Spline interpolation in java.

SplineInterpolation.java

/*
 * Copyright (C) 2012 The Android Open Source Project
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 * http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */
package lecho.lib.hellocharts.utils;

import java.util.List;

/**
 * Performs spline interpolation given a set of control points.
 * 
 */
public class SplineInterpolator {

	private final List<Float> mX;
	private final List<Float> mY;
	private final float[] mM;

	private SplineInterpolator(List<Float> x, List<Float> y, float[] m) {
		mX = x;
		mY = y;
		mM = m;
	}

	/**
	 * Creates a monotone cubic spline from a given set of control points.
	 * 
	 * The spline is guaranteed to pass through each control point exactly. Moreover, assuming the control points are
	 * monotonic (Y is non-decreasing or non-increasing) then the interpolated values will also be monotonic.
	 * 
	 * This function uses the Fritsch-Carlson method for computing the spline parameters.
	 * http://en.wikipedia.org/wiki/Monotone_cubic_interpolation
	 * 
	 * @param x
	 *            The X component of the control points, strictly increasing.
	 * @param y
	 *            The Y component of the control points
	 * @return
	 * 
	 * @throws IllegalArgumentException
	 *             if the X or Y arrays are null, have different lengths or have fewer than 2 values.
	 */
	public static SplineInterpolator createMonotoneCubicSpline(List<Float> x, List<Float> y) {
		if (x == null || y == null || x.size() != y.size() || x.size() < 2) {
			throw new IllegalArgumentException("There must be at least two control "
					+ "points and the arrays must be of equal length.");
		}

		final int n = x.size();
		float[] d = new float[n - 1]; // could optimize this out
		float[] m = new float[n];

		// Compute slopes of secant lines between successive points.
		for (int i = 0; i < n - 1; i++) {
			float h = x.get(i + 1) - x.get(i);
			if (h <= 0f) {
				throw new IllegalArgumentException("The control points must all "
						+ "have strictly increasing X values.");
			}
			d[i] = (y.get(i + 1) - y.get(i)) / h;
		}

		// Initialize the tangents as the average of the secants.
		m[0] = d[0];
		for (int i = 1; i < n - 1; i++) {
			m[i] = (d[i - 1] + d[i]) * 0.5f;
		}
		m[n - 1] = d[n - 2];

		// Update the tangents to preserve monotonicity.
		for (int i = 0; i < n - 1; i++) {
			if (d[i] == 0f) { // successive Y values are equal
				m[i] = 0f;
				m[i + 1] = 0f;
			} else {
				float a = m[i] / d[i];
				float b = m[i + 1] / d[i];
				float h = (float) Math.hypot(a, b);
				if (h > 9f) {
					float t = 3f / h;
					m[i] = t * a * d[i];
					m[i + 1] = t * b * d[i];
				}
			}
		}
		return new SplineInterpolator(x, y, m);
	}

	/**
	 * Interpolates the value of Y = f(X) for given X. Clamps X to the domain of the spline.
	 * 
	 * @param x
	 *            The X value.
	 * @return The interpolated Y = f(X) value.
	 */
	public float interpolate(float x) {
		// Handle the boundary cases.
		final int n = mX.size();
		if (Float.isNaN(x)) {
			return x;
		}
		if (x <= mX.get(0)) {
			return mY.get(0);
		}
		if (x >= mX.get(n - 1)) {
			return mY.get(n - 1);
		}

		// Find the index 'i' of the last point with smaller X.
		// We know this will be within the spline due to the boundary tests.
		int i = 0;
		while (x >= mX.get(i + 1)) {
			i += 1;
			if (x == mX.get(i)) {
				return mY.get(i);
			}
		}

		// Perform cubic Hermite spline interpolation.
		float h = mX.get(i + 1) - mX.get(i);
		float t = (x - mX.get(i)) / h;
		return (mY.get(i) * (1 + 2 * t) + h * mM[i] * t) * (1 - t) * (1 - t)
				+ (mY.get(i + 1) * (3 - 2 * t) + h * mM[i + 1] * (t - 1)) * t * t;
	}

	// For debugging.
	@Override
	public String toString() {
		StringBuilder str = new StringBuilder();
		final int n = mX.size();
		str.append("[");
		for (int i = 0; i < n; i++) {
			if (i != 0) {
				str.append(", ");
			}
			str.append("(").append(mX.get(i));
			str.append(", ").append(mY.get(i));
			str.append(": ").append(mM[i]).append(")");
		}
		str.append("]");
		return str.toString();
	}
}

Line 90 Error: Must be "if (h > 3f) {"

what is mM??