TY - JOUR
T1 - A remark on parameterizing nonsingular cubic surfaces
AU - Polo-Blanco, Irene
AU - Top, Jaap
N1 - Relation: http://www.rug.nl/informatica/organisatie/overorganisatie/iwi
Rights: University of Groningen, Research Institute for Mathematics and Computing Science (IWI)
PY - 2009/11
Y1 - 2009/11
N2 - 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. (C) 2009 Elsevier B.V. All rights reserved.
AB - 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. (C) 2009 Elsevier B.V. All rights reserved.
U2 - 10.1016/j.cagd.2009.06.001
DO - 10.1016/j.cagd.2009.06.001
M3 - Article
SN - 0167-8396
VL - 26
SP - 842
EP - 849
JO - Computer aided geometric design
JF - Computer aided geometric design
IS - 8
ER -