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

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Abstract
The behaviour of plane-curve algorithms under transformation is studied systematically with a view to the construction of new algorithms, for computer-aided design applications, with any required invariance characteristics built in. The results obtained may also be used for the determination of invariance properties of algorithms in current use and for evaluating the relative merits of alternative parameterizations of a given algorithm. A number of common algorithms of practical importance are considered and some generalizations are discussed including the extension to surfaces.

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