation
A new implicit representation of a planar rational curve with high order singularity
Computer Aided Geometric Design
Reparametrization of a rational ruled surface using the μ-basis
Computer Aided Geometric Design
The µ-basis of a planar rational curve: properties and computation
Graphical Models
Revisiting the µ-basis of a rational ruled surface
Journal of Symbolic Computation
Axial moving lines and singularities of rational planar curves
Computer Aided Geometric Design
Matrix-based implicit representations of rational algebraic curves and applications
Computer Aided Geometric Design
Bernstein Bezoutians and application to intersection problems
Computer Aided Geometric Design
Interpolation function of generalized q−bernstein-type basis polynomials and applications
Proceedings of the 7th international conference on Curves and Surfaces
The Bernstein polynomial basis: A centennial retrospective
Computer Aided Geometric Design
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Three division algorithms are presented for univariate Bernstein polynomials: an algorithm for finding the quotient and remainder of two univariate polynomials, an algorithm for calculating the GCD of an arbitrary collection of univariate polynomials, and an algorithm for computing a @m-basis for the syzygy module of an arbitrary collection of univariate polynomials. Division algorithms for multivariate Bernstein polynomials and analogues in the multivariate Bernstein setting of Grobner bases are also discussed. All these algorithms are based on a simple ring isomorphism that converts each of these problems from the Bernstein basis to an equivalent problem in the monomial basis. This isomorphism allows all the computations to be performed using only the original Bernstein coefficients; no conversion to monomial coefficients is required.