The approximation of non-degenerate offset surfaces
Computer Aided Geometric Design
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
Hermite interpolation by piecewise polynomial surfaces with rational offsets
Computer Aided Geometric Design
Comparing Offset Curve Approximation Methods
IEEE Computer Graphics and Applications
Polynomial and Rational Pythagorean-Hodograph Curves Reconciled
Proceedings of the 6th IMA Conference on the Mathematics of Surfaces
Rational space curves are not “unit speed”
Computer Aided Geometric Design
Rational hypersurfaces with rational convolutions
Computer Aided Geometric Design
Computing exact rational offsets of quadratic triangular Bézier surface patches
Computer-Aided Design
PN surfaces and their convolutions with rational surfaces
Computer Aided Geometric Design
Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable
Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable
Rational surfaces with linear normals and their convolutions with rational surfaces
Computer Aided Geometric Design
Euclidean and Minkowski Pythagorean hodograph curves over planar cubics
Computer Aided Geometric Design
On convolutions of algebraic curves
Journal of Symbolic Computation
Rational Pythagorean-hodograph space curves
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
Algebraic curves of low convolution degree
Proceedings of the 7th international conference on Curves and Surfaces
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Computing offset curves and surfaces is a fundamental operation in many technical applications. This paper discusses some issues that are encountered during the process of designing offsets, especially the problems of their reducibility and rationality (which are closely related). This study is crucial especially for formulating subsequent algorithms when the number and quality of offset components must be revealed. We will formulate new algebraic and geometric conditions on reducibility of offsets and demonstrate how they can be applied. In addition, we will present that our investigations can also serve to better understand the varieties fulfilling the Pythagorean conditions (PH curves/PN surfaces). A certain analogy of the PH condition for parameterized curves (or general parameterized hypersurfaces) will be presented also for implicitly given (not necessarily rational) curves (or hypersurfaces).