Package arc.math

Class Mathf

java.lang.Object

arc.math.Mathf

public final class Mathf
extends Object

Field Summary

Fields

Modifier and Type	Field	Description
static final boolean[]	booleans
static final float	degRad
static final float	degreesToRadians	multiply by this to convert from degrees to radians
static final double	doubleDegRad
static final double	doubleRadDeg
static final float	E
static final float	FLOAT_ROUNDING_ERROR
static final float	halfPi
static final float	pi
static final float	PI
static final float	PI2
static final float	radDeg
static final float	radiansToDegrees	multiply by this to convert from radians to degrees
static Rand	rand
static final int[]	signs
static final float	sqrt2
static final float	sqrt3
static final int[]	zeroOne

Constructor Summary

Constructors

Constructor	Description
Mathf()

Method Summary

Modifier and Type	Method	Description
static float	absin(float scl, float mag)
static float	absin(float in, float scl, float mag)
static float	angle(float x, float y)
static float	angleExact(float x, float y)
static float	approach(float from, float to, float speed)	Approaches a value at linear speed.
static float	approachDelta(float from, float to, float speed)	Approaches a value at linear speed.
static Vec2	arrive(float x, float y, float destX, float destY, Vec2 curVel, float radius, float tolerance, float speed, float accel)
static Vec2	arrive(Position pos, Position target, Vec2 curVel, float radius, float tolerance, float speed, float smoothTime)
static float	atan2(float x, float y)	Close approximation of the frequently-used trigonometric method atan2, with higher precision than libGDX's atan2 approximation.
static int	ceil(float value)	Returns the smallest integer greater than or equal to the specified float.
static int	ceilPositive(float value)	Returns the smallest integer greater than or equal to the specified float.
static boolean	chance(double d)
static boolean	chanceDelta(double d)
static double	clamp(double value, double min, double max)
static float	clamp(float value)	Clamps to [0, 1].
static float	clamp(float value, float min, float max)
static int	clamp(int value, int min, int max)
static long	clamp(long value, long min, long max)
static float	cos(float radians)	Returns the cosine in radians from a lookup table.
static float	cos(float radians, float scl, float mag)
static float	cosDeg(float degrees)	Returns the cosine in radians from a lookup table.
static float	curve(float f, float offset)	Converts a 0-1 value to 0-1 when it is in [offset, 1].
static float	curve(float f, float from, float to)	Converts a 0-1 value to 0-1 when it is in [offset, to].
static float	curveMargin(float f, float margin)	Transforms a 0-1 value to a value with a 0.5 plateau in the middle.
static float	curveMargin(float f, float marginLeft, float marginRight)	Transforms a 0-1 value to a value with a 0.5 plateau in the middle.
static int	digits(int n)
static int	digits(long n)
static float	dot(float x1, float y1, float x2, float y2)
static float	dst(float x1, float y1)
static float	dst(float x1, float y1, float x2, float y2)
static float	dst2(float x1, float y1)
static float	dst2(float x1, float y1, float x2, float y2)
static float	dstm(float x1, float y1, float x2, float y2)	Manhattan distance.
static boolean	equal(float a, float b)	Returns true if a is nearly equal to b.
static boolean	equal(float a, float b, float tolerance)	Returns true if a is nearly equal to b.
static int	floor(float value)	Returns the largest integer less than or equal to the specified float.
static int	floorPositive(float value)	Returns the largest integer less than or equal to the specified float.
static boolean	isPowerOfTwo(int value)
static float	len(float x, float y)
static float	len2(float x, float y)
static float	lerp(float fromValue, float toValue, float progress)	Linearly interpolates between fromValue to toValue on progress position.
static float	lerpDelta(float fromValue, float toValue, float progress)	Linearly interpolates between fromValue to toValue on progress position.
static float	log(float a, float value)
static float	log2(float value)
static int	log2(int value)
static float	map(float value, float from, float to)	Map value from [0, 1].
static float	map(float value, float froma, float toa, float fromb, float tob)
