java.lang.Object
- gaia.cu9.ari.gaiaorbit.util.math.MathUtilsd

```
public final class MathUtilsd
extends java.lang.Object
```
Utility and fast math functions.
Thanks to Riven on JavaGaming.org for the basis of sin/cos/atan2/floor/ceil.

Field Summary

Fields
Modifier and Type	Field	Description
`static double`	`degRad`
`static double`	`degreesToRadians`	multiply by this to convert from degrees to radians
`static double`	`E`
`static double`	`FLOAT_ROUNDING_ERROR`
`static double`	`nanoToSec`
`static double`	`PI`
`static double`	`PI2`
`static double`	`radDeg`
`static double`	`radiansToDegrees`	multiply by this to convert from radians to degrees
`static java.util.Random`	`random`

Constructor Summary

Constructors
Constructor Description

MathUtilsd()

Method Summary

All Methods Static Methods Concrete Methods
Modifier and Type	Method	Description
`static double`	`atan2(double y, double x)`	Returns atan2 in radians, faster but less accurate than Math.atan2.
`static double`	`clamp(double value, double min, double max)`
`static float`	`clamp(float value, float min, float max)`
`static int`	`clamp(int value, int min, int max)`
`static short`	`clamp(short value, short min, short max)`
`static double`	`cos(double radians)`	Returns the cosine in radians from a lookup table.
`static double`	`cosDeg(double degrees)`	Returns the cosine in radians from a lookup table.
`static double`	`distancePointLine(double x1, double y1, double z1, double x2, double y2, double z2, double x0, double y0, double z0)`	Gets the distance from the point x0 to the line denoted by x1-x2. Check this link
`static double`	`distancePointSegment(double x1, double y1, double z1, double x2, double y2, double z2, double x0, double y0, double z0)`	Gets the distance from the point p0 to the segment denoted by p1-p2. Check this link.
`static double`	`eint(double x, double x0, double x1, double y0, double y1, double exp)`	Does an exponential interpolation: y = y0 + (y1-y0) * 10 ^ (exp * (x-x0)/(x1-x0))
`static Vector3d`	`getClosestPoint(double x1, double y1, double z1, double x2, double y2, double z2, double x0, double y0, double z0)`	Gets the closest point on the line p1-p2 from p0. Check this link.
`static Vector3d`	`getClosestPoint2(double x1, double y1, double z1, double x2, double y2, double z2, double x0, double y0, double z0)`
`static boolean`	`isEqual(double a, double b)`	Returns true if a is nearly equal to b.
`static boolean`	`isEqual(double a, double b, double tolerance)`	Returns true if a is nearly equal to b.
`static boolean`	`isZero(double value)`	Returns true if the value is zero (using the default tolerance as upper bound)
`static boolean`	`isZero(double value, double tolerance)`	Returns true if the value is zero.
`static double`	`lint(double x, double x0, double x1, double y0, double y1)`	Linear interpolation
`static float`	`lint(float x, float x0, float x1, float y0, float y1)`	Linear interpolation
`static float`	`lint(long x, long x0, long x1, float y0, float y1)`	Linear interpolation
`static Vector3d`	`perpendicular(Vector3d in, Vector3d out)`	Gets perpendicular vector to in vector
`static double`	`random()`	Returns random number between 0.0 (inclusive) and 1.0 (exclusive).
`static double`	`random(double range)`	Returns a random number between 0 (inclusive) and the specified value (exclusive).
`static double`	`random(double start, double 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(double chance)`	Returns true if a random value between 0 and 1 is less than the specified value.
`static int`	`randomSign()`	Returns -1 or 1, randomly.
`static double`	`randomTriangular()`	Returns a triangularly distributed random number between -1.0 (exclusive) and 1.0 (exclusive), where values around zero are more likely.
`static double`	`randomTriangular(double max)`	Returns a triangularly distributed random number between `-max` (exclusive) and `max` (exclusive), where values around zero are more likely.
`static double`	`randomTriangular(double min, double 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 double`	`randomTriangular(double min, double max, double mode)`	Returns a triangularly distributed random number between `min` (inclusive) and `max` (exclusive), where values around `mode` are more likely.
`static double`	`roundAvoid(double value, int places)`	Rounds the double value to a number of decimal places
`static double`	`sin(double radians)`	Returns the sine in radians from a lookup table.
`static double`	`sinDeg(double degrees)`	Returns the sine in radians from a lookup table.
`static double`	`sqrt(double value)`	Fast sqrt method.

