Package com.jme3.math

Class FastMath

java.lang.Object

com.jme3.math.FastMath

public final class FastMath
extends Object

FastMath provides 'fast' math approximations and float equivalents of Math functions. These are all used as static values and functions.

Field Summary

Fields

Modifier and Type	Field	Description
static final double	DBL_EPSILON	A "close to zero" double epsilon value for use
static final float	DEG_TO_RAD	A value to multiply a degree value by, to convert it to radians.
static final float	FLT_EPSILON	A "close to zero" float epsilon value for use
static final float	HALF_PI	The value PI/2 as a float.
static final float	INV_PI	The value 1/PI as a float.
static final float	INV_TWO_PI	The value 1/(2PI) as a float.
static final float	ONE_THIRD	The value 1/3, as a float.
static final float	PI	The value PI as a float.
static final float	QUARTER_PI	The value PI/4 as a float.
static final float	RAD_TO_DEG	A value to multiply a radian value by, to convert it to degrees.
static final Random	rand	A precreated random object for random numbers.
static final float	TWO_PI	The value 2PI as a float.
static final float	ZERO_TOLERANCE	A "close to zero" float epsilon value for use

Method Summary

Modifier and Type	Method	Description
static float	abs(float fValue)	Returns Absolute value of a float.
static float	acos(float fValue)	Returns the arc cosine of a value. Special cases: If fValue is smaller than -1, then the result is PI.
static boolean	approximateEquals(float a, float b)	Determine if two floats are approximately equal.
static float	asin(float fValue)	Returns the arc sine of a value. Special cases: If fValue is smaller than -1, then the result is -HALF_PI.
static float	atan(float fValue)	Returns the arc tangent of an angle given in radians.
static float	atan2(float fY, float fX)	A direct call to Math.atan2.
static Vector3f	cartesianToSpherical(Vector3f cartCoords, Vector3f store)	Converts a point from Cartesian coordinates (using positive Y as up) to Spherical and stores the results in the store var.
static Vector3f	cartesianZToSpherical(Vector3f cartCoords, Vector3f store)	Converts a point from Cartesian coordinates (using positive Z as up) to Spherical and stores the results in the store var.
static float	ceil(float fValue)	Rounds a fValue up.
static float	clamp(float input, float min, float max)	Take a float input and clamp it between min and max.
static Vector3f	computeNormal(Vector3f v1, Vector3f v2, Vector3f v3)	A method that computes normal for a triangle defined by three vertices.
static short	convertFloatToHalf(float flt)	Convert a single-precision (32-bit) floating-point value to half precision.
static float	convertHalfToFloat(short half)	Converts a single precision (32 bit) floating point value into half precision (16 bit).
static float	copysign(float x, float y)
static float	cos(float v)	Returns cosine of an angle.
static int	counterClockwise(Vector2f p0, Vector2f p1, Vector2f p2)	Given 3 points in a 2d plane, this function computes if the points going from A-B-C are moving counter clock wise.
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)	Returns the determinant of a 4x4 matrix.
static float	exp(float fValue)	Returns E^fValue
static float	extrapolateLinear(float scale, float startValue, float endValue)	Linear extrapolation from startValue to endValue by the given scale.
static Vector3f	extrapolateLinear(float scale, Vector3f startValue, Vector3f endValue)	Linear extrapolation from startValue to endValue by the given scale.
static Vector3f	extrapolateLinear(float scale, Vector3f startValue, Vector3f endValue, Vector3f store)	Linear extrapolation from startValue to endValue by the given scale.
static float	fastInvSqrt(float x)	Quickly estimate 1/sqrt(fValue).
static float	floor(float fValue)	Returns a number rounded down.
static float	getBezierP1toP2Length(Vector3f p0, Vector3f p1, Vector3f p2, Vector3f p3)	Compute the length on a Bezier spline between control points 1 and 2.
static float	getCatmullRomP1toP2Length(Vector3f p0, Vector3f p1, Vector3f p2, Vector3f p3, float startRange, float endRange, float curveTension)	Compute the length of a Catmull–Rom spline between control points 1 and 2
static Vector2f	insideUnitCircle()	Returns a random point inside or on a circle with radius 1.0.
static Vector3f	insideUnitSphere()	Returns a random point inside or on a sphere with radius 1.0 This method uses spherical coordinates combined with a cubed-root radius.
static float	interpolateBezier(float u, float p0, float p1, float p2, float p3)	Interpolate a spline between at least 4 control points following the Bezier equation.