static float	maxZero(float val)
static float	mod(float f, float n)	Mod function that works properly for negative numbers.
static int	mod(int x, int n)	Mod function that works properly for negative numbers.
static int	nextPowerOfTwo(int value)	Returns the next power of two.
static int	num(boolean b)	Converts a boolean to an integer: 1 if true, 0, if false.
static float	pow(float a, float b)
static int	pow(int a, int b)
static float	random()	Returns random number between 0.0 (inclusive) and 1.0 (exclusive).
static float	random(float range)	Returns a random number between 0 (inclusive) and the specified value (exclusive).
static float	random(float start, float end)	Returns a random number between start (inclusive) and end (exclusive).
static int	random(int range)	Returns a random number between 0 (inclusive) and the specified value (inclusive).
static int	random(int start, int end)	Returns a random number between start (inclusive) and end (inclusive).
static long	random(long range)	Returns a random number between 0 (inclusive) and the specified value (inclusive).
static long	random(long start, long end)	Returns a random number between start (inclusive) and end (inclusive).
static boolean	randomBoolean()	Returns a random boolean value.
static boolean	randomBoolean(float chance)	Returns true if a random value between 0 and 1 is less than the specified value.
static float	randomSeed(long seed)
static float	randomSeed(long seed, float max)
static float	randomSeed(long seed, float min, float max)	Inclusive.
static int	randomSeed(long seed, int min, int max)	Inclusive.
static float	randomSeedRange(long seed, float range)
static int	randomSign()	Returns -1 or 1, randomly.
static float	randomTriangular()	Returns a triangularly distributed random number between -1.0 (exclusive) and 1.0 (exclusive), where values around zero are more likely.
static float	randomTriangular(float max)	Returns a triangularly distributed random number between -max (exclusive) and max (exclusive), where values around zero are more likely.
static float	randomTriangular(float min, float max)	Returns a triangularly distributed random number between min (inclusive) and max (exclusive), where the mode argument defaults to the midpoint between the bounds, giving a symmetric distribution.
static float	randomTriangular(float min, float max, float mode)	Returns a triangularly distributed random number between min (inclusive) and max (exclusive), where values around mode are more likely.
static float	range(float range)
static float	range(float min, float max)
static int	range(int range)
static int	round(float value)	Returns the closest integer to the specified float.
static float	round(float value, float step)
static int	round(float value, int step)
static int	round(int value, int step)
static int	roundPositive(float value)	Returns the closest integer to the specified float.
static float	sample(float[] values, float time)
static int	sign(boolean b)	Returns 1 if true, -1 if false.
static int	sign(float f)	Returns -1 if f<0, 1 otherwise.
static float	sin(float radians)	Returns the sine in radians from a lookup table.
static float	sin(float scl, float mag)
static float	sin(float radians, float scl, float mag)
static float	sinDeg(float degrees)	Returns the sine in radians from a lookup table.
static float	slerp(float fromDegrees, float toDegrees, float progress)	Linearly interpolates between two angles in degrees.
static float	slerpDelta(float fromDegrees, float toDegrees, float progress)
static float	slerpRad(float fromRadians, float toRadians, float progress)	Linearly interpolates between two angles in radians.
static float	slope(float fin)
static float	sqr(float x)
static float	sqrt(float x)
static float	tan(float radians, float scl, float mag)
static boolean	within(float x1, float y1, float dst)
static boolean	within(float x1, float y1, float x2, float y2, float dst)
static float	wrapAngleAroundZero(float a)	Wraps the given angle to the range [-PI, PI]
static boolean	zero(double value)	Returns true if the value is zero (using the default tolerance as upper bound)
static boolean	zero(float value)	Returns true if the value is zero (using the default tolerance as upper bound)
static boolean	zero(float value, float tolerance)	Returns true if the value is zero.

