A remark on parameterizing nonsingular cubic surfaces

Authors:
Irene Polo-Blanco;Jaap Top
Affiliations:
Department Matesco, University of Cantabria, Avda de los Castros s/n, 39005, Santander, Spain;IWI-RuG, University of Groningen, Nijenborgh 9, 9747 AG Groningen, The Netherlands
Venue:
Computer Aided Geometric Design
Year:
2009

Citing 4
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Abstract

Extending a geometric construction due to Sederberg and to Bajaj, Holt, and Netravali, an algorithm is presented for parameterizing a nonsingular cubic surface by polynomials of degree three. The fact that such a parametrization exists is classical. The present algorithm is, by its purely geometric nature, a very natural one. Moreover, it contains a practical way of finding all lines in an implicitly given cubic surface. Two explicit examples are presented, namely the classical Clebsch diagonal surface and the cubic Fermat surface.