static Vector3f	interpolateBezier(float u, Vector3f p0, Vector3f p1, Vector3f p2, Vector3f p3)	Interpolate a spline between at least 4 control points following the Bezier equation.
static Vector3f	interpolateBezier(float u, Vector3f p0, Vector3f p1, Vector3f p2, Vector3f p3, Vector3f store)	Interpolate a spline between at least 4 control points following the Bezier equation.
static float	interpolateCatmullRom(float u, float T, float p0, float p1, float p2, float p3)	Interpolate a spline between at least 4 control points following the Catmull-Rom equation.
static Vector3f	interpolateCatmullRom(float u, float T, Vector3f p0, Vector3f p1, Vector3f p2, Vector3f p3)	Interpolate a spline between at least 4 control points using the Catmull-Rom equation.
static Vector3f	interpolateCatmullRom(float u, float T, Vector3f p0, Vector3f p1, Vector3f p2, Vector3f p3, Vector3f store)	Interpolate a spline between at least 4 control points following the Catmull-Rom equation.
static float	interpolateLinear(float scale, float startValue, float endValue)	Linear interpolation from startValue to endValue by the given percent.
static Vector3f	interpolateLinear(float scale, Vector3f startValue, Vector3f endValue)	Linear interpolation from startValue to endValue by the given percent.
static Vector3f	interpolateLinear(float scale, Vector3f startValue, Vector3f endValue, Vector3f store)	Linear interpolation from startValue to endValue by the given percent.
static float	invSqrt(float fValue)	Returns 1/sqrt(fValue)
static boolean	isPowerOfTwo(int number)	Returns true if the number is a power of 2 (2,4,8,16...) A good implementation found on the Java boards.
static float	log(float fValue)	Returns the log base E of a value.
static float	log(float value, float base)	Returns the logarithm of value with given base, calculated as log(value)/log(base), so that pow(base, return)==value (contributed by vear)
static int	nearestPowerOfTwo(int number)	Get the next power of two of the given number.
static float	nextRandomFloat()	Generates a pseudorandom float in the range [0.0, 1.0).
static float	nextRandomFloat(float min, float max)	Generates a pseudorandom float in the range [min, max)
static int	nextRandomInt()	Generates a pseudorandom, uniformly-distributed int value.
static int	nextRandomInt(int min, int max)	Generates a pseudorandom int in the range [min, max] (inclusive).
static float	normalize(float val, float min, float max)	Takes a value and expresses it in terms of min to max.
static Vector3f	onUnitSphere()	Returns a random point on the surface of a sphere with radius 1.0
static int	pointInsideTriangle(Vector2f t0, Vector2f t1, Vector2f t2, Vector2f p)	Test if a point is inside a triangle.
static float	pow(float fBase, float fExponent)	Returns a number raised to an exponent power.
static float	saturate(float input)	Clamps the given float to be between 0 and 1.
static float	sign(float fValue)	Returns 1 if the number is positive, -1 if the number is negative, and 0 otherwise
static int	sign(int iValue)	Returns 1 if the number is positive, -1 if the number is negative, and 0 otherwise
static float	sin(float v)	Returns the sine of an angle.
static Vector3f	sphericalToCartesian(Vector3f sphereCoords, Vector3f store)	Converts a point from Spherical coordinates to Cartesian (using positive Y as up) and stores the results in the store var.
static Vector3f	sphericalToCartesianZ(Vector3f sphereCoords, Vector3f store)	Converts a point from Spherical coordinates to Cartesian (using positive Z as up) and stores the results in the store var.
static float	sqr(float fValue)	Returns the value squared.
static float	sqrt(float fValue)	Returns the square root of a given value.
static float	tan(float fValue)	Returns the tangent of the specified angle.
static int	toMultipleOf(int n, int p)	Round n to a multiple of p
static float	unInterpolateLinear(float value, float min, float max)	Converts a range of min/max to a 0-1 range.

Methods inherited from class java.lang.Object

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

Field Details

DBL_EPSILON

public static final double DBL_EPSILON

A "close to zero" double epsilon value for use

See Also:

• Constant Field Values

FLT_EPSILON

public static final float FLT_EPSILON

A "close to zero" float epsilon value for use

See Also:

• Constant Field Values

ZERO_TOLERANCE

public static final float ZERO_TOLERANCE

A "close to zero" float epsilon value for use

See Also:

• Constant Field Values

ONE_THIRD

public static final float ONE_THIRD

The value 1/3, as a float.