Methods inherited from class java.lang.Object

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

Field Details

signs

public static final int[] signs

zeroOne

public static final int[] zeroOne

booleans

public static final boolean[] booleans

FLOAT_ROUNDING_ERROR

public static final float FLOAT_ROUNDING_ERROR

See Also:

• Constant Field Values

PI

public static final float PI

See Also:

• Constant Field Values

pi

public static final float pi

See Also:

• Constant Field Values

halfPi

public static final float halfPi

See Also:

• Constant Field Values

PI2

public static final float PI2

See Also:

• Constant Field Values

E

public static final float E

See Also:

• Constant Field Values

sqrt2

public static final float sqrt2

sqrt3

public static final float sqrt3

radiansToDegrees

public static final float radiansToDegrees

multiply by this to convert from radians to degrees

See Also:

• Constant Field Values

radDeg

public static final float radDeg

See Also:

• Constant Field Values

degreesToRadians

public static final float degreesToRadians

multiply by this to convert from degrees to radians

See Also:

• Constant Field Values

degRad

public static final float degRad

See Also:

• Constant Field Values

doubleDegRad

public static final double doubleDegRad

See Also:

• Constant Field Values

doubleRadDeg

public static final double doubleRadDeg

See Also:

• Constant Field Values

rand

public static Rand rand

Constructor Details

Mathf

public Mathf()

Method Details

sin

public static float sin(float radians)

Returns the sine in radians from a lookup table.

cos

public static float cos(float radians)

Returns the cosine in radians from a lookup table.

sinDeg

public static float sinDeg(float degrees)

Returns the sine in radians from a lookup table.

cosDeg

public static float cosDeg(float degrees)

Returns the cosine in radians from a lookup table.

absin

public static float absin(float scl,
 float mag)

absin

public static float absin(float in,
 float scl,
 float mag)

tan

public static float tan(float radians,
 float scl,
 float mag)

sin

public static float sin(float scl,
 float mag)

sin

public static float sin(float radians,
 float scl,
 float mag)

cos

public static float cos(float radians,
 float scl,
 float mag)

angle

public static float angle(float x,
 float y)

angleExact

public static float angleExact(float x,
 float y)

wrapAngleAroundZero

public static float wrapAngleAroundZero(float a)

Wraps the given angle to the range [-PI, PI]

Parameters:

a - the angle in radians

Returns:

the given angle wrapped to the range [-PI, PI]

atan2

public static float atan2(float x,
 float y)

Close approximation of the frequently-used trigonometric method atan2, with higher precision than libGDX's atan2 approximation. Average error is 1.057E-6 radians; maximum error is 1.922E-6. Takes y and x (in that unusual order) as floats, and returns the angle from the origin to that point in radians. It is about 4 times faster than Math.atan2(double, double) (roughly 15 ns instead of roughly 60 ns for Math, on Java 8 HotSpot).
Credit for this goes to the 1955 research study "Approximations for Digital Computers," by RAND Corporation. This is sheet 11's algorithm, which is the fourth-fastest and fourth-least precise. The algorithms on sheets 8-10 are faster, but only by a very small degree, and are considerably less precise. That study provides an atan method, and that cleanly translates to atan2().

Parameters:

y - y-component of the point to find the angle towards; note the parameter order is unusual by convention

x - x-component of the point to find the angle towards; note the parameter order is unusual by convention

Returns:

the angle to the given point, in radians as a float; ranges from -PI to PI

digits

public static int digits(int n)

digits

public static int digits(long n)

sqrt

public static float sqrt(float x)

sqr

public static float sqr(float x)

map

public static float map(float value,
 float froma,
 float toa,
 float fromb,
 float tob)

map

public static float map(float value,
 float from,
 float to)

Map value from [0, 1].

sign

public static int sign(float f)

Returns -1 if f<0, 1 otherwise.

sign

public static int sign(boolean b)

Returns 1 if true, -1 if false.

num

public static int num(boolean b)

Converts a boolean to an integer: 1 if true, 0, if false.

pow

public static float pow(float a,
 float b)

pow

public static int pow(int a,
 int b)

range

public static float range(float range)

range

public static int range(int range)

range

public static float range(float min,
 float max)

chanceDelta

public static boolean chanceDelta(double d)

chance

public static boolean chance(double d)

random

public static int random(int range)

Returns a random number between 0 (inclusive) and the specified value (inclusive).

random

public static int random(int start,
 int end)

Returns a random number between start (inclusive) and end (inclusive).

random

public static long random(long range)

Returns a random number between 0 (inclusive) and the specified value (inclusive).

random

public static long random(long start,
 long end)

Returns a random number between start (inclusive) and end (inclusive).

randomBoolean

public static boolean randomBoolean()

