Abstract
This paper develops the exponential function as an alternative to the classical Hermite basis. Other alternatives such as a Hermite-type basis produced from B-splines are also discussed. These alternatives allow the user greater flexibility in creating free-form curves and surfaces. The cardinal bases permit the introduction of intuitive and tractable control parameters. Arc length and surface area as well as derivative data are placed under user control. Changes in these parameters have only a local effect on the curve or surface. These bases are constructed in such a way as to allow interchanges between different sets of bases. This yields even greater flexibility.
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