See Also:

• Constant Field Values

PI

public static final float PI

The value PI as a float. (180 degrees)

See Also:

• Constant Field Values

TWO_PI

public static final float TWO_PI

The value 2PI as a float. (360 degrees)

See Also:

• Constant Field Values

HALF_PI

public static final float HALF_PI

The value PI/2 as a float. (90 degrees)

See Also:

• Constant Field Values

QUARTER_PI

public static final float QUARTER_PI

The value PI/4 as a float. (45 degrees)

See Also:

• Constant Field Values

INV_PI

public static final float INV_PI

The value 1/PI as a float.

See Also:

• Constant Field Values

INV_TWO_PI

public static final float INV_TWO_PI

The value 1/(2PI) as a float.

See Also:

• Constant Field Values

DEG_TO_RAD

public static final float DEG_TO_RAD

A value to multiply a degree value by, to convert it to radians.

See Also:

• Constant Field Values

RAD_TO_DEG

public static final float RAD_TO_DEG

A value to multiply a radian value by, to convert it to degrees.

See Also:

• Constant Field Values

rand

public static final Random rand

A precreated random object for random numbers.

Method Details

isPowerOfTwo

public static boolean isPowerOfTwo(int number)

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.

Parameters:

number - The number to test.

Returns:

True if it is a power of two.

nearestPowerOfTwo

public static int nearestPowerOfTwo(int number)

Get the next power of two of the given number. E.g. for an input 100, this returns 128. Returns 1 for all numbers less than or equal to 1.

Parameters:

number - The number to obtain the POT for.

Returns:

The next power of two.

interpolateLinear

public static float interpolateLinear(float scale,
 float startValue,
 float endValue)

Linear interpolation from startValue to endValue by the given percent. Basically: ((1 - percent) * startValue) + (percent * endValue)

Parameters:

scale - scale value to use. if 1, use endValue, if 0, use startValue.

startValue - Beginning value. 0% of f

endValue - ending value. 100% of f

Returns:

The interpolated value between startValue and endValue.

interpolateLinear

public static Vector3f interpolateLinear(float scale,
 Vector3f startValue,
 Vector3f endValue,
 Vector3f store)

Linear interpolation from startValue to endValue by the given percent. Basically: ((1 - percent) * startValue) + (percent * endValue)

Parameters:

scale - scale value to use. if 1, use endValue, if 0, use startValue.

startValue - Beginning value. 0% of f

endValue - ending value. 100% of f

store - a vector3f to store the result

Returns:

The interpolated value between startValue and endValue.

interpolateLinear

public static Vector3f interpolateLinear(float scale,
 Vector3f startValue,
 Vector3f endValue)

Linear interpolation from startValue to endValue by the given percent. Basically: ((1 - percent) * startValue) + (percent * endValue)

Parameters:

scale - scale value to use. if 1, use endValue, if 0, use startValue.

startValue - Beginning value. 0% of f

endValue - ending value. 100% of f

Returns:

The interpolated value between startValue and endValue.

extrapolateLinear

public static float extrapolateLinear(float scale,
 float startValue,
 float endValue)

Linear extrapolation from startValue to endValue by the given scale. if scale is between 0 and 1 this method returns the same result as interpolateLinear if the scale is over 1 the value is linearly extrapolated. Note that the end value is the value for a scale of 1.

Parameters:

scale - the scale for extrapolation

startValue - the starting value (scale = 0)

endValue - the end value (scale = 1)

Returns:

an extrapolation for the given parameters

extrapolateLinear

public static Vector3f extrapolateLinear(float scale,
 Vector3f startValue,
 Vector3f endValue,
 Vector3f store)

Linear extrapolation from startValue to endValue by the given scale. if scale is between 0 and 1 this method returns the same result as interpolateLinear if the scale is over 1 the value is linearly extrapolated. Note that the end value is the value for a scale of 1.

Parameters:

scale - the scale for extrapolation

startValue - the starting value (scale = 0)

endValue - the end value (scale = 1)

store - an initialized vector to store the return value

Returns:

an extrapolation for the given parameters

extrapolateLinear

public static Vector3f extrapolateLinear(float scale,
 Vector3f startValue,
 Vector3f endValue)

Linear extrapolation from startValue to endValue by the given scale. if scale is between 0 and 1 this method returns the same result as interpolateLinear if the scale is over 1 the value is linearly extrapolated. Note that the end value is the value for a scale of 1.

