/*
* 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
* LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
* NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
* SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
package org.mt4j.util.math;
import java.util.Random;
/**
* This class provides 'fast' math approximations and float equivalents of Math
* functions. These are all used as static values and functions.
* Copyright by JMonkeyEngine
*
* @author Various
*/
final public class ToolsMath {
/**
* Instantiates a new fast math.
*/
private ToolsMath(){}
/** 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;
/** The Constant ONE_THIRD. */
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;
}
/**
* Nearest power of two.
*
* @param number the number
*
* @return the int
*/
public static int nearestPowerOfTwo(int number) {
return (int)Math.pow(2, Math.ceil(Math.log(number) / Math.log(2)));
}
/**
* Returns the power of two number nearest to the given number.
*
* @param value the value
*
* @return the int
*/
public static int nearestPower(int value) {
int i = 1;
if (value == 0) {
return (-1);
}
for (;;) {
if (value == 1) {
return (i);
} else if (value == 3) {
return (i * 4);
}
value = value >> 1;
i *= 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 the f y
* @param fX the f x
*
* @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
*
* @param radians the radians
*
* @return the float
*/
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));
}
/**
* Returns the log base E of a value.
*
* @param fValue The value to log.
*
* @return The log of fValue base E
*
* @see java.lang.Math#log(double)
*/
public static float log(float fValue) {
return (float) Math.log(fValue);
}
/**
* Returns the logarithm of value with given base, calculated as log(value)/log(base),
* so that pow(base, return)==value (contributed by vear).
*
* @param value The value to log.
* @param base Base of logarithm.
*
* @return The logarithm of value with given base
*/
public static float log(float value, float base) {
return (float)(Math.log(value)/Math.log(base));
}
/**
* Returns a number raised to an exponent power. fBase^fExponent
*
* @param fBase The base value (IE 2)
* @param fExponent The exponent value (IE 3)
*
* @return base raised to exponent (IE 8)
*
* @see java.lang.Math#pow(double, double)
*/
public static float pow(float fBase, float fExponent) {
return (float) Math.pow(fBase, fExponent);
}
/**
* Returns the value squared. fValue ^ 2
*
* @param fValue The vaule to square.
*
* @return The square of the given value.
*/
public static float sqr(float fValue) {
return fValue * fValue;
}
/**
* Returns the square root of a given value.
*
* @param fValue The value to sqrt.
*
* @return The square root of the given value.
*
* @see java.lang.Math#sqrt(double)
*/
public static float sqrt(float fValue) {
return (float) Math.sqrt(fValue);
}
/**
* Returns the tangent of a value. If USE_FAST_TRIG is enabled, an approximate value
* is returned. Otherwise, a direct value is used.
*
* @param fValue The value to tangent, in radians.
*
* @return The tangent of fValue.
*
* @see java.lang.Math#tan(double)
*/
public static float tan(float fValue) {
return (float) Math.tan(fValue);
}
/**
* Returns 1 if the number is positive, -1 if the number is negative, and 0 otherwise.
*
* @param iValue The integer to examine.
*
* @return The integer's sign.
*/
public static int sign(int iValue) {
if (iValue > 0) return 1;
if (iValue < 0) return -1;
return 0;
}
/**
* Returns 1 if the number is positive, -1 if the number is negative, and 0 otherwise.
*
* @param fValue The float to examine.
*
* @return The float's sign.
*/
public static float sign(float fValue) {
return Math.signum(fValue);
}
/**
* Given 3 points in a 2d plane, this function computes if the points going from A-B-C
* are moving counter clock wise.
*
* @param p0 Point 0.
* @param p1 Point 1.
* @param p2 Point 2.
*
* @return 1 If they are CCW, -1 if they are not CCW, 0 if p2 is between p0 and p1.
