fastmath.java

java 3d game jme 工程开发源代码

/*
 * Copyright (c) 2003-2009 jMonkeyEngine
 * All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions are
 * met:
 *
 * * Redistributions of source code must retain the above copyright
 *   notice, this list of conditions and the following disclaimer.
 *
 * * Redistributions in binary form must reproduce the above copyright
 *   notice, this list of conditions and the following disclaimer in the
 *   documentation and/or other materials provided with the distribution.
 *
 * * Neither the name of 'jMonkeyEngine' nor the names of its contributors 
 *   may be used to endorse or promote products derived from this software 
 *   without specific prior written permission.
 *
 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
 * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
 * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
 * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
 * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
 * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
 * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
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 * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
 * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 */

package com.jme.math;

import java.util.Random;

/**
 * <code>FastMath</code> provides 'fast' math approximations and float equivalents of Math
 * functions.  These are all used as static values and functions.
 *
 * @author Various
 * @version $Id: FastMath.java,v 1.45 2007/08/26 08:44:20 irrisor Exp $
 */

final public class FastMath {

    private FastMath(){}

    /** A "close to zero" double epsilon value for use*/
    public static final double DBL_EPSILON = 2.220446049250313E-16d;

    /** A "close to zero" float epsilon value for use*/
    public static final float FLT_EPSILON = 1.1920928955078125E-7f;

    /** A "close to zero" float epsilon value for use*/
    public static final float ZERO_TOLERANCE = 0.0001f;
    
    public static final float ONE_THIRD = 1f/3f;

    /** The value PI as a float. (180 degrees) */
    public static final float PI = (float)Math.PI;

    /** The value 2PI as a float. (360 degrees) */
    public static final float TWO_PI = 2.0f * PI;

    /** The value PI/2 as a float. (90 degrees) */
    public static final float HALF_PI = 0.5f * PI;

    /** The value PI/4 as a float. (45 degrees) */
    public static final float QUARTER_PI = 0.25f * PI;

    /** The value 1/PI as a float. */
    public static final float INV_PI = 1.0f / PI;

    /** The value 1/(2PI) as a float. */
    public static final float INV_TWO_PI = 1.0f / TWO_PI;

    /** A value to multiply a degree value by, to convert it to radians. */
    public static final float DEG_TO_RAD = PI / 180.0f;

    /** A value to multiply a radian value by, to convert it to degrees. */
    public static final float RAD_TO_DEG = 180.0f / PI;

    /** A precreated random object for random numbers. */
    public static final Random rand = new Random(System.currentTimeMillis());


    /**
     * Returns true if the number is a power of 2 (2,4,8,16...)
     * 
     * A good implementation found on the Java boards. note: a number is a power
     * of two if and only if it is the smallest number with that number of
     * significant bits. Therefore, if you subtract 1, you know that the new
     * number will have fewer bits, so ANDing the original number with anything
     * less than it will give 0.
     * 
     * @param number
     *            The number to test.
     * @return True if it is a power of two.
     */
    public static boolean isPowerOfTwo(int number) {
        return (number > 0) && (number & (number - 1)) == 0;
    }
    
    public static int nearestPowerOfTwo(int number) {
        return (int)Math.pow(2, Math.ceil(Math.log(number) / Math.log(2)));
    }

    /**
     * Linear interpolation from startValue to endValue by the given percent.
     * Basically: ((1 - percent) * startValue) + (percent * endValue)
     * 
     * @param percent
     *            Percent value to use.
     * @param startValue
     *            Begining value. 0% of f
     * @param endValue
     *            ending value. 100% of f
     * @return The interpolated value between startValue and endValue.
     */
    public static float LERP(float percent, float startValue, float endValue) {
        if (startValue == endValue) return startValue;
        return ((1 - percent) * startValue) + (percent * endValue);
    }


