Fast computation of the C-space of convex 2D algebraic objects
International Journal of Robotics Research
An algorithm to compute the Minkowski sum outer-face of two simple polygons
Proceedings of the twelfth annual symposium on Computational geometry
Neural, Parallel & Scientific Computations - computer aided geometric design
Rational parametrization of surfaces
Journal of Symbolic Computation
Polynomial/rational approximation of Minkowski sum boundary curves
Graphical Models and Image Processing
A Laguerre geometric approach to rational offsets
Computer Aided Geometric Design
Hermite interpolation by piecewise polynomial surfaces with rational offsets
Computer Aided Geometric Design
Proper parametrization of real tubular surfaces
Journal of Symbolic Computation
The parametrization of canal surfaces and the decomposition of polynomials into a sum of two squares
Journal of Symbolic Computation - Special issue on computer algebra and mechanized reasoning: selected St. Andrews' ISSAC/Calculemus 2000 contributions
The Minkowski Sum of Two Simple Surfaces Generated by Slope-Monotone Closed Curves
GMP '02 Proceedings of the Geometric Modeling and Processing — Theory and Applications (GMP'02)
Computing the Minkowski sum of ruled surfaces
Graphical Models
Computing the convolution and the Minkowski sum of surfaces
Proceedings of the 21st spring conference on Computer graphics
On convolutions of algebraic curves
Journal of Symbolic Computation
Proceedings of the 2010 ACM Symposium on Applied Computing
Reparameterization of curves and surfaces with respect to their convolution
MMCS'08 Proceedings of the 7th international conference on Mathematical Methods for Curves and Surfaces
Algebraic curves of low convolution degree
Proceedings of the 7th international conference on Curves and Surfaces
Exploring hypersurfaces with offset-like convolutions
Computer Aided Geometric Design
Parameterizing rational offset canal surfaces via rational contour curves
Computer-Aided Design
Reducibility of offsets to algebraic curves
Computer Aided Geometric Design
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It is shown that polynomial (or rational) parametric surfaces with a linear field of normal vectors are dual to graphs bivariate polynomials (or rational functions). We discuss the geometric properties of these surfaces. In particular, using the dual representation it is shown that the convolution with general rational surfaces yields again rational surfaces. Similar results hold in the case of curves.