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Zbl 0875.68860
Coffman, Adam; Schwartz, Art J.; Stanton, Charles
The algebra and geometry of Steiner and other quadratically parametrizable surfaces.
(English)
[J] Comput. Aided Geom. Des. 13, No. 3, 257-286 (1996). ISSN 0167-8396

Summary: Quadratically parametrizable surfaces $(x_1,x_2,x_3,x_4)=(\varphi_1({\bold u}), \varphi_{2}({\bold u}), \varphi_{3}({\bold u}), \varphi_{4}({\bold u}))$ where $\varphi_{k}$ are homogeneous functions are studied in ${\bbfP}^{3}({\bbfR})$. These correspond to rationally parametrizable surfaces in ${\bbfR}^{3}$. All such surfaces of order greater than two are completely catalogued and described. The geometry of the parametrizations as well as the geometry of the surfaces are revealed by the use of basic matrix algebra. The relationship of these two geometries is briefly discussed. The presentation is intended to be accessible to applied mathematicians and does not presume a knowledge of algebraic geometry.
MSC 2000:
*68U05 Computational geometry, etc.

Keywords: Projective geometry; Parametrized surfaces; Linear algebra; Analytic geometry

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