//
// Nenya library - tools for developing networked games
// Copyright (C) 2002-2012 Three Rings Design, Inc., All Rights Reserved
// https://github.com/threerings/nenya
//
// This library is free software; you can redistribute it and/or modify it
// under the terms of the GNU Lesser General Public License as published
// by the Free Software Foundation; either version 2.1 of the License, or
// (at your option) any later version.
//
// This library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
// Lesser General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License along with this library; if not, write to the Free Software
// Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
package com.threerings.media.util;
import java.awt.Point;
/**
* Provides miscellaneous useful utility routines for mathematical calculations.
*/
public class MathUtil
{
/**
* Bounds the supplied value within the specified range.
*
* @return low if {@code value < low}, high if {@code value > high} and value otherwise.
*/
public static int bound (int low, int value, int high)
{
return Math.min(high, Math.max(low, value));
}
/**
* Return the squared distance between the given points.
*/
public static int distanceSq (int x0, int y0, int x1, int y1)
{
return ((x1 - x0) * (x1 - x0)) + ((y1 - y0) * (y1 - y0));
}
/**
* Return the distance between the given points.
*/
public static float distance (int x0, int y0, int x1, int y1)
{
return (float)Math.sqrt(((x1 - x0) * (x1 - x0)) +
((y1 - y0) * (y1 - y0)));
}
/**
* Return the distance between the given points.
*/
public static float distance (Point source, Point dest)
{
return MathUtil.distance(source.x, source.y, dest.x, dest.y);
}
/**
* Return a string representation of the given line.
*/
public static String lineToString (int x0, int y0, int x1, int y1)
{
return "(" + x0 + ", " + y0 + ") -> (" + x1 + ", " + y1 + ")";
}
/**
* Return a string representation of the given line.
*/
public static String lineToString (Point p1, Point p2)
{
return lineToString(p1.x, p1.y, p2.x, p2.y);
}
/**
* Returns the approximate circumference of the ellipse defined by the specified minor and
* major axes. The formula used (due to Ramanujan, via a paper of his entitled "Modular
* Equations and Approximations to Pi"), is <code>Pi(3a + 3b - sqrt[(a+3b)(b+3a)])</code>.
*/
public static double ellipseCircum (double a, double b)
{
return Math.PI * (3*a + 3*b - Math.sqrt((a + 3*b) * (b + 3*a)));
}
/**
* Returns positive 1 if the sign of the argument is positive, or -1 if the sign of the
* argument is negative.
*/
public static int sign (int value)
{
return (value < 0) ? -1 : 1;
}
/**
* Computes the floored division <code>dividend/divisor</code> which
* is useful when dividing potentially negative numbers into bins.
*
* <p> For example, the following numbers floorDiv 10 are:
* <pre>
* -15 -10 -8 -2 0 2 8 10 15
* -2 -1 -1 -1 0 0 0 1 1
* </pre>
*/
public static int floorDiv (int dividend, int divisor)
{
return ((dividend >= 0) == (divisor >= 0)) ?
dividend / divisor : (divisor >= 0 ?
(dividend - divisor + 1) / divisor : (dividend - divisor - 1) / divisor);
}
/**
* Computes the standard deviation of the supplied values.
*
* @return an array of three values: the mean, variance and standard deviation, in that order.
*/
public static float[] stddev (int[] values, int start, int length)
{
// first we need the mean
float mean = 0f;
for (int ii = start, end = start + length; ii < end; ii++) {
mean += values[ii];
}
mean /= length;
// next we compute the variance
float variance = 0f;
for (int ii = start, end = start + length; ii < end; ii++) {
float value = values[ii] - mean;
variance += value * value;
}
variance /= (length - 1);
// the standard deviation is the square root of the variance
return new float[] { mean, variance, (float)Math.sqrt(variance) };
}
/**
* Computes (N choose K), the number of ways to select K different elements from a set of size
* N.
*/
public static int choose (int n, int k)
{
// Base case: One way to select or not select the whole set
if (k <= 0 || k >= n) {
return 1;
}
// Recurse using pascal's triangle
return (choose(n-1, k-1) + choose(n-1, k));
}
}