Returns a random boolean value.

randomBoolean

public static boolean randomBoolean(float chance)

Returns true if a random value between 0 and 1 is less than the specified value.

random

public static float random()

Returns random number between 0.0 (inclusive) and 1.0 (exclusive).

random

public static float random(float range)

Returns a random number between 0 (inclusive) and the specified value (exclusive).

random

public static float random(float start,
 float end)

Returns a random number between start (inclusive) and end (exclusive).

randomSign

public static int randomSign()

Returns -1 or 1, randomly.

randomSeed

public static int randomSeed(long seed,
 int min,
 int max)

Inclusive.

randomSeed

public static float randomSeed(long seed,
 float min,
 float max)

Inclusive.

randomSeed

public static float randomSeed(long seed)

randomSeed

public static float randomSeed(long seed,
 float max)

randomSeedRange

public static float randomSeedRange(long seed,
 float range)

randomTriangular

public static float randomTriangular()

Returns a triangularly distributed random number between -1.0 (exclusive) and 1.0 (exclusive), where values around zero are more likely.

This is an optimized version of randomTriangular(-1, 1, 0)

randomTriangular

public static float randomTriangular(float max)

Returns a triangularly distributed random number between -max (exclusive) and max (exclusive), where values around zero are more likely.

This is an optimized version of randomTriangular(-max, max, 0)

Parameters:

max - the upper limit

randomTriangular

public static float randomTriangular(float min,
 float max)

Returns a triangularly distributed random number between min (inclusive) and max (exclusive), where the mode argument defaults to the midpoint between the bounds, giving a symmetric distribution.

This method is equivalent of randomTriangular(min, max, (min + max) * .5f)

Parameters:

min - the lower limit

max - the upper limit

randomTriangular

public static float randomTriangular(float min,
 float max,
 float mode)

Returns a triangularly distributed random number between min (inclusive) and max (exclusive), where values around mode are more likely.

Parameters:

min - the lower limit

max - the upper limit

mode - the point around which the values are more likely

nextPowerOfTwo

public static int nextPowerOfTwo(int value)

Returns the next power of two. Returns the specified value if the value is already a power of two.

isPowerOfTwo

public static boolean isPowerOfTwo(int value)

clamp

public static int clamp(int value,
 int min,
 int max)

clamp

public static long clamp(long value,
 long min,
 long max)

clamp

public static float clamp(float value,
 float min,
 float max)

clamp

public static float clamp(float value)

Clamps to [0, 1].

clamp

public static double clamp(double value,
 double min,
 double max)

maxZero

public static float maxZero(float val)

approach

public static float approach(float from,
 float to,
 float speed)

Approaches a value at linear speed.

approachDelta

public static float approachDelta(float from,
 float to,
 float speed)

Approaches a value at linear speed. Multiplied by the delta.

lerp

public static float lerp(float fromValue,
 float toValue,
 float progress)

Linearly interpolates between fromValue to toValue on progress position.

lerpDelta

public static float lerpDelta(float fromValue,
 float toValue,
 float progress)

Linearly interpolates between fromValue to toValue on progress position. Multiplied by Time.delta().

slerpRad

public static float slerpRad(float fromRadians,
 float toRadians,
 float progress)

Linearly interpolates between two angles in radians. Takes into account that angles wrap at two pi and always takes the direction with the smallest delta angle.

Parameters:

fromRadians - start angle in radians

toRadians - target angle in radians

progress - interpolation value in the range [0, 1]

Returns:

the interpolated angle in the range [0, PI2[

slerp

public static float slerp(float fromDegrees,
 float toDegrees,
 float progress)

Linearly interpolates between two angles in degrees. Takes into account that angles wrap at 360 degrees and always takes the direction with the smallest delta angle.

