public class Spline {
	private double y[];
	private double y2[];

	/**
	 * The constructor calculates the second derivatives of the interpolating function
	 * at the tabulated points xi, with xi = (i, y[i]).
	 * Based on numerical recipes in C, http://www.library.cornell.edu/nr/bookcpdf/c3-3.pdf .
	 * @param y Array of y coordinates for cubic-spline interpolation.
	 */
	public Spline(double y[]) {
		this.y = y;
		int n = y.length;
		y2 = new double[n];
		double u[] = new double[n];
		for (int i = 1; i < n - 1; i++) {
			y2[i] = -1.0 / (4.0 + y2[i - 1]);
			u[i] = (6.0 * (y[i + 1] - 2.0 * y[i] + y[i - 1]) - u[i - 1]) / (4.0 + y2[i - 1]);
		}
		for (int i = n - 2; i >= 0; i--) {
			y2[i] = y2[i] * y2[i + 1] + u[i];
		}
	}

	/**
	 * Returns a cubic-spline interpolated value y for the point between
	 * point (n, y[n]) and (n+1, y[n+1), with t ranging from 0 for (n, y[n])
	 * to 1 for (n+1, y[n+1]).  
	 * @param n The start point.
	 * @param t The distance to the next point (0..1).
	 * @return A cubic-spline interpolated value.
	 */
	public double fn(int n, double t) {
		return t * y[n + 1] - ((t - 1.0) * t * ((t - 2.0) * y2[n] - (t + 1.0) * y2[n + 1])) / 6.0 + y[n] - t * y[n];
	}
}