The approximation of non-degenerate offset surfaces
Computer Aided Geometric Design
Generation of configuration space obstacles: moving algebraic surfaces
International Journal of Robotics Research
IBM Journal of Research and Development
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
A Laguerre geometric approach to rational offsets
Computer Aided Geometric Design
Minkowski pythagorean hodographs
Computer Aided Geometric Design
Hermite interpolation by piecewise polynomial surfaces with rational offsets
Computer Aided Geometric Design
Comparing Offset Curve Approximation Methods
IEEE Computer Graphics and Applications
Problem Reduction to Parameter Space
Proceedings of the 9th IMA Conference on the Mathematics of Surfaces
Rational hypersurfaces with rational convolutions
Computer Aided Geometric Design
Minkowski sum boundary surfaces of 3D-objects
Graphical Models
Computing exact rational offsets of quadratic triangular Bézier surface patches
Computer-Aided Design
Curves and surfaces represented by polynomial support functions
Theoretical Computer Science
On rationally supported surfaces
Computer Aided Geometric Design
PN surfaces and their convolutions with rational surfaces
Computer Aided Geometric Design
Journal of Symbolic Computation
Rational surfaces with linear normals and their convolutions with rational surfaces
Computer Aided Geometric Design
G1 Hermite interpolation by Minkowski Pythagorean hodograph cubics
Computer Aided Geometric Design
On convolutions of algebraic curves
Journal of Symbolic Computation
MOS surfaces: medial surface transforms with rational domain boundaries
Proceedings of the 12th IMA international conference on Mathematics of surfaces XII
On rational Minkowski Pythagorean hodograph curves
Computer Aided Geometric Design
Computer Aided Geometric Design
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
On a special class of polynomial surfaces with pythagorean normal vector fields
Proceedings of the 7th international conference on Curves and Surfaces
Algebraic curves of low convolution degree
Proceedings of the 7th international conference on Curves and Surfaces
Approximate convolution with pairs of cubic Bézier LN curves
Computer Aided Geometric Design
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Offsetting is one of the fundamental operations in Computer Aided Design. Due to their high applicability, studying offsets of hypersurfaces has become a popular research area and many interesting problems related to this topic have arisen. In addition, various generalizations of classical offsets have been introduced and then investigated. In this paper we study a generalization which is based on considering offsets to (not only parameterized) hypersurfaces as convolutions with hyperspheres. In other words, we study hypersurfaces sharing the same convolution properties with hyperspheres and thus yielding offset-like convolutions. We will present an algebraic analysis of these hypersurfaces and study their properties suitable for subsequent applications, e.g. in geometric modelling. Moreover, our approach allows to derive distinguished properties of the well-known PH/PN parameterizations as special subcases of the introduced QN parameterizations.