Parameters:

scale - the scale for extrapolation

startValue - the starting value (scale = 0)

endValue - the end value (scale = 1)

Returns:

an extrapolation for the given parameters

interpolateCatmullRom

public static float interpolateCatmullRom(float u,
 float T,
 float p0,
 float p1,
 float p2,
 float p3)

Interpolate a spline between at least 4 control points following the Catmull-Rom equation. here is the interpolation matrix m = [ 0.0 1.0 0.0 0.0 ] [-T 0.0 T 0.0 ] [ 2T T-3 3-2T -T ] [-T 2-T T-2 T ] where T is the curve tension the result is a value between p1 and p2, t=0 for p1, t=1 for p2

Parameters:

u - value from 0 to 1

T - The tension of the curve

p0 - control point 0

p1 - control point 1

p2 - control point 2

p3 - control point 3

Returns:

Catmull–Rom interpolation

interpolateCatmullRom

public static Vector3f interpolateCatmullRom(float u,
 float T,
 Vector3f p0,
 Vector3f p1,
 Vector3f p2,
 Vector3f p3,
 Vector3f store)

Interpolate a spline between at least 4 control points following the Catmull-Rom equation. here is the interpolation matrix m = [ 0.0 1.0 0.0 0.0 ] [-T 0.0 T 0.0 ] [ 2T T-3 3-2T -T ] [-T 2-T T-2 T ] where T is the tension of the curve the result is a value between p1 and p2, t=0 for p1, t=1 for p2

Parameters:

u - value from 0 to 1

T - The tension of the curve

p0 - control point 0

p1 - control point 1

p2 - control point 2

p3 - control point 3

store - a Vector3f to store the result

Returns:

Catmull–Rom interpolation

interpolateCatmullRom

public static Vector3f interpolateCatmullRom(float u,
 float T,
 Vector3f p0,
 Vector3f p1,
 Vector3f p2,
 Vector3f p3)

Interpolate a spline between at least 4 control points using the Catmull-Rom equation. Here is the interpolation matrix: m = [ 0.0 1.0 0.0 0.0 ] [-T 0.0 T 0.0 ] [ 2T T-3 3-2T -T ] [-T 2-T T-2 T ] where T is the tension of the curve the result is a value between p1 and p2, t=0 for p1, t=1 for p2

Parameters:

u - value from 0 to 1

T - The tension of the curve

p0 - control point 0

p1 - control point 1

p2 - control point 2

p3 - control point 3

Returns:

Catmull–Rom interpolation

interpolateBezier

public static float interpolateBezier(float u,
 float p0,
 float p1,
 float p2,
 float p3)

Interpolate a spline between at least 4 control points following the Bezier equation. here is the interpolation matrix m = [ -1.0 3.0 -3.0 1.0 ] [ 3.0 -6.0 3.0 0.0 ] [ -3.0 3.0 0.0 0.0 ] [ 1.0 0.0 0.0 0.0 ] where T is the curve tension the result is a value between p1 and p3, t=0 for p1, t=1 for p3

Parameters:

u - value from 0 to 1

p0 - control point 0

p1 - control point 1

p2 - control point 2

p3 - control point 3

Returns:

Bezier interpolation

interpolateBezier

public static Vector3f interpolateBezier(float u,
 Vector3f p0,
 Vector3f p1,
 Vector3f p2,
 Vector3f p3,
 Vector3f store)

Interpolate a spline between at least 4 control points following the Bezier equation. here is the interpolation matrix m = [ -1.0 3.0 -3.0 1.0 ] [ 3.0 -6.0 3.0 0.0 ] [ -3.0 3.0 0.0 0.0 ] [ 1.0 0.0 0.0 0.0 ] where T is the tension of the curve the result is a value between p1 and p3, t=0 for p1, t=1 for p3

Parameters:

u - value from 0 to 1

p0 - control point 0

p1 - control point 1

p2 - control point 2

p3 - control point 3

store - a Vector3f to store the result

Returns:

Bezier interpolation

interpolateBezier

public static Vector3f interpolateBezier(float u,
 Vector3f p0,
 Vector3f p1,
 Vector3f p2,
 Vector3f p3)

