A Simple Method for the Parameterization of Quadric Surfaces

A new method for the parameterization of quadric surfaces is presented. To parameterize a general quadric implicit surface, the new method first translates the implicit surface to make it pass through the origin point, and then the parametric surface is obtained by substituting the coefficients of the implicit equation into the parameterization formula. As to the parameterization of a quadric implicit triangular patch, the domain of parameters can be determined by a simple universal inversion formula, which thus makes the process of parameterization very easy and fast. Several examples are included to demonstrate the simplicity and the efficiency of the new method in the end.