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|Table of Contents Bivariate Data Smoothing Curve Fitting by Splines|
Assume that we have n+1 data points [xi, yi] with i=0 to n, and x0 < x1 < .... < xn. Then the function S(x) is called a Cubic Spline if there exist n cubic polynomials si(x) having the coefficients ai,0, ai,1, ai,2, ai,3 that satisfy the following conditions:
|Click on this image to experiment with spline interpolation.|
Please note that there exists a unique cubic spline (called natural spline) with the boundary conditions S"(x0) = 0 and S"(xn) = 0. The natural spline is the curve obtained by forcing a flexible elastic rod through the points but letting the slope at the ends be free to equilibrate to the position that minimizes the oscillatory behavior of the curve.
Last Update: 2006-Jšn-18