Interpolate a spline between at least 4 control points following the Bezier equation. here is the interpolation matrix m = [ -1.0 3.0 -3.0 1.0 ] [ 3.0 -6.0 3.0 0.0 ] [ -3.0 3.0 0.0 0.0 ] [ 1.0 0.0 0.0 0.0 ] where T is the tension of the curve the result is a value between p1 and p3, t=0 for p1, t=1 for p3

Parameters:

u - value from 0 to 1

p0 - control point 0

p1 - control point 1

p2 - control point 2

p3 - control point 3

Returns:

Bezier interpolation

getCatmullRomP1toP2Length

public static float getCatmullRomP1toP2Length(Vector3f p0,
 Vector3f p1,
 Vector3f p2,
 Vector3f p3,
 float startRange,
 float endRange,
 float curveTension)

Compute the length of a Catmull–Rom spline between control points 1 and 2

Parameters:

p0 - control point 0

p1 - control point 1

p2 - control point 2

p3 - control point 3

startRange - the starting range on the segment (use 0)

endRange - the end range on the segment (use 1)

curveTension - the curve tension

Returns:

the length of the segment

getBezierP1toP2Length

public static float getBezierP1toP2Length(Vector3f p0,
 Vector3f p1,
 Vector3f p2,
 Vector3f p3)

Compute the length on a Bezier spline between control points 1 and 2.

Parameters:

p0 - control point 0

p1 - control point 1

p2 - control point 2

p3 - control point 3

Returns:

the length of the segment

acos

public static float acos(float fValue)

Returns the arc cosine of a value.
Special cases:

• If fValue is smaller than -1, then the result is PI.
• If the argument is greater than 1, then the result is 0.

Parameters:

fValue - The value to arc cosine.

Returns:

The angle, in radians.

See Also:

• Math.acos(double)

asin

public static float asin(float fValue)

Returns the arc sine of a value.
Special cases:

• If fValue is smaller than -1, then the result is -HALF_PI.
• If the argument is greater than 1, then the result is HALF_PI.

Parameters:

fValue - The value to arc sine.

Returns:

the angle in radians.

See Also:

• Math.asin(double)

atan

public static float atan(float fValue)

Returns the arc tangent of an angle given in radians.

Parameters:

fValue - The angle, in radians.

Returns:

fValue's atan

See Also:

• Math.atan(double)

atan2

public static float atan2(float fY,
 float fX)

A direct call to Math.atan2.

Parameters:

fY - ordinate

fX - abscissa

Returns:

Math.atan2(fY,fX)

See Also:

• Math.atan2(double, double)

ceil

public static float ceil(float fValue)

Rounds a fValue up. A call to Math.ceil

Parameters:

fValue - The value.

Returns:

The fValue rounded up

See Also:

• Math.ceil(double)

cos

public static float cos(float v)

Returns cosine of an angle. Direct call to java.lang.Math

Parameters:

v - The angle to cosine.

Returns:

the cosine of the angle.

See Also:

• Math.cos(double)

sin

public static float sin(float v)

Returns the sine of an angle. Direct call to java.lang.Math

Parameters:

v - The angle to sine.

Returns:

the sine of the angle.

See Also:

• Math.sin(double)

exp

public static float exp(float fValue)

Returns E^fValue

Parameters:

fValue - Value to raise to a power.

Returns:

The value E^fValue

See Also:

• Math.exp(double)

abs

public static float abs(float fValue)

Returns Absolute value of a float.

Parameters:

fValue - The value to abs.

Returns:

The abs of the value.

See Also:

• Math.abs(float)

floor

public static float floor(float fValue)

Returns a number rounded down.

Parameters:

fValue - The value to round

Returns:

The given number rounded down

See Also:

• Math.floor(double)

invSqrt

public static float invSqrt(float fValue)

Returns 1/sqrt(fValue)

Parameters:

fValue - The value to process.

Returns:

1/sqrt(fValue)

See Also:

• Math.sqrt(double)

fastInvSqrt

public static float fastInvSqrt(float x)

Quickly estimate 1/sqrt(fValue).

Parameters:

x - the input value (≥0)

Returns:

an approximate value for 1/sqrt(x)

log

public static float log(float fValue)

Returns the log base E of a value.

Parameters:

fValue - The value to log.

