@**techreport**{RISC2047,author = {I. Szil\'agyi and B. J\"uttler and J. Schicho},

title = {{Local Parametrization of Cubic Surfaces}},

language = {english},

abstract = {Algebraic surfaces -- which are frequently used in geometric
modelling -- are represented either in implicit or parametric
form. Several techniques for parameterizing a rational algebraic
surface as a whole exist. However, in many applications, it
suffices to parameterize a small portion of the surface. This
motivates the analysis of local parametrizations, i.e.,
parametrizations of a small neighborhood of a given point $P$ of
the surface $S$. In this paper we introduce several techniques for
generating such parameterizations for nonsingular cubic surfaces.
For this class of surfaces, it is shown that the local
parametrization problem can be solved for all points, and any such
surface can be covered completely.},

number = {2004-31},

year = {2004},

institution = {J.~Kepler University, Linz},

keywords = {parametrization, cubics, algorithm, surfaces},

length = {22},

url = {http://www.sfb013.uni-linz.ac.at/},

type = {SFB-Report}

}