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The sphere as a rational Bézier surface
Computer Aided Geometric Design, 1986The rational Bézier approximation scheme for the surfaces looks like \[ s(u,v)=\sum^{2}_{i,j=0}h_{ij}b_{ij}B_ i(u)B_ j(v)/\sum^{2}_{i,j=0}h_{ij}B_ i(u)B_ j(v);\quad u,v\in [0,1], \] where the \(h_{ij}\) are specially defined parameters, the \(b_{ij}\in {\mathbb{R}}^ 3\) form a ``Bézier net'' and the \(B_ i\) are second order Berstein polynomials.
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Two projective varieties are said to be Cremona equivalent if there is a Cremona modification sending one onto the other. In the last decade, Cremona equivalence has been investigated widely, and we now have a complete theory for non-divisorial reduced schemes.
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Drawing closed rational surfaces
Proceedings of the thirteenth annual symposium on Computational geometry - SCG '97, 1997Jean Gallier Department of Computer and Information Science University of Pennsylvania Philadelphia, PA 19104, USA jean@saul.cis.upenn.edu Abstract. In this short paper, we consider the practical problem of drawing a closed rational surface speci ed by a net of control points.
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Entropy of Real Rational Surface Automorphisms
Experimental Mathematics, 2021Jeffrey Diller, Kyounghee Kim
exaly
RATIONAL SURFACES WITH A PENCIL OF RATIONAL CURVES
Mathematics of the USSR-Sbornik, 1967openaire +2 more sources
Poincaré series of a rational surface singularity
Inventiones Mathematicae, 2003A Campillo, F Delgado, S M Gusein-Zade
exaly
A new characterization of rational surface singularities
Inventiones Mathematicae, 1990Steven Dale Cutkosky +1 more
exaly