Returns:

The log of fValue base E

See Also:

• Math.log(double)

log

public static float log(float value,
 float base)

Returns the logarithm of value with given base, calculated as log(value)/log(base), so that pow(base, return)==value (contributed by vear)

Parameters:

value - The value to log.

base - Base of logarithm.

Returns:

The logarithm of value with given base

pow

public static float pow(float fBase,
 float fExponent)

Returns a number raised to an exponent power. fBase^fExponent

Parameters:

fBase - The base value (IE 2)

fExponent - The exponent value (IE 3)

Returns:

base raised to exponent (IE 8)

See Also:

• Math.pow(double, double)

sqr

public static float sqr(float fValue)

Returns the value squared. fValue ^ 2

Parameters:

fValue - The value to square.

Returns:

The square of the given value.

sqrt

public static float sqrt(float fValue)

Returns the square root of a given value.

Parameters:

fValue - The value to sqrt.

Returns:

The square root of the given value.

See Also:

• Math.sqrt(double)

tan

public static float tan(float fValue)

Returns the tangent of the specified angle.

Parameters:

fValue - The value to tangent, in radians.

Returns:

The tangent of fValue.

See Also:

• Math.tan(double)

sign

public static int sign(int iValue)

Returns 1 if the number is positive, -1 if the number is negative, and 0 otherwise

Parameters:

iValue - The integer to examine.

Returns:

The integer's sign.

sign

public static float sign(float fValue)

Returns 1 if the number is positive, -1 if the number is negative, and 0 otherwise

Parameters:

fValue - The float to examine.

Returns:

The float's sign.

counterClockwise

public static int counterClockwise(Vector2f p0,
 Vector2f p1,
 Vector2f p2)

Given 3 points in a 2d plane, this function computes if the points going from A-B-C are moving counter clock wise.

Parameters:

p0 - Point 0.

p1 - Point 1.

p2 - Point 2.

Returns:

1 If they are CCW, -1 if they are not CCW, 0 if p2 is between p0 and p1.

pointInsideTriangle

public static int pointInsideTriangle(Vector2f t0,
 Vector2f t1,
 Vector2f t2,
 Vector2f p)

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.

Parameters:

t0 - First point of the triangle.

t1 - Second point of the triangle.

t2 - Third point of the triangle.

p - The point to test.

Returns:

Value 1 or -1 if inside triangle, 0 otherwise.

computeNormal

public static Vector3f computeNormal(Vector3f v1,
 Vector3f v2,
 Vector3f v3)

A method that computes normal for a triangle defined by three vertices.

Parameters:

v1 - first vertex

v2 - second vertex

v3 - third vertex

Returns:

a normal for the face

determinant

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)

Returns the determinant of a 4x4 matrix.

Parameters:

m00 - the element in row 0, column 0 of the matrix

m01 - the element in row 0, column 1 of the matrix

m02 - the element in row 0, column 2 of the matrix

m03 - the element in row 0, column 3 of the matrix

m10 - the element in row 1, column 0 of the matrix

m11 - the element in row 1, column 1 of the matrix

m12 - the element in row 1, column 2 of the matrix

m13 - the element in row 1, column 3 of the matrix

m20 - the element in row 2, column 0 of the matrix

m21 - the element in row 2, column 1 of the matrix

m22 - the element in row 2, column 2 of the matrix

m23 - the element in row 2, column 3 of the matrix

m30 - the element in row 3, column 0 of the matrix

m31 - the element in row 3, column 1 of the matrix

m32 - the element in row 3, column 2 of the matrix

m33 - the element in row 3, column 3 of the matrix

Returns:

the determinant

nextRandomFloat

public static float nextRandomFloat()

Generates a pseudorandom float in the range [0.0, 1.0).

Returns:

A random float value.

nextRandomFloat

public static float nextRandomFloat(float min,
 float max)

Generates a pseudorandom float in the range [min, max)

Parameters:

min - The lower bound (inclusive).

max - The upper bound (exclusive).

Returns:

A random float value within the specified range.

nextRandomInt

public static int nextRandomInt()

Generates a pseudorandom, uniformly-distributed int value.

Returns:

The next pseudorandom int value.

nextRandomInt

public static int nextRandomInt(int min,
 int max)

Generates a pseudorandom int in the range [min, max] (inclusive).

Parameters:

min - The lower bound (inclusive).

max - The upper bound (inclusive).

