fr.cnes.sirius.patrius.math.interval

Class AngleTools

java.lang.Object

fr.cnes.sirius.patrius.math.interval.AngleTools

public final class AngleTools
extends Object

This class provides static methods for angles :

- angles computation,

- comparison,

- arithmetic and trigonometric operations.

Since:

1.0

Version:

$Id: AngleTools.java 18021 2017-09-29 15:56:26Z bignon $

Author:

Julie Anton, Thomas Trapier

Use sample :

- In order to compute the angle between two vectors :

double angle = AngleTools.getAngleBewteen2Vector3D(vector1, vector2);

- To compute the angle 2PI modulo in the given interval : (can throw a MathIllegalArgumentException)

double res = AngleTools.angleInInterval(angle, angleInterval);

- To compare two angles in a given interval : (can throw a MathIllegalArgumentException)

boolean isEqual = AngleTools.equal(angle1, angle2, angleInterval);

- To compute the complementary angle in a given interval : (can throw a MathIllegalArgumentException)

double res = AngleTools.complementaryAngle(angle, angleInterval);

See DV-MATHS_60, 70, 80, 90, 100 .

Concurrency :

unconditionally thread-safe

Method Summary

Modifier and Type	Method and Description
static double	angleInInterval(double angle, AngleInterval interval) Computes the angle in the given interval modulo 2pi.
static double	complementaryAngle(double angle, AngleInterval interval) Computes the complementary (PI/2 - angle) of the input angle, and then tries to express it in the input interval.
static boolean	equal(double alpha, double beta, AngleInterval interval) Tests the equality of two angles after expressing them in the same interval.
static double	getAngleBewteen2Vector3D(Vector3D vector1, Vector3D vector2) Computes the angle between 2 vectors 3D.
static double	getAngleFromCosineAndSine(double cos, double sin) Computes an angle from the sine and the cosine
static double	getOrientedAngleBetween2Vector2D(Vector2D vector1, Vector2D vector2) Computes the oriented angle between 2 vectors 2D.
static double	getOrientedAngleBewteen2Vector3D(Vector3D vector1, Vector3D vector2, Vector3D vector3) Computes the oriented angle between 2 vectors 3D.
static boolean	greaterOrEqual(double alpha, double beta, AngleInterval interval) Tests if one angle is greater or equal to another after expressing them in the same interval.
static boolean	greaterStrict(double alpha, double beta, AngleInterval interval) Tests if one angle is strictly greater than another after expressing them in the same interval.
static boolean	lowerOrEqual(double alpha, double beta, AngleInterval interval) Tests if one angle is lower or equal to another after expressing them in the same interval.
static boolean	lowerStrict(double alpha, double beta, AngleInterval interval) Tests if one angle is strictly lower than another after expressing them in the same interval.
static double	oppositeAngle(double angle, AngleInterval interval) Computes the opposite of the input angle, and then tries to express it in the input interval.
static double	supplementaryAngle(double angle, AngleInterval interval) Computes the supplementary (PI - angle) of the input angle, and then tries to express it in the input interval.

Methods inherited from class java.lang.Object

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

Method Detail

getAngleBewteen2Vector3D

public static double getAngleBewteen2Vector3D(Vector3D vector1,
                                              Vector3D vector2)

Computes the angle between 2 vectors 3D. To do so, we use the method angle(Vector3D, Vector3D) of Vector3D .

Parameters:

vector1 - the first vector

vector2 - the second vector

Returns:

double angle = the positive value of the angle between the two vