Spline Functions

This page describes AMA Spline Library functions to evaluate, differentiate and integrate tensor product splines and other functions for manipulating a AMA_SPLINE structure.

The AMA Spline Library provides the Univariate Data Functions and Multivariate Data Functions to compute a spline which either approximates or interpolates univariate data, , or multivariate data, , respectively. These splines are represented as where is a vector of independent variables . The 's are the coefficients of the tensor product B-splines where the 's are the univariate B-splines of degree defined by the knot vector This section presents AMA Spline Library functions which can be employed to compute the spline's partial derivative where the partial order and is the partial order in , for ; to compute the spline's indefinite integral where is the integral order in , for ; to compute the spline's value at a point ; and to compute the value of the spline's partial derivative at a point . Functions for reading, writing, freeing and insuring the AMA Spline Library AMA_SPLINE structure is properly defined are also provided. Following is a list of the AMA Spline Library functions for working with the AMA_SPLINE structure:

The program exampleAMA_Spline.c provides an example of using these functions. It was used to produced Figure Interpolants, Derivatives and Integrals of Lift Coefficient which contains the interpolant of the data computed by AMA_UnvInterp() and the monotonic interpolant computed by AMA_UnvMonoInterp(), see Univariate Data Functions. Both interpolants are shown in the left hand panel where the AMA_UnvInterp() interpolant is given in blue and the interpolant computed by AMA_UnvMonoInterp() is given in green, the red squares represent the data. The center panel contains the derivative of the two interpolants computed with AMA_SplinePartial() and the right hand panel contains their indefinite integrals computed with AMA_SplineIntegral().

Interpolants, Derivatives and Integrals of Lift Coefficient
Interpolant of Derivative of Integral of    