Parameters:

fromDegrees - start angle in degrees

toDegrees - target angle in degrees

progress - interpolation value in the range [0, 1]

Returns:

the interpolated angle in the range [0, 360[

slerpDelta

public static float slerpDelta(float fromDegrees,
 float toDegrees,
 float progress)

floor

public static int floor(float value)

Returns the largest integer less than or equal to the specified float. This method will only properly floor floats from -(2^14) to (Float.MAX_VALUE - 2^14).

floorPositive

public static int floorPositive(float value)

Returns the largest integer less than or equal to the specified float. This method will only properly floor floats that are positive. Note this method simply casts the float to int.

ceil

public static int ceil(float value)

Returns the smallest integer greater than or equal to the specified float. This method will only properly ceil floats from -(2^14) to (Float.MAX_VALUE - 2^14).

ceilPositive

public static int ceilPositive(float value)

Returns the smallest integer greater than or equal to the specified float. This method will only properly ceil floats that are positive.

round

public static int round(float value)

Returns the closest integer to the specified float. This method will only properly round floats from -(2^14) to (Float.MAX_VALUE - 2^14).

round

public static int round(int value,
 int step)

round

public static float round(float value,
 float step)

round

public static int round(float value,
 int step)

roundPositive

public static int roundPositive(float value)

Returns the closest integer to the specified float. This method will only properly round floats that are positive.

zero

public static boolean zero(float value)

Returns true if the value is zero (using the default tolerance as upper bound)

zero

public static boolean zero(double value)

Returns true if the value is zero (using the default tolerance as upper bound)

zero

public static boolean zero(float value,
 float tolerance)

Returns true if the value is zero.

Parameters:

tolerance - represent an upper bound below which the value is considered zero.

equal

public static boolean equal(float a,
 float b)

Returns true if a is nearly equal to b. The function uses the default floating error tolerance.

Parameters:

a - the first value.

b - the second value.

equal

public static boolean equal(float a,
 float b,
 float tolerance)

Returns true if a is nearly equal to b.

Parameters:

a - the first value.

b - the second value.

tolerance - represent an upper bound below which the two values are considered equal.

log

public static float log(float a,
 float value)

Returns:

the logarithm of value with base a

log2

public static float log2(float value)

Returns:

the logarithm of value with base 2

log2

public static int log2(int value)

Returns:

base-2 logarithm of the specified integer

mod

public static float mod(float f,
 float n)

Mod function that works properly for negative numbers.

mod

public static int mod(int x,
 int n)

Mod function that works properly for negative numbers.

sample

public static float sample(float[] values,
 float time)

Returns:

a sampled value based on position in an array of float values.

slope

public static float slope(float fin)

Returns:

the input 0-1 value scaled to 0-1-0.

curve

public static float curve(float f,
 float offset)

Converts a 0-1 value to 0-1 when it is in [offset, 1].

curve

public static float curve(float f,
 float from,
 float to)

Converts a 0-1 value to 0-1 when it is in [offset, to].

curveMargin

public static float curveMargin(float f,
 float margin)

Transforms a 0-1 value to a value with a 0.5 plateau in the middle. When margin = 0.5, this method doesn't do anything.

curveMargin

public static float curveMargin(float f,
 float marginLeft,
 float marginRight)

Transforms a 0-1 value to a value with a 0.5 plateau in the middle. When margin = 0.5, this method doesn't do anything.

len

public static float len(float x,
 float y)

len2

public static float len2(float x,
 float y)

dot

public static float dot(float x1,
 float y1,
 float x2,
 float y2)

dst

public static float dst(float x1,
 float y1)

dst2

public static float dst2(float x1,
 float y1)

dst

public static float dst(float x1,
 float y1,
 float x2,
 float y2)

dst2

public static float dst2(float x1,
 float y1,
 float x2,
 float y2)

dstm

public static float dstm(float x1,
 float y1,
 float x2,
 float y2)

Manhattan distance.

arrive

public static Vec2 arrive(Position pos,
 Position target,
 Vec2 curVel,
 float radius,
 float tolerance,
 float speed,
 float smoothTime)

arrive

public static Vec2 arrive(float x,
 float y,
 float destX,
 float destY,
 Vec2 curVel,
 float radius,
 float tolerance,
 float speed,
 float accel)

within

public static boolean within(float x1,
 float y1,
 float x2,
 float y2,
 float dst)

Returns:

whether dst(x1, y1, x2, y2) < dst

within

public static boolean within(float x1,
 float y1,
 float dst)

Returns:

whether dst(x, y, 0, 0) < dst