toxi.math
Class MathUtils

java.lang.Object
  toxi.math.MathUtils

public final class MathUtils
extends java.lang.Object

Miscellaneous math utilities.

Field Summary

static float	DEG2RAD Degrees to radians conversion factor
static float	EPS Epsilon value
static float	HALF_PI PI/2
static float	INV_PI The reciprocal of PI: (1/PI)
static float	LOG2 Log(2)
static float	PI PI
static float	PI_SQUARED PI*PI
static float	QUARTER_PI PI/4
static float	RAD2DEG Radians to degrees conversion factor
static java.util.Random	RND Default random number generator used by random methods of this class which don't use a passed in Random instance.
static float	SQRT2 Square root of 2
static float	SQRT3 Square root of 3
static float	THIRD_PI PI/3
static float	THREE_HALVES_PI PI*1.5
static float	TWO_PI PI*2

Constructor Summary

MathUtils()

Method Summary

static double	abs(double x)
static float	abs(float x)
static int	abs(int x)
static int	ceilPowerOf2(int x) Rounds up the value to the nearest higher power^2 value.
static double	clip(double a, double min, double max)
static float	clip(float a, float min, float max)
static int	clip(int a, int min, int max)
static float	clipNormalized(float a) Clips the value to the 0.0 ..
static double	cos(double theta)
static float	cos(float theta) Returns fast cosine approximation of a value.
static float	degrees(float radians)
static double	fastCos(double x) Fast cosine approximation.
static int	fastFloor(float x) Deprecated. renamed into floor(float)
static float	fastInverseSqrt(float x) Deprecated.
static float	fastPow(float a, float b) Computes a fast approximation to Math.pow(a, b).
static double	fastSin(double x) Fast sine approximation.
static boolean	flipCoin()
static boolean	flipCoin(java.util.Random rnd)
static int	floor(double x)
static int	floor(float x) This method is a *lot* faster than using (int)Math.floor(x).
static int	floorPowerOf2(int x) Rounds down the value to the nearest lower power^2 value.
static double	max(double a, double b)
static double	max(double a, double b, double c)
static float	max(float a, float b)
static float	max(float a, float b, float c) Returns the maximum value of three floats.
static int	max(int a, int b)
static int	max(int a, int b, int c) Returns the maximum value of three ints.
static double	min(double a, double b)
static double	min(double a, double b, double c)
static float	min(float a, float b)
static float	min(float a, float b, float c) Returns the minimum value of three floats.
static int	min(int a, int b)
static int	min(int a, int b, int c) Returns the minimum value of three ints.
static float	normalizedRandom() Returns a random number in the interval -1 ..
static float	normalizedRandom(java.util.Random rnd) Returns a random number in the interval -1 ..
static float	radians(float degrees)
static float	random(float max)
static float	random(float min, float max)
static int	random(int max)
static int	random(int min, int max)
static double	random(java.util.Random rnd, double max)
static double	random(java.util.Random rnd, double min, double max)
static float	random(java.util.Random rnd, float max)
static float	random(java.util.Random rnd, float min, float max)
static int	random(java.util.Random rnd, int max)
static int	random(java.util.Random rnd, int min, int max)
static double	reduceAngle(double theta)
static float	reduceAngle(float theta) Reduces the given angle into the -PI/4 ...
static void	setDefaultRandomGenerator(java.util.Random rnd) Sets the default Random number generator for this class.
static int	sign(double x)
static int	sign(float x)
static int	sign(int x)
static double	sin(double theta)
static float	sin(float theta) Returns a fast sine approximation of a value.
static float	sqrt(float x) Deprecated.

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

SQRT2

public static final float SQRT2

Square root of 2

SQRT3

public static final float SQRT3

Square root of 3

LOG2

public static final float LOG2

Log(2)

PI

public static final float PI

PI

See Also:

Constant Field Values

INV_PI

public static final float INV_PI

The reciprocal of PI: (1/PI)

See Also:

Constant Field Values

HALF_PI

public static final float HALF_PI

PI/2

See Also:

Constant Field Values

THIRD_PI

public static final float THIRD_PI

PI/3

See Also:

Constant Field Values

QUARTER_PI

public static final float QUARTER_PI

PI/4

See Also:

Constant Field Values

TWO_PI

public static final float TWO_PI

PI*2

See Also:

Constant Field Values

THREE_HALVES_PI

public static final float THREE_HALVES_PI

PI*1.5

See Also:

Constant Field Values

PI_SQUARED

public static final float PI_SQUARED

PI*PI

See Also:

Constant Field Values

EPS

public static final float EPS

Epsilon value

See Also:

Constant Field Values

DEG2RAD

public static final float DEG2RAD

Degrees to radians conversion factor

See Also:

Constant Field Values

RAD2DEG

public static final float RAD2DEG

Radians to degrees conversion factor

See Also:

Constant Field Values

RND

public static java.util.Random RND

Default random number generator used by random methods of this class which don't use a passed in Random instance.

