Approximation of 2-D Data by Natural Cubic Spline

Approximation (Data Fitting) by Natural Cubic Spline.

ncs2dapprox.m
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Function for cubic spline approximation of 2D data.

Syntax of Usage:
[arg1out,arg2out,arg3out,arg4out]=ncs2dapprox(arg1in,arg2in,arg3in,arg4in)

arg1in: Input x-Data e.g. [x1, x2, x3,...,xn]
arg2in: Input y-Data e.g. [y1, y2, y3,...,yn]
arg3in: Maximum allowed Square Distance between Data and parametric values (Optional argument)
arg4in: Indices of Data where Spline MUST interpolate (Optional argument)

arg1out: x-values of output break points
arg2out: y-values of output break points
arg3out: Indices of output break points
arg4out: max squared distance b/w input and output values

Testncs2dapprox.m
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A Test program that shows how to use ncs2dapprox.m

Details
Suppose we have set of continuous points (xi,yi), 1<=i<=n (e.g. boundary or some signal) and we want to approximate them using Natural Cubic Spline.

A general concept of fitting Algorithm is following:

1. Fit the spline to Data using initial break points.
2. Find the Max. square distance b/w spline approximated data and original data.
3. while(Max. Square Distance > Max Allowed Square Distance)
4. Add point of max. distance to set of break points.
5. Fit the spline using new set of break points.
6. Find the Max. square distance b/w spline approximated data and original data.
7. Go to step 3.
8. end while
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