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
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
The μ-basis and implicitization of a rational parametric surface
Journal of Symbolic Computation
Real implicitization of curves and geometric extraneous components
Proceedings of the 2007 international workshop on Symbolic-numeric computation
Implicitization and parametrization of quadratic surfaces with one simple base point
Proceedings of the twenty-first international symposium on Symbolic and algebraic computation
Approximate µ-bases of rational curves and surfaces
GMP'06 Proceedings of the 4th international conference on Geometric Modeling and Processing
Certified approximation of parametric space curves with cubic B-spline curves
Computer Aided Geometric Design
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The μ-bases of rational curves/surfaces are newly developed tools which play an important role in connecting parametric forms and implicit forms of the rational curves/surfaces. They provide efficient algorithms to implicitize rational curves/surfaces as well as algorithms to compute singular points of rational curves and to reparametrize rational ruled surfaces. In this paper, we present an efficient algorithm to compute the μbasis of a rational curve/surface by using polynomial matrix factorization followed by a technique similar to Gaussian elimination. The algorithm is shown superior than previous algorithms to compute the μ-basis of a rational curve, and it is the only known algorithm that can rigorously compute the μ-basis of a general rational surface. We present some examples to illustrate the algorithm.