Cyclides in computer aided geometric design
Computer Aided Geometric Design
Cyclides in computer aided geometric design II
Computer Aided Geometric Design
Applications of Laguerre geometry in CAGD
Computer Aided Geometric Design
The moving line ideal basis of planar rational curves
Computer Aided Geometric Design
Studying cyclides with Laguerre geometry
Computer Aided Geometric Design
The mu-basis of a rational ruled surface
Computer Aided Geometric Design
The µ-basis of a planar rational curve: properties and computation
Graphical Models
Degree formulae for offset curves
Journal of Pure And Applied Algebra
Analytic and algebraic properties of canal surfaces
Journal of Computational and Applied Mathematics - Special issue: The international symposium on computing and information (ISCI2004)
Minimal rational parametrizations of canal surfaces
Computing - Special issue on Geometric Modeling (Dagstuhl 2005)
Resultant-based methods for plane curves intersection problems
CASC'05 Proceedings of the 8th international conference on Computer Algebra in Scientific Computing
Parameterizing rational offset canal surfaces via rational contour curves
Computer-Aided Design
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A canal surface is an envelope of a one-parameter family of spheres. In this paper we present an efficient algorithm for computing the implicit equation of a canal surface generated by a rational family of spheres. By using Laguerre and Lie geometries, we relate the equation of the canal surface to the equation of a dual variety of a certain curve in 5-dimensional projective space. We define the @m-basis for arbitrary dimension and give a simple algorithm for its computation. This is then applied to the dual variety, which allows us to deduce the implicit equations of the dual variety, the canal surface and any offset to the canal surface.