     /**
     * Returns the arc cosine of an angle given in radians.<br>
     * Special cases:
     * <ul><li>If fValue is smaller than -1, then the result is PI.
     * <li>If the argument is greater than 1, then the result is 0.</ul>
     * @param fValue The angle, in radians.
     * @return fValue's acos
     * @see java.lang.Math#acos(double)
     */
    public static float acos(float fValue) {
        if (-1.0f < fValue) {
            if (fValue < 1.0f)
                return (float) Math.acos(fValue);
            
            return 0.0f;
        } 
        
        return PI;       
    }

     /**
     * Returns the arc sine of an angle given in radians.<br>
     * Special cases:
     * <ul><li>If fValue is smaller than -1, then the result is -HALF_PI.
     * <li>If the argument is greater than 1, then the result is HALF_PI.</ul>
     * @param fValue The angle, in radians.
     * @return fValue's asin
     * @see java.lang.Math#asin(double)
     */
    public static float asin(float fValue) {
        if (-1.0f < fValue) {
            if (fValue < 1.0f)
                return (float) Math.asin(fValue);
            
            return HALF_PI;
        }
        
        return -HALF_PI;        
    }

     /**
     * Returns the arc tangent of an angle given in radians.<br>
     * @param fValue The angle, in radians.
     * @return fValue's asin
     * @see java.lang.Math#atan(double)
     */
    public static float atan(float fValue) {
        return (float) Math.atan(fValue);
    }

    /**
     * A direct call to Math.atan2.
     * @param fY
     * @param fX
     * @return Math.atan2(fY,fX)
     * @see java.lang.Math#atan2(double, double)
     */
    public static float atan2(float fY, float fX) {
        return (float) Math.atan2(fY, fX);
    }

    /**
     * Rounds a fValue up.  A call to Math.ceil
     * @param fValue The value.
     * @return The fValue rounded up
     * @see java.lang.Math#ceil(double)
     */
    public static float ceil(float fValue) {
        return (float) Math.ceil(fValue);
    }
    
    /**
     * Fast Trig functions for x86. This forces the trig functiosn to stay
     * within the safe area on the x86 processor (-45 degrees to +45 degrees)
     * The results may be very slightly off from what the Math and StrictMath
     * trig functions give due to rounding in the angle reduction but it will be
     * very very close. 
     * 
     * note: code from wiki posting on java.net by jeffpk
     */
    public static float reduceSinAngle(float radians) {
        radians %= TWO_PI; // put us in -2PI to +2PI space
        if (Math.abs(radians) > PI) { // put us in -PI to +PI space
            radians = radians - (TWO_PI);
        }
        if (Math.abs(radians) > HALF_PI) {// put us in -PI/2 to +PI/2 space
            radians = PI - radians;
        }

        return radians;
    }

    /**
     * Returns sine of a value. 
     * 
     * note: code from wiki posting on java.net by jeffpk
     * 
     * @param fValue
     *            The value to sine, in radians.
     * @return The sine of fValue.
     * @see java.lang.Math#sin(double)
     */
    public static float sin(float fValue) {
        fValue = reduceSinAngle(fValue); // limits angle to between -PI/2 and +PI/2
        if (Math.abs(fValue)<=Math.PI/4){
           return (float)Math.sin(fValue);
        }
        
        return (float)Math.cos(Math.PI/2-fValue);        
    }

    /**
     * Returns cos of a value.
     * 
     * @param fValue
     *            The value to cosine, in radians.
     * @return The cosine of fValue.
     * @see java.lang.Math#cos(double)
     */
    public static float cos(float fValue) {
        return sin(fValue+HALF_PI);
    }

    /**
     * Returns E^fValue
     * @param fValue Value to raise to a power.
     * @return The value E^fValue
     * @see java.lang.Math#exp(double)
     */
    public static float exp(float fValue) {
        return (float) Math.exp(fValue);
    }

    /**
     * Returns Absolute value of a float.
     * @param fValue The value to abs.
     * @return The abs of the value.
     * @see java.lang.Math#abs(float)
     */
    public static float abs(float fValue) {
        if (fValue < 0) return -fValue;
        return fValue;
    }

    /**
     * Returns a number rounded down.
     * @param fValue The value to round
     * @return The given number rounded down
     * @see java.lang.Math#floor(double)
     */
    public static float floor(float fValue) {
        return (float) Math.floor(fValue);
    }

    /**
     * Returns 1/sqrt(fValue)
     * @param fValue The value to process.
     * @return 1/sqrt(fValue)
     * @see java.lang.Math#sqrt(double)
     */
    public static float invSqrt(float fValue) {
        return (float) (1.0f / Math.sqrt(fValue));