Rational curves and surfaces with rational offsets
Computer Aided Geometric Design
Parametric generalized offsets to hypersurfaces
Journal of Symbolic Computation - Special issue: parametric algebraic curves and applications
Rational parametrization of surfaces
Journal of Symbolic Computation
A Laguerre geometric approach to rational offsets
Computer Aided Geometric Design
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
Local shape of offsets to algebraic curves
Journal of Symbolic Computation
A delineability-based method for computing critical sets of algebraic surfaces
Journal of Symbolic Computation
Curves and surfaces represented by polynomial support functions
Theoretical Computer Science
On rationally supported surfaces
Computer Aided Geometric Design
Local parametrization of cubic surfaces
Journal of Symbolic Computation
Computing Isophotes on Free-Form Surfaces Based on Support Function Approximation
Proceedings of the 13th IMA International Conference on Mathematics of Surfaces XIII
Rational two-parameter families of spheres and rational offset surfaces
Journal of Symbolic Computation
On convolutions of algebraic curves
Journal of Symbolic Computation
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
Support function of pythagorean hodograph cubics and G1 hermite interpolation
GMP'10 Proceedings of the 6th international conference on Advances in Geometric Modeling and Processing
G2 hermite interpolation with curves represented by multi-valued trigonometric support functions
Proceedings of the 7th international conference on Curves and Surfaces
Approximate convolution with pairs of cubic Bézier LN curves
Computer Aided Geometric Design
Exploring hypersurfaces with offset-like convolutions
Computer Aided Geometric Design
Computer Aided Geometric Design
Journal of Symbolic Computation
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We discuss rational parameterizations of surfaces whose support functions are rational functions of the coordinates specifying the normal vector and of a given non-degenerate quadratic form. The class of these surfaces is closed under offsetting. It comprises surfaces with rational support functions and non-developable quadric surfaces, and it is a subset of the class of rational surfaces with rational offset surfaces. We show that a particular parameterization algorithm for del Pezzo surfaces can be used to construct rational parameterizations of these surfaces. If the quadratic form is diagonalized and has rational coefficients, then the resulting parameterizations are almost always described by rational functions with rational coefficients.