Spline Curve Fit

Two spline curve fit programs, SplineCurvFit1 and SplineCurvFit2, have been developed to curve fit data for algorithm definition. The programs, designed for the personal computer (Microsoft Windows), determine the equation coefficients for three dimensional functions, y = f (x,z). Data plotting software is included. PlotXYZ.

The link, (Spline Curve Fit Program), provides y = f(x) data plot samples from the software SplineCurvFit. 4th Order (cubic), 5th order and 6th order examples are shown.

Data analysis consulting and programming are available. An equation form can be developed that best fits any given data set. If programming is required, an executable program along with the C++ source code is provided. The source code allows the user to easily install curve fit functions into other software. For those interested in data analysis consulting, see link "Consulting Services for Data Analysis".

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Spline Curve Fit Algorithm Example

Ordering Information

Other Software (Curve Fit XYZ Computer Program)

Consulting Services for Data Analysis

Computer program SplineCurvFit1 uses a cubic spline to fit data y = f (x). For polynomial
y = f (x,z) function, as many as 5 different z values may be fit. Each z value curve uses the cubic spline fit. While variation with z are as follows:

With 2 curves z value variation is a linear function
With 3 curves z value variation is a quadratic function
With 4 curves z value variation is a cubic function
With 5 curves z value variation is a quartic function

Computer program SplineCurvFit2 uses a cubic spline fit throughout to define the equation coefficients for the three dimensional function. As many as 48,000 data points may be input.

An example of the form of the equation for y = f (x) of order 4 (cubic equation) is:

Similarly, the form of the equation for y = f (x,z) of order 4 in x and z is:

An example of a three dimensional object suitable for curve fitting, using the SplineCurvFit2 program, is shown in the following XYZ plot.

Six cross sections of the 3D object are shown at their respective Z station (Z1 thru Z6). The six 3D segments of the object, shown color coded, are defined by six cubic equations, with mating segments spline fit.

Both programs provide an output file of equation coefficients for easy incorporation into programs utilizing curve fit algorithms. The listing order of the coefficients output file for y = f (x,z) cubic equation in x and z is as follows: