IBM Journal of Research and Development
Rational curves and surfaces with rational offsets
Computer Aided Geometric Design
Offset-rational parametric plane curves
Computer Aided Geometric Design
Parametric generalized offsets to hypersurfaces
Journal of Symbolic Computation - Special issue: parametric algebraic curves and applications
Curves and surfaces for CAGD: a practical guide
Curves and surfaces for CAGD: a practical guide
Polynomial and Rational Pythagorean-Hodograph Curves Reconciled
Proceedings of the 6th IMA Conference on the Mathematics of Surfaces
Rational hypersurfaces with rational convolutions
Computer Aided Geometric Design
Convolution surfaces of quadratic triangular Bézier surfaces
Computer Aided Geometric Design
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
Pythagorean-hodograph preserving mappings
Journal of Computational and Applied Mathematics
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
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
Exploring hypersurfaces with offset-like convolutions
Computer Aided Geometric Design
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Rational shapes with rational offsets, especially Pythagorean hodograph (PH) curves and Pythagorean normal vector (PN) surfaces, have been thoroughly studied for many years. However compared to PH curves, Pythagorean normal vector surfaces were introduced using dual approach only in their rational version and a complete characterization of polynomial surfaces with rational offsets, i.e., a polynomial solution of the well-known surface Pythagorean condition, still remains an open and challenging problem. In this contribution, we study a remarkable family of cubic polynomial PN surfaces with birational Gauss mapping, which represent a surface counterpart to the planar Tschirnhausen cubic. A full description of these surfaces is presented and their properties are discussed.