Returns:

A random int value within the specified range.

onUnitSphere

public static Vector3f onUnitSphere()

Returns a random point on the surface of a sphere with radius 1.0

Returns:

A new Vector3f representing a random point on the surface of the unit sphere.

insideUnitSphere

public static Vector3f insideUnitSphere()

Returns a random point inside or on a sphere with radius 1.0 This method uses spherical coordinates combined with a cubed-root radius.

Returns:

A new Vector3f representing a random point within the unit sphere.

insideUnitCircle

public static Vector2f insideUnitCircle()

Returns a random point inside or on a circle with radius 1.0. This method uses polar coordinates combined with a square-root radius.

Returns:

A new Vector2f representing a random point within the unit circle.

sphericalToCartesian

public static Vector3f sphericalToCartesian(Vector3f sphereCoords,
 Vector3f store)

Converts a point from Spherical coordinates to Cartesian (using positive Y as up) and stores the results in the store var.

Parameters:

sphereCoords - the input spherical coordinates: x=distance from origin, y=longitude in radians, z=latitude in radians (not null, unaffected)

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

Returns:

the Cartesian coordinates (either store or a new vector)

cartesianToSpherical

public static Vector3f cartesianToSpherical(Vector3f cartCoords,
 Vector3f 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)

Parameters:

cartCoords - the input Cartesian coordinates (not null, unaffected)

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

Returns:

the Cartesian coordinates: x=distance from origin, y=longitude in radians, z=latitude in radians (either store or a new vector)

sphericalToCartesianZ

public static Vector3f sphericalToCartesianZ(Vector3f sphereCoords,
 Vector3f store)

Converts a point from Spherical coordinates to Cartesian (using positive Z as up) and stores the results in the store var.

Parameters:

sphereCoords - the input spherical coordinates: x=distance from origin, y=latitude in radians, z=longitude in radians (not null, unaffected)

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

Returns:

the Cartesian coordinates (either store or a new vector)

cartesianZToSpherical

public static Vector3f cartesianZToSpherical(Vector3f cartCoords,
 Vector3f 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)

Parameters:

cartCoords - the input Cartesian coordinates (not null, unaffected)

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

Returns:

the Cartesian coordinates: x=distance from origin, y=latitude in radians, z=longitude in radians (either store or a new vector)

normalize

public static float normalize(float val,
 float min,
 float max)

Takes a value and expresses it in terms of min to max.

Parameters:

val - the angle to normalize (in radians)

min - the lower limit of the range

max - the upper limit of the range

Returns:

the normalized angle (also in radians)

copysign

public static float copysign(float x,
 float y)

Parameters:

x - the value whose sign is to be adjusted.

y - the value whose sign is to be used.

Returns:

x with its sign changed to match the sign of y.

clamp

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

Take a float input and clamp it between min and max.

Parameters:

input - the value to be clamped

min - the minimum output value

max - the maximum output value

Returns:

clamped input

saturate

public static float saturate(float input)

Clamps the given float to be between 0 and 1.

Parameters:

input - the value to be clamped

Returns:

input clamped between 0 and 1.

approximateEquals

public static boolean approximateEquals(float a,
 float b)

Determine if two floats are approximately equal. This takes into account the magnitude of the floats, since large numbers will have larger differences be close to each other. Should return true for a=100000, b=100001, but false for a=10000, b=10001.

Parameters:

a - The first float to compare

b - The second float to compare

Returns:

True if a and b are approximately equal, false otherwise.

convertHalfToFloat

public static float convertHalfToFloat(short half)

Converts a single precision (32 bit) floating point value into half precision (16 bit).

Source: ftp://www.fox-toolkit.org/pub/fasthalffloatconversion.pdf

Parameters:

half - The half floating point value as a short.

Returns:

floating point value of the half.

convertFloatToHalf

public static short convertFloatToHalf(float flt)

Convert a single-precision (32-bit) floating-point value to half precision.

Parameters:

flt - the input value (not a NaN)

Returns:

a near-equivalent value in half precision

Throws:

UnsupportedOperationException - if flt is a NaN

unInterpolateLinear

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

Converts a range of min/max to a 0-1 range.

Parameters:

value - the value between min-max (inclusive).

min - the minimum of the range.

max - the maximum of the range.

Returns:

A value between 0-1 if the given value is between min/max.

toMultipleOf

public static int toMultipleOf(int n,
 int p)

Round n to a multiple of p