  In this paper we consider a family of algorithms for approximate
implicitization of rational parametric curves and surfaces. The main
approximation tool in all of the approaches is the singular value
decomposition, and they are therefore well suited to floating point
implementation in computer aided geometric design (CAGD) systems. We unify the
approaches under the names of commonly known polynomial basis functions, and
consider various theoretical and practical aspects of the algorithms. We offer
new methods for a least squares approach to approximate implicitization using
orthogonal polynomials, which tend to be faster and more numerically stable
than some existing algorithms. We propose several simple propositions relating
the properties of the polynomial bases to their implicit approximation
properties.
