A Unified Treatment of Invariance for Curve- and Surface-defining Algorithms

The behaviour of plane-curve algorithms under transformationis studied systematically with a view to the construction ofnew algorithms, for computer-aided design applications, withany required invariance characteristics built in. The resultsobtained may also be used for the determination of invarianceproperties of algorithms in current use and for evaluating therelative merits of alternative parameterizations of a givenalgorithm. A number of common algorithms of practical importanceare considered and some generalizations are discussed includingthe extension to surfaces.