For curves such as straight lines, circles, ellipses and hyperbolas both rational parametric and implicit representations exist. The same is true for planes, spheres, ellipsoids, hyperboloids, etc. However, for curves and surfaces that have an implicit description of total degree higher than two, we do not have this attractive duality.
The GAIA II project has addressed two approaches to implicitization:
The GAIA II project has thus addressed two approaches to parameterization:
Published June 7, 2005