SplineFitter.java

package ij.measure;

/** This class fits a spline function to a set of points.
	It is based on the InitSpline() and EvalSine() functions from 
	XY (http://www.trilon.com/xv/), an interactive image manipulation
	program for the X Window System written by John Bradley. Eric Kischell
	(keesh@ieee.org) converted these functions to Java and inteegrated
	them into the PolygonRoi class.
*/
public class SplineFitter {
	private double[] y2;

	public SplineFitter(int[] x, int[] y, int n) {
		initSpline(x, y, n);
	}

	/** Given arrays of data points x[0..n-1] and y[0..n-1], computes the
		values of the second derivative at each of the data points
		y2[0..n-1] for use in the splint function.
	*/
	void initSpline(int[] x, int[] y, int n) {
		int i,k;
		double p,qn,sig,un;
		y2 = new double[n];	 // cached
		double[] u	= new double[n];
		for (i=1; i<n-1; i++) {
			// 888 chk for div by 0?
			sig = ((double) x[i]-x[i-1]) / ((double) x[i+1] - x[i-1]);
			p = sig * y2[i-1] + 2.0;
			y2[i] = (sig-1.0) / p;
			u[i] = (((double) y[i+1]-y[i]) / (x[i+1]-x[i])) -
				   (((double) y[i]-y[i-1]) / (x[i]-x[i-1]));
			u[i] = (6.0 * u[i]/ (x[i+1]-x[i-1]) - sig*u[i-1]) / p;
		}
		qn = un = 0.0;
		y2[n-1] = (un-qn*u[n-2]) / (qn*y2[n-2]+1.0);
		for (k=n-2; k>=0; k--)
			y2[k] = y2[k]*y2[k+1]+u[k];
	}

	/** Evalutes spline function at given point */
	public double evalSpline(int x[], int y[], int n, double xp) {
		int klo,khi,k;
		double h,b,a;
		klo = 0;
		khi = n-1;
		while (khi-klo > 1) {
			k = (khi+klo) >> 1;
			if (x[k] > xp) khi = k;
			else klo = k;
		}
		h = x[khi] - x[klo];
		/* orig code */
		/* if (h==0.0) FatalError("bad xvalues in splint\n"); */
		if (h==0.0) return (0.0);  /* arbitr ret for now */
		a = (x[khi]-xp)/h;
		b = (xp-x[klo])/h;

		// should have better err checking
		if(y2==null) return (0.0);

		return (a*y[klo] + b*y[khi] + ((a*a*a-a)*y2[klo] +(b*b*b-b)*y2[khi])
				* (h*h) / 6.0);
	}
}