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail
- nanoToSec
```
public static final double nanoToSec
```
  See Also:
  
  Constant Field Values
- FLOAT_ROUNDING_ERROR
```
public static final double FLOAT_ROUNDING_ERROR
```
  See Also:
  
  Constant Field Values
- PI
```
public static final double PI
```
  See Also:
  
  Constant Field Values
- PI2
```
public static final double PI2
```
  See Also:
  
  Constant Field Values
- E
```
public static final double E
```
  See Also:
  
  Constant Field Values
- radiansToDegrees
```
public static final double radiansToDegrees
```
  multiply by this to convert from radians to degrees
  
  See Also:
  
  Constant Field Values
- radDeg
```
public static final double radDeg
```
  See Also:
  
  Constant Field Values
- degreesToRadians
```
public static final double degreesToRadians
```
  multiply by this to convert from degrees to radians
  
  See Also:
  
  Constant Field Values
- degRad
```
public static final double degRad
```
  See Also:
  
  Constant Field Values
- random
```
public static java.util.Random random
```

Constructor Detail
- MathUtilsd
```
public MathUtilsd()
```

Method Detail

sin
```
public static double sin(double radians)
```
Returns the sine in radians from a lookup table.

cos
```
public static double cos(double radians)
```
Returns the cosine in radians from a lookup table.

sinDeg
```
public static double sinDeg(double degrees)
```
Returns the sine in radians from a lookup table.

cosDeg
```
public static double cosDeg(double degrees)
```
Returns the cosine in radians from a lookup table.

atan2
```
public static double atan2(double y,
                           double x)
```
Returns atan2 in radians, faster but less accurate than Math.atan2. Average error of 0.00231 radians (0.1323 degrees), largest error of 0.00488 radians (0.2796 degrees).

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(double chance)
```
Returns true if a random value between 0 and 1 is less than the specified value.

random
```
public static double random()
```
Returns random number between 0.0 (inclusive) and 1.0 (exclusive).

random
```
public static double random(double range)
```
Returns a random number between 0 (inclusive) and the specified value (exclusive).

random

public static double random(double start,
                            double end)

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

randomSign
```
public static int randomSign()
```
Returns -1 or 1, randomly.

randomTriangular
```
public static double 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 double randomTriangular(double 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 double randomTriangular(double min,
                                      double 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 double randomTriangular(double min,
                                      double max,
                                      double 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

clamp

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

clamp

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

clamp

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

clamp

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

isZero
```
public static boolean isZero(double value)
```
Returns true if the value is zero (using the default tolerance as upper bound)

isZero
```
public static boolean isZero(double value,
                             double tolerance)
```
Returns true if the value is zero.

Parameters:

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

isEqual
```
public static boolean isEqual(double a,
                              double b)
```
Returns true if a is nearly equal to b. The function uses the default doubleing error tolerance.

