TRANSPLINE--A system for representing curves using transformations among four spline formulations

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Abstract
Various techniques of curve representation have been developed and each has properties that make it more appropriate in certain situations than in others. Thus, it is very beneficial to be able to transform between formulations in order to invoke the one which is best suited to any particular instance. This concept has been applied to a set of four parametric spline curve formulations and is demonstrated in the TRANSPLINE interactive curve representation system. The available formulations are the interpolatory spline, uniform B-spline, spline under tension, and ν-spline. The mathematical theory of each formulation is briefly reviewed, the transformations between them are derived, and the system implementation is described.

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