Constructor Detail

MathUtils

public MathUtils()

Method Detail

abs

public static final double abs(double x)

Parameters:

x -

Returns:

absolute value of x

abs

public static final float abs(float x)

Parameters:

x -

Returns:

absolute value of x

abs

public static final int abs(int x)

Parameters:

x -

Returns:

absolute value of x

ceilPowerOf2

public static final int ceilPowerOf2(int x)

Rounds up the value to the nearest higher power^2 value.

Parameters:

x -

Returns:

power^2 value

clip

public static final double clip(double a,
                                double min,
                                double max)

clip

public static final float clip(float a,
                               float min,
                               float max)

clip

public static final int clip(int a,
                             int min,
                             int max)

clipNormalized

public static final float clipNormalized(float a)

Clips the value to the 0.0 .. 1.0 interval.

Parameters:

a -

Returns:

clipped value

Since:

0012

cos

public static final double cos(double theta)

cos

public static final float cos(float theta)

Returns fast cosine approximation of a value. Note: code from wiki posting on java.net by jeffpk

Parameters:

theta - angle in radians.

Returns:

cosine of theta.

degrees

public static final float degrees(float radians)

fastCos

public static final double fastCos(double x)

Fast cosine approximation.

Parameters:

x - angle in -PI/2 .. +PI/2 interval

Returns:

cosine

fastFloor

@Deprecated
public static final int fastFloor(float x)

Deprecated. renamed into floor(float)

fastInverseSqrt

@Deprecated
public static final float fastInverseSqrt(float x)

Deprecated.

fastPow

public static final float fastPow(float a,
                                  float b)

Computes a fast approximation to Math.pow(a, b). Adapted from http://www.dctsystems.co.uk/Software/power.html.

Parameters:

a - a positive number

b - a number

Returns:

a^b

fastSin

public static final double fastSin(double x)

Fast sine approximation.

Parameters:

x - angle in -PI/2 .. +PI/2 interval

Returns:

sine

flipCoin

public static final boolean flipCoin()

flipCoin

public static final boolean flipCoin(java.util.Random rnd)

floor

public static final int floor(double x)

floor

public static final int floor(float x)

This method is a *lot* faster than using (int)Math.floor(x).

Parameters:

x - value to be floored

Returns:

floored value as integer

Since:

0012

floorPowerOf2

public static final int floorPowerOf2(int x)

Rounds down the value to the nearest lower power^2 value.

Parameters:

x -

Returns:

power^2 value

max

public static final double max(double a,
                               double b)

max

public static final double max(double a,
                               double b,
                               double c)

max

public static final float max(float a,
                              float b)

max

public static final float max(float a,
                              float b,
                              float c)

Returns the maximum value of three floats.

Parameters:

a -

b -

c -

Returns:

max val

max

public static final int max(int a,
                            int b)

max

public static final int max(int a,
                            int b,
                            int c)

Returns the maximum value of three ints.

Parameters:

a -

b -

c -

Returns:

max val

min

public static final double min(double a,
                               double b)

min

public static final double min(double a,
                               double b,
                               double c)

min

public static final float min(float a,
                              float b)

min

public static final float min(float a,
                              float b,
                              float c)

Returns the minimum value of three floats.

Parameters:

a -

b -

c -

Returns:

min val

min

public static final int min(int a,
                            int b)

min

public static final int min(int a,
                            int b,
                            int c)

Returns the minimum value of three ints.

Parameters:

a -

b -

c -

Returns:

min val

normalizedRandom

public static final float normalizedRandom()

Returns a random number in the interval -1 .. +1.

Returns:

random float

normalizedRandom

public static final float normalizedRandom(java.util.Random rnd)

Returns a random number in the interval -1 .. +1 using the Random instance provided.

Returns:

random float

radians

public static final float radians(float degrees)

random

public static final float random(float max)

random

public static final float random(float min,
                                 float max)

random

public static final int random(int max)

random

public static final int random(int min,
                               int max)

random

public static final double random(java.util.Random rnd,
                                  double max)

random

public static final double random(java.util.Random rnd,
                                  double min,
                                  double max)

random

public static final float random(java.util.Random rnd,
                                 float max)

random

public static final float random(java.util.Random rnd,
                                 float min,
                                 float max)

random

public static final int random(java.util.Random rnd,
                               int max)

random

public static final int random(java.util.Random rnd,
                               int min,
                               int max)

reduceAngle

public static final double reduceAngle(double theta)

reduceAngle

public static final float reduceAngle(float theta)

Reduces the given angle into the -PI/4 ... PI/4 interval for faster computation of sin/cos. This method is used by sin(float) & cos(float).

Parameters:

theta - angle in radians

Returns:

reduced angle

See Also:

sin(float), cos(float)

setDefaultRandomGenerator

public static void setDefaultRandomGenerator(java.util.Random rnd)

Sets the default Random number generator for this class. This generator is being reused by all future calls to random() method versions which don't explicitly ask for a Random instance to be used.

Parameters:

rnd -

sign

public static int sign(double x)

sign

public static int sign(float x)

sign

public static int sign(int x)

sin

public static final double sin(double theta)

sin

public static final float sin(float theta)

Returns a fast sine approximation of a value. Note: code from wiki posting on java.net by jeffpk

Parameters:

theta - angle in radians.

Returns:

sine of theta.

sqrt

@Deprecated
public static final float sqrt(float x)

Deprecated.