# Normalizes an angle to be near an absolute angle : Math Functions « Development « Java Tutorial

```/*******************************************************************************
* Copyright (c) 2001, 2008 Mathew A. Nelson and Robocode contributors
* are made available under the terms of the Common Public License v1.0
* which accompanies this distribution, and is available at
*
* Contributors:
*     Mathew A. Nelson
*     - Initial API and implementation
*     Flemming N. Larsen
*     - Moved all methods to classes like FileUtil, StringUtil, WindowUtil,
*       Logger etc. exception for the following methods, which have been kept
*       here as legacy robots make use of these methods:
*       - normalAbsoluteAngle()
*       - normalNearAbsoluteAngle()
*       - normalRelativeAngle()
*     - The isNear() was made public
*     - Optimized and provided javadocs for all methods
*******************************************************************************/

import static java.lang.Math.PI;
import java.util.Random;

/**
* Utility class that provide methods for normalizing angles.
*
* @author Mathew A. Nelson (original)
* @author Flemming N. Larsen (contributor)
*/

public class Utils {
private final static double TWO_PI = 2 * PI;
private final static double THREE_PI_OVER_TWO = 3 * PI / 2;
private final static double PI_OVER_TWO = PI / 2;
public static final double NEAR_DELTA = .00001;
/**
* Normalizes an angle to be near an absolute angle.
* The normalized angle will be in the range from 0 to 2*PI, where 2*PI
* itself is not included.
* If the normalized angle is near to 0, PI/2, PI, 3*PI/2 or 2*PI, that
* angle will be returned. The {@link #isNear(double, double) isNear}
* method is used for defining when the angle is near one of angles listed
* above.
*
* @param angle the angle to normalize
* @return the normalized angle that will be in the range of [0,2*PI[
* @see #normalAbsoluteAngle(double)
* @see #isNear(double, double)
*/
public static double normalNearAbsoluteAngle(double angle) {
angle = (angle %= TWO_PI) >= 0 ? angle : (angle + TWO_PI);

if (isNear(angle, PI)) {
return PI;
} else if (angle < PI) {
if (isNear(angle, 0)) {
return 0;
} else if (isNear(angle, PI_OVER_TWO)) {
return PI_OVER_TWO;
}
} else {
if (isNear(angle, THREE_PI_OVER_TWO)) {
return THREE_PI_OVER_TWO;
} else if (isNear(angle, TWO_PI)) {
return 0;
}
}
return angle;
}
/**
* Tests if the two {@code double} values are near to each other.
* It is recommended to use this method instead of testing if the two
* doubles are equal using an this expression: {@code value1 == value2}.
* The reason being, that this expression might never become
* {@code true} due to the precision of double values.
* Whether or not the specified doubles are near to each other is defined by
* the following expression:
* {@code (Math.abs(value1 - value2) < .00001)}
*
* @param value1 the first double value
* @param value2 the second double value
* @return {@code true} if the two doubles are near to each other;
*         {@code false} otherwise.
*/
public static boolean isNear(double value1, double value2) {
return (Math.abs(value1 - value2) < NEAR_DELTA);
}
}
```
 6.17.Math Functions 6.17.1. Math Class Methods 6.17.2. Use math functions 6.17.3. Testing the Math class methods 6.17.4. Floating Point Number Enhancements in JDK 6 6.17.5. Math.scalb 6.17.6. Math.getExponent 6.17.7. Math.nextAfter 6.17.8. Math.nextUp 6.17.9. Math.copySign 6.17.10. Demonstrate toDegrees() and toRadians(). 6.17.11. Find absolute value of float, int, double and long using Math.abs 6.17.12. Find ceiling value of a number using Math.ceil 6.17.13. Find exponential value of a number using Math.exp 6.17.14. Find floor value of a number using Math.floor 6.17.15. Find maximum of two numbers using Math.max 6.17.16. Find natural logarithm value of a number using Math.log 6.17.17. Find power using Math.pow 6.17.18. Find square root of a number using Math.sqrt 6.17.19. Round Java float and double numbers using Math.round 6.17.20. Math.min 6.17.21. Normalizes an angle to a relative angle. 6.17.22. Normalizes an angle to an absolute angle. 6.17.23. Normalizes an angle to be near an absolute angle 6.17.24. Calculate the floor of the log, base 2 6.17.25. Greatest Common Divisor (GCD) of positive integer numbers 6.17.26. Least Common Multiple (LCM) of two strictly positive integer numbers 6.17.27. Moving Average 6.17.28. Normalize an angle in a 2&pi wide interval around a center value. 6.17.29. Returns n!. Shorthand for n Factorial, the product of the numbers 1,...,n as a double. 6.17.30. Returns n!. Shorthand for n Factorial, the product of the numbers 1,...,n. 6.17.31. Returns the hyperbolic cosine of x. 6.17.32. Returns the hyperbolic sine of x. 6.17.33. Returns the natural log of the (http://mathworld.wolfram.com/BinomialCoefficient.html) Binomial Coefficient 6.17.34. Returns the natural logarithm of n!. 6.17.35. Round the given value to the specified number of decimal places. The value is rounded using the BigDecimal.ROUND_HALF_UP method. 6.17.36. Value is rounded using the given method which is any method defined in BigDecimal 6.17.37. sqrt(a^2 + b^2) without under/overflow