jme3utilities.math

Class MyMath

java.lang.Object

jme3utilities.math.MyMath

public final class MyMath
extends java.lang.Object

Mathematical utility methods.

Field Summary

Fields

Modifier and Type	Field and Description
static java.util.logging.Logger	logger message logger for this class
static float	phi golden ratio = 1.618...
static float	root2 square root of 2
static float	rootHalf square root of 1/2

Method Summary

Modifier and Type	Method and Description
static double	area(Triangle triangle) Return the (one-sided) area of the specified triangle.
static double	circle(double abscissa) Return the circle function sqrt(1 - x^2) for a double-precision value.
static float	circle(float abscissa) Return the circle function sqrt(1 - x^2) for a single-precision value.
static double	clamp(double dValue, double min, double max) Clamp a double-precision value between 2 limits.
static int	clamp(int iValue, int min, int max) Clamp an integer value between 2 limits.
static Transform	combine(Transform child, Transform parent, Transform storeResult) Combine the specified transforms.
static float	cube(float fValue) Cube the specified single-precision value.
static Matrix3f	fromAngles(float xAngle, float yAngle, float zAngle, Matrix3f storeResult) Sets a rotation matrix from the specified Tait-Bryan angles, applying the rotations in x-z-y extrinsic order or y-z'-x" intrinsic order.
static float	hypotenuse(float... fValues) Return the root sum of squares of some single-precision values.
static double	hypotenuseDouble(double... dValues) Return the root sum of squares of some double-precision values.
static boolean	isBetween(float a, float b, float c) Test whether b is between a and c.
static boolean	isFinite(float value) Test whether the specified floating-point value is finite.
static boolean	isFiniteDouble(double value) Test whether the specified floating-point value is finite.
static boolean	isIdentity(Transform transform) Test the specified transform for exact identity.
static boolean	isOdd(int iValue) Test whether an integer value is odd.
static float	lerp(float t, float y0, float y1) Interpolate linearly between (or extrapolate linearly from) 2 single-precision values.
static int	log2(int iValue) Calculate the floor of the base-2 logarithm of the input value.
static float	max(float... fValues) Find the maximum of some single-precision values.
static int	maxInt(int... iValues) Find the maximum of some int values.
static float	mid(float a, float b, float c) Find the median of 3 single-precision values.
static float	min(float... fValues) Find the minimum of some single-precision values.
static float	modulo(float fValue, float modulus) Return the least non-negative value congruent with the input value with respect to the specified modulus.
static int	modulo(int iValue, int modulus) Return the least non-negative value congruent with the input value with respect to the specified modulus.
static float	standardize(float fValue) Standardize a single-precision value in preparation for hashing.
static float	standardizeAngle(float angle) Standardize a rotation angle to the range [-Pi, Pi).
static double	sumOfSquares(float... fValues) Return the sum of squares of some single-precision values.
static float	toDegrees(float radians) Convert an angle from radians to degrees.
static float	toRadians(float degrees) Convert an angle from degrees to radians.
static Vector3f	transform(Transform transform, Vector3f input, Vector3f storeResult) Apply the specified transform to a Vector3f.
static Triangle	transformInverse(Transform transform, Triangle input, Triangle storeResult) Apply the inverse of the specified transform to each vertex of a Triangle.
static Vector3f	transformInverse(Transform transform, Vector3f input, Vector3f storeResult) Apply the inverse of the specified transform to a Vector3f.

Methods inherited from class java.lang.Object

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

Field Detail

phi

public static final float phi

golden ratio = 1.618...

root2

public static final float root2

square root of 2

rootHalf

public static final float rootHalf

square root of 1/2

logger

public static final java.util.logging.Logger logger

message logger for this class

Method Detail

area

public static double area(Triangle triangle)

Return the (one-sided) area of the specified triangle.

Parameters:

triangle - (not null, unaffected)

Returns:

the area (≥0)

circle

public static double circle(double abscissa)

Return the circle function sqrt(1 - x^2) for a double-precision value.