*
* @throws Exception the exception
*/
public static int counterClockwise(Vector3D p0,Vector3D p1,Vector3D p2) throws Exception{
if (p0.z != 0 || p1.z!=0 || p2.z!=0){
throw new Exception("Can only check if all vectors are in the z=0 plane!");
}
float dx1,dx2,dy1,dy2;
dx1=p1.x-p0.x;
dy1=p1.y-p0.y;
dx2=p2.x-p0.x;
dy2=p2.y-p0.y;
if (dx1*dy2>dy1*dx2) return 1;
if (dx1*dy2<dy1*dx2) return -1;
if ((dx1*dx2 < 0) || (dy1*dy2 <0)) return -1;
if ((dx1*dx1+dy1*dy1) < (dx2*dx2+dy2*dy2)) return 1;
return 0;
}
// /**
// * Test if a point is inside a triangle. 1 if the point is on the ccw side,
// * -1 if the point is on the cw side, and 0 if it is on neither.
// * @param t0 First point of the triangle.
// * @param t1 Second point of the triangle.
// * @param t2 Third point of the triangle.
// * @param p The point to test.
// * @return Value 1 or -1 if inside triangle, 0 otherwise.
// */
// public static int pointInsideTriangle(Vector2f t0,Vector2f t1,Vector2f t2,Vector2f p){
// int val1=counterClockwise(t0,t1,p);
// if (val1==0) return 1;
// int val2=counterClockwise(t1,t2,p);
// if (val2==0) return 1;
// if (val2!=val1) return 0;
// int val3=counterClockwise(t2,t0,p);
// if (val3==0) return 1;
// if (val3!=val1) return 0;
// return val3;
// }
/**
* Returns the determinant of a 4x4 matrix.
*
* @param m00 the m00
* @param m01 the m01
* @param m02 the m02
* @param m03 the m03
* @param m10 the m10
* @param m11 the m11
* @param m12 the m12
* @param m13 the m13
* @param m20 the m20
* @param m21 the m21
* @param m22 the m22
* @param m23 the m23
* @param m30 the m30
* @param m31 the m31
* @param m32 the m32
* @param m33 the m33
*
* @return the float
*/
public static float determinant(double m00, double m01, double m02,
double m03, double m10, double m11, double m12, double m13,
double m20, double m21, double m22, double m23, double m30,
double m31, double m32, double m33) {
double det01 = m20 * m31 - m21 * m30;
double det02 = m20 * m32 - m22 * m30;
double det03 = m20 * m33 - m23 * m30;
double det12 = m21 * m32 - m22 * m31;
double det13 = m21 * m33 - m23 * m31;
double det23 = m22 * m33 - m23 * m32;
return (float) (m00 * (m11 * det23 - m12 * det13 + m13 * det12) - m01
* (m10 * det23 - m12 * det03 + m13 * det02) + m02
* (m10 * det13 - m11 * det03 + m13 * det01) - m03
* (m10 * det12 - m11 * det02 + m12 * det01));
}
/**
* Returns a random float between 0 and 1.
*
* @return A random float between <tt>0.0f</tt> (inclusive) to
* <tt>1.0f</tt> (exclusive).
*/
public static float nextRandomFloat() {
return rand.nextFloat();
}
/**
* Returns a random float between min and max.
*
* @param min the min
* @param max the max
*
* @return A random int between <tt>min</tt> (inclusive) to
* <tt>max</tt> (inclusive).
*/
public static int nextRandomInt(int min, int max) {
return (int)(nextRandomFloat() * (max - min + 1)) + min;
}
/**
* Next random int.
*
* @return the int
*/
public static int nextRandomInt() {
return rand.nextInt();
}
/**
* Converts a point from Spherical coordinates to Cartesian (using positive
* Y as up) and stores the results in the store var.
