IBM Journal of Research and Development
Gro¨bner bases: a computational approach to commutative algebra
Gro¨bner bases: a computational approach to commutative algebra
Rational curves and surfaces with rational offsets
Computer Aided Geometric Design
Hermite interpolation by Pythagorean hodograph quintics
Mathematics of Computation
Offset-rational parametric plane curves
Computer Aided Geometric Design
Pipe surfaces with rational spine curve are rational
Computer Aided Geometric Design
Parametric generalized offsets to hypersurfaces
Journal of Symbolic Computation - Special issue: parametric algebraic curves and applications
Applications of Laguerre geometry in CAGD
Computer Aided Geometric Design
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
Hermite interpolation by pythagorean hodograph curves of degree seven
Mathematics of 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 the problem of proper reparametrization for rational curves and surfaces
Computer Aided Geometric Design
A control polygon scheme for design of planar C2 PH quintic spline curves
Computer Aided Geometric Design
Rational space curves are not “unit speed”
Computer Aided Geometric Design
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
On rationally supported surfaces
Computer Aided Geometric Design
Approximating curves and their offsets using biarcs and Pythagorean hodograph quintics
Computer-Aided Design
A symbolic-numerical envelope algorithm using quadratic MOS patches
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
G1 Hermite interpolation by PH cubics revisited
Computer Aided Geometric Design
A unified Pythagorean hodograph approach to the medial axis transform and offset approximation
Journal of Computational and Applied Mathematics
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
Approximate convolution with pairs of cubic Bézier LN curves
Computer Aided Geometric Design
Exploring hypersurfaces with offset-like convolutions
Computer Aided Geometric Design
Reducibility of offsets to algebraic curves
Computer Aided Geometric Design
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Rationally parameterized hypersurfaces can be classified with respect to their RC properties (Rational Convolutions) with the help of the Grobner bases theory. This classification focuses on special classes of rational parameterizations which provide a rational description of convolution hypersurfaces generally (GRC parameterizations), or just in some special cases (SRC parameterizations). The main aim of this paper is to bring the theory of the so-called PN surfaces (surfaces with Pythagorean Normal vectors) and their PN parameterizations (parameterizations fulfilling the PN condition) in relation to the theory of SRC parameterizations and to show that this type of parameterizations can be further classified with respect to the degree of the construction of convolution surfaces. The connection of SRC PN parameterizations to the well-known concepts of proper and square-root parameterizations is also investigated.