Extraction of parametrically defined geometric primitives

Extraction is a generalization of fitting, and is sometimes given the name robust fitting. In ordinary fitting the assumption is made that all the points belong to the curve or surface being fit. In extraction, or robust fitting, this assumption does not hold. Thus an extraction routine must return not only the equation of the best primitive (curve or surface), but also which of the data points are described by this primitive. We give a short description of our extraction algorithm which is based on random sampling. Previously we have shown how our extraction algorithm can deal with curves and surfaces defined implicitly. In this paper we extend this algorithm to curves and surfaces defined parametrically. Being able to extract curves and surfaces defined both implicitly and parametrically makes this algorithm unique. We show a number of experimental results that demonstrate the extraction algorithm in operation.