Parameters:

abscissa - input (≤1, ≥-1)

Returns:

positive ordinate of the unit circle at the abscissa (≤1, ≥0)

circle

public static float circle(float abscissa)

Return the circle function sqrt(1 - x^2) for a single-precision value. Double-precision arithmetic is used to reduce the risk of overflow.

Parameters:

abscissa - input (≤1, ≥-1)

Returns:

positive ordinate of the unit circle at the abscissa (≤1, ≥0)

clamp

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

Clamp a double-precision value between 2 limits.

Parameters:

dValue - input value to be clamped

min - lower limit of the clamp

max - upper limit of the clamp

Returns:

the value between min and max inclusive that is closest to fValue

See Also:

FastMath.clamp(float,float,float)

clamp

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

Clamp an integer value between 2 limits.

Parameters:

iValue - input value to be clamped

min - the lower limit

max - the upper limit

Returns:

the value between min and max inclusive that is closest to iValue

combine

public static Transform combine(Transform child,
                                Transform parent,
                                Transform storeResult)

Combine the specified transforms.

It is safe for any or all of child, parent, and storeResult to be the same object.

This method works on transforms containing non-normalized quaternions.

Parameters:

child - the transform applied first (not null, unaffected unless it's storeResult)

parent - the transform applied last (not null, unaffected unless it's storeResult)

storeResult - (modified if not null)

Returns:

a Transform equivalent to child followed by parent (either storeResult or a new instance)

cube

public static float cube(float fValue)

Cube the specified single-precision value. Logs a warning in case of overflow.

Parameters:

fValue - input value to be cubed

Returns:

fValue raised to the third power

fromAngles

public static Matrix3f fromAngles(float xAngle,
                                  float yAngle,
                                  float zAngle,
                                  Matrix3f storeResult)

Sets a rotation matrix from the specified Tait-Bryan angles, applying the rotations in x-z-y extrinsic order or y-z'-x" intrinsic order.

Parameters:

xAngle - the X angle (in radians)

yAngle - the Y angle (in radians)

zAngle - the Z angle (in radians)

storeResult - storage for the result (modified if not null)

Returns:

a rotation matrix (either storeResult or a new instance)

hypotenuse

public static float hypotenuse(float... fValues)

Return the root sum of squares of some single-precision values. Double-precision arithmetic is used to reduce the risk of overflow.

Parameters:

fValues - the input values

Returns:

the positive square root of the sum of squares (≥0)

hypotenuseDouble

public static double hypotenuseDouble(double... dValues)

Return the root sum of squares of some double-precision values.

Parameters:

dValues - the input values

Returns:

the positive square root of the sum of squares (≥0)

isBetween

public static boolean isBetween(float a,
                                float b,
                                float c)

Test whether b is between a and c.

Parameters:

a - the first input value

b - the 2nd input value

c - the 3rd input value

Returns:

true if b is between a and c (inclusive), otherwise false

isFinite

public static boolean isFinite(float value)

Test whether the specified floating-point value is finite. Note that Java 8 provides Float.isFinite(float).

Parameters:

value - the value to test

Returns:

true if finite, false if NaN or infinity

isFiniteDouble

public static boolean isFiniteDouble(double value)

Test whether the specified floating-point value is finite. Note that Java 8 provides Double.isFinite(double).

Parameters:

value - the value to test

Returns:

true if finite, false if NaN or infinity

isIdentity

public static boolean isIdentity(Transform transform)

Test the specified transform for exact identity.

Parameters:

transform - which transform to test (not null, unaffected)

Returns:

true if exact identity, otherwise false

isOdd

public static boolean isOdd(int iValue)

Test whether an integer value is odd.

Parameters:

iValue - the value to be tested

Returns:

true if x is odd, false if it's even

lerp

public static float lerp(float t,
                         float y0,
                         float y1)

Interpolate linearly between (or extrapolate linearly from) 2 single-precision values.

No rounding error is introduced when y0==y1.

Parameters:

t - the weight given to y1

y0 - the function value at t=0

y1 - the function value at t=1

Returns:

the interpolated function value

log2

public static int log2(int iValue)

Calculate the floor of the base-2 logarithm of the input value.

Parameters:

iValue - the input value (≥1)

Returns:

the largest integer N≤30 for which (1 << N) <= iValue (≥0, ≤30)

max

public static float max(float... fValues)

Find the maximum of some single-precision values.