*
* @param sphereCoords the sphere coords
* @param store the store
*
* @return the vector3 d
*/
public static Vector3D sphericalToCartesian(Vector3D sphereCoords,
Vector3D store) {
store.y = sphereCoords.x * ToolsMath.sin(sphereCoords.z);
float a = sphereCoords.x * ToolsMath.cos(sphereCoords.z);
store.x = a * ToolsMath.cos(sphereCoords.y);
store.z = a * ToolsMath.sin(sphereCoords.y);
return store;
}
/**
* Converts a point from Cartesian coordinates (using positive Y as up) to
* Spherical and stores the results in the store var. (Radius, Azimuth,
* Polar)
*
* @param cartCoords the cart coords
* @param store the store
*
* @return the vector3 d
*/
public static Vector3D cartesianToSpherical(Vector3D cartCoords,
Vector3D store) {
if (cartCoords.x == 0)
cartCoords.x = ToolsMath.FLT_EPSILON;
store.x = ToolsMath
.sqrt((cartCoords.x * cartCoords.x)
+ (cartCoords.y * cartCoords.y)
+ (cartCoords.z * cartCoords.z));
store.y = ToolsMath.atan(cartCoords.z / cartCoords.x);
if (cartCoords.x < 0)
store.y += ToolsMath.PI;
store.z = ToolsMath.asin(cartCoords.y / store.x);
return store;
}
/**
* Converts a point from Spherical coordinates to Cartesian (using positive
* Z as up) and stores the results in the store var.
*
* @param sphereCoords the sphere coords
* @param store the store
*
* @return the vector3 d
*/
public static Vector3D sphericalToCartesianZ(Vector3D sphereCoords,
Vector3D store) {
store.z = sphereCoords.x * ToolsMath.sin(sphereCoords.z);
float a = sphereCoords.x * ToolsMath.cos(sphereCoords.z);
store.x = a * ToolsMath.cos(sphereCoords.y);
store.y = a * ToolsMath.sin(sphereCoords.y);
return store;
}
/**
* Converts a point from Cartesian coordinates (using positive Z as up) to
* Spherical and stores the results in the store var. (Radius, Azimuth,
* Polar)
*
* @param cartCoords the cart coords
* @param store the store
*
* @return the vector3 d
*/
public static Vector3D cartesianZToSpherical(Vector3D cartCoords,
Vector3D store) {
if (cartCoords.x == 0)
cartCoords.x = ToolsMath.FLT_EPSILON;
store.x = ToolsMath
.sqrt((cartCoords.x * cartCoords.x)
+ (cartCoords.y * cartCoords.y)
+ (cartCoords.z * cartCoords.z));
store.z = ToolsMath.atan(cartCoords.z / cartCoords.x);
if (cartCoords.x < 0)
store.z += ToolsMath.PI;
store.y = ToolsMath.asin(cartCoords.y / store.x);
return store;
}
/**
* Takes an value and expresses it in terms of min to max.
*
* @param val -
* the angle to normalize (in radians)
* @param min the min
* @param max the max
*
* @return the normalized angle (also in radians)
*/
public static float normalize(float val, float min, float max) {
if (Float.isInfinite(val) || Float.isNaN(val))
return 0f;
float range = max-min;
while (val > max)
val -= range;
while (val < min)
val += range;
return val;
}
/**
* Copysign.
*
* @param x the value whose sign is to be adjusted.
* @param y the value whose sign is to be used.
*
* @return x with its sign changed to match the sign of y.
*/
public static float copysign(float x, float y) {
if (y >= 0 && x <= -0)
return -x;
else if (y < 0 && x >= 0)
return -x;
else
return x;
}
/**
* Take a float input and clamp it between min and max.
*
* @param input the input
* @param min the min
* @param max the max
*
* @return clamped input
*/
public static float clamp(float input, float min, float max) {
return (input < min) ? min : (input > max) ? max : input;
}
/**
* Convenience function to map a variable from one value range
* to another.
*
* @param theValue the the value
* @param theInStart the the in start
* @param theInEnd the the in end
* @param theOutStart the the out start
* @param theOutEnd the the out end
*
* @return the float
*/
public static final float map(float theValue, float theInStart, float theInEnd, float theOutStart, float theOutEnd) {
return theOutStart + (theOutEnd - theOutStart) * ((theValue - theInStart) / (theInEnd - theInStart));
}
/**
* Calculates a random number ranging in between the floor and the ceiling value.
*
* @param floor the floor
* @param ceiling the ceiling
*
* @return the random
*
* the generated random number
*/
public static float getRandom(float floor, float ceiling){
return (floor + (float)Math.random()*(ceiling-floor));
}
// /**
// * Checks if is power of two.
// *
// * @param i the i
// *
// * @return true, if is power of two
// */
// public static boolean isPowerOfTwo(int i){
// return ((i&(i-1)) == 0);
// }
}