Parameters:

a - the first value.

b - the second value.

isEqual
```
public static boolean isEqual(double a,
                              double b,
                              double 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.

sqrt
```
public static double sqrt(double value)
```
Fast sqrt method. Default passes it through one round of Newton's method

Parameters:

value - The value

Returns:

The square root value

eint

public static double eint(double x,
                          double x0,
                          double x1,
                          double y0,
                          double y1,
                          double exp)

Does an exponential interpolation: y = y0 + (y1-y0) * 10 ^ (exp * (x-x0)/(x1-x0))

Parameters:: x -; x0 -; x1 -; y0 -; y1 -; exp -
Returns:

lint
```
public static double lint(double x,
                          double x0,
                          double x1,
                          double y0,
                          double y1)
```
Linear interpolation

Parameters:

x - The value to interpolate

x0 - Inferior limit to the independent value

x1 - Superior limit to the independent value

y0 - Inferior limit to the dependent value

y1 - Superior limit to the dependent value

Returns:

The interpolated value

lint
```
public static float lint(float x,
                         float x0,
                         float x1,
                         float y0,
                         float y1)
```
Linear interpolation

Parameters:

x - The value to interpolate

x0 - Inferior limit to the independent value

x1 - Superior limit to the independent value

y0 - Inferior limit to the dependent value

y1 - Superior limit to the dependent value

Returns:

The interpolated value

lint
```
public static float lint(long x,
                         long x0,
                         long x1,
                         float y0,
                         float y1)
```
Linear interpolation

Parameters:

x - The value to interpolate

x0 - Inferior limit to the independent value

x1 - Superior limit to the independent value

y0 - Inferior limit to the dependent value

y1 - Superior limit to the dependent value

Returns:

The interpolated value

distancePointLine

public static double distancePointLine(double x1,
                                       double y1,
                                       double z1,
                                       double x2,
                                       double y2,
                                       double z2,
                                       double x0,
                                       double y0,
                                       double z0)

Gets the distance from the point x0 to the line denoted by x1-x2.
Check this link

Parameters:: x1 - The first point in the line; x2 - The second point in the line; x0 - The point
Returns:: The Euclidean distance between the line (x1, x2) and x0

distancePointSegment

public static double distancePointSegment(double x1,
                                          double y1,
                                          double z1,
                                          double x2,
                                          double y2,
                                          double z2,
                                          double x0,
                                          double y0,
                                          double z0)

Gets the distance from the point p0 to the segment denoted by p1-p2.
Check this link.

Parameters:: x1 - The first segment delimiter.; x2 - The second segment delimiter.; x0 - The point.
Returns:: The Euclidean distance between the segment (x1, x2)

getClosestPoint

public static Vector3d getClosestPoint(double x1,
                                       double y1,
                                       double z1,
                                       double x2,
                                       double y2,
                                       double z2,
                                       double x0,
                                       double y0,
                                       double z0)

Gets the closest point on the line p1-p2 from p0.
Check this link.

Parameters:: x1 - The first segment delimiter.; x2 - The second segment delimiter.; x0 - The point.
Returns:: The vector with the closest point on the line to p0

getClosestPoint2

public static Vector3d getClosestPoint2(double x1,
                                        double y1,
                                        double z1,
                                        double x2,
                                        double y2,
                                        double z2,
                                        double x0,
                                        double y0,
                                        double z0)

perpendicular

public static Vector3d perpendicular(Vector3d in,
                                     Vector3d out)

Gets perpendicular vector to in vector

Parameters:: in -
Returns:

roundAvoid
```
public static double roundAvoid(double value,
                                int places)
```
Rounds the double value to a number of decimal places

Parameters:

value - The value to round

places - The number of decimal places

Returns:

The rounded value

Class MathUtilsd

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

nanoToSec

FLOAT_ROUNDING_ERROR

PI

PI2

E

radiansToDegrees

radDeg

degreesToRadians

degRad

random

Constructor Detail

MathUtilsd

Method Detail

sin

cos

sinDeg

cosDeg

atan2

random

random

random

random

randomBoolean

randomBoolean

random

random

random

randomSign

randomTriangular

randomTriangular

randomTriangular

randomTriangular

clamp

clamp

clamp

clamp

isZero

isZero

isEqual

isEqual

sqrt

eint

lint

lint

lint

distancePointLine

distancePointSegment

getClosestPoint

getClosestPoint2

perpendicular

roundAvoid