Automatic parametrization of rational curves and surfaces II: cubics and cubicoids
Computer-Aided Design
Parametrization of cubic algebraic surfaces
Proceedings on Mathematics of surfaces II
An algebraic approach to curves and surfaces on the sphere and on other quadrics
Selected papers of the international symposium on Free-form curves and free-form surfaces
ACM Transactions on Graphics (TOG)
Rational parametrizations of nonsingular real cubic surfaces
ACM Transactions on Graphics (TOG)
Rational parametrization of surfaces
Journal of Symbolic Computation
Implicitization and parametrization of nonsingular cubic surfaces
Computer Aided Geometric Design
Techniques for Cubic Algebraic Surfaces
IEEE Computer Graphics and Applications
SCCG '01 Proceedings of the 17th Spring conference on Computer graphics
Almost universal parametrizations for cubic surfaces
Computer Aided Geometric Design
A new bivariate rational interpolation based on function values
Information Sciences—Informatics and Computer Science: An International Journal
A bivariate rational interpolation with a bi-quadratic denominator
Journal of Computational and Applied Mathematics - Special issue: The international symposium on computing and information (ISCI2004)
Bounded Property and Point Control of a Bivariate Rational Interpolating Surface
Computers & Mathematics with Applications
Rational Biquartic Interpolating Surface Based on Function Values
Edutainment '08 Proceedings of the 3rd international conference on Technologies for E-Learning and Digital Entertainment
Shape control of a bivariate interpolating spline surface
International Journal of Computer Mathematics
Local control of interpolating rational cubic spline curves
Computer-Aided Design
Technical Section: A blending interpolator with value control and minimal strain energy
Computers and Graphics
A bivariate rational interpolation based on scattered data on parallel lines
Journal of Visual Communication and Image Representation
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Universal parametrizations make it possible to find all rational parametrizations and all rational curves on an implicit surface. The rational curves and patches can be described with optimal degree as images under such a universal parametrization. Hence, the rational curves on the surface can be classified in a systematic way.Interpolation problems on the surface are reduced to ordinary interpolation problems. Other than a usual parametrization, a universal parametrizations allows to control the degree of the interpolating curve or patch on the surface. To avoid nonlinear equation systems, simpler parametrizations can be derived from a universal parametrization.We present universal parametrizations for three different classes of cubic surfaces. According to a conjecture by Krasauskas, this covers all cubic surfaces, which possess a universal parametrization.