Some Piecewise Polynomial Alternatives to Splines under Tension.

摘要

Splines under tension are analogs of the cubic spline (which is a simply supported,linear elastic beam) which allow for the application of uniform tension. This additional flexibility has proven to be useful in the application of spline functions to problems of curve design and curve fitting. In the paper,splines under tension are characterized as having a certain minimum property. This property motivates the characterization of some alternative splines which are piecewise polynomial as opposed to the normal splines under tension which are piecewise functions of the form a + bx + c.sinh (alpha x) + d.cosh (alpha x). These alternatives are shown to have many of the properties of splines in tension. (Author)