Parameters:

fValues - the input values

Returns:

the most positive value

See Also:

Math.max(float, float)

maxInt

public static int maxInt(int... iValues)

Find the maximum of some int values.

Parameters:

iValues - the input values

Returns:

the most positive value

See Also:

Collections.max(java.util.Collection), Math.max(int, int)

mid

public static float mid(float a,
                        float b,
                        float c)

Find the median of 3 single-precision values.

Parameters:

a - the first input value

b - the 2nd input value

c - the 3rd input value

Returns:

the median of the 3 values

min

public static float min(float... fValues)

Find the minimum of some single-precision values.

Parameters:

fValues - the input values

Returns:

the most negative value

See Also:

Math.min(float, float)

modulo

public static int modulo(int iValue,
                         int modulus)

Return the least non-negative value congruent with the input value with respect to the specified modulus.

This differs from remainder for negative input values. For instance, modulo(-1, 4) == 3, while -1 % 4 == -1.

Parameters:

iValue - the input value

modulus - (>0)

Returns:

iValue MOD modulus (<modulus, ≥0)

modulo

public static float modulo(float fValue,
                           float modulus)

Return the least non-negative value congruent with the input value with respect to the specified modulus.

This differs from remainder for negative input values. For instance, modulo(-1f, 4f) == 3f, while -1f % 4f == -1f.

Parameters:

fValue - the input value

modulus - (>0)

Returns:

fValue MOD modulus (<modulus, ≥0)

standardize

public static float standardize(float fValue)

Standardize a single-precision value in preparation for hashing.

Parameters:

fValue - input value

Returns:

an equivalent value that's not -0

standardizeAngle

public static float standardizeAngle(float angle)

Standardize a rotation angle to the range [-Pi, Pi).

Parameters:

angle - the input angle (in radians)

Returns:

the standardized angle (in radians, <Pi, ≥-Pi)

sumOfSquares

public static double sumOfSquares(float... fValues)

Return the sum of squares of some single-precision values. Double-precision arithmetic is used to reduce the risk of overflow.

Parameters:

fValues - the input values

Returns:

the sum of squares (≥0)

toDegrees

public static float toDegrees(float radians)

Convert an angle from radians to degrees.

Parameters:

radians - input angle

Returns:

equivalent in degrees

See Also:

Math.toDegrees(double)

toRadians

public static float toRadians(float degrees)

Convert an angle from degrees to radians.

Parameters:

degrees - input angle

Returns:

equivalent in radians

See Also:

Math.toRadians(double)

transform

public static Vector3f transform(Transform transform,
                                 Vector3f input,
                                 Vector3f storeResult)

Apply the specified transform to a Vector3f.

It is safe for input and storeResult to be the same object.

This method works on transforms containing non-normalized quaternions.

Parameters:

transform - the transform to apply (not null, unaffected unless storeResult is its translation or scaling component)

input - the input vector (not null, unaffected unless it's storeResult)

storeResult - storage for the result (modified if not null)

Returns:

the transformed vector (either storeResult or a new instance)

transformInverse

public static Triangle transformInverse(Transform transform,
                                        Triangle input,
                                        Triangle storeResult)

Apply the inverse of the specified transform to each vertex of a Triangle.

It is safe for input and storeResult to be the same object.

Parameters:

transform - the transform to apply (not null, unaffected)

input - the input triangle (not null, unaffected unless it's storeResult)

storeResult - storage for the result (modified if not null)

Returns:

the transformed triangle (either storeResult or a new instance)

transformInverse

public static Vector3f transformInverse(Transform transform,
                                        Vector3f input,
                                        Vector3f storeResult)

Apply the inverse of the specified transform to a Vector3f.

It is safe for input and storeResult to be the same object.

This method works on transforms containing non-normalized quaternions.

Parameters:

transform - the transform to un-apply (not null, unaffected unless storeResult is its translation or scaling component)

input - the input vector (not null, unaffected unless it's storeResult)

storeResult - storage for the result (modified if not null)

Returns:

the transformed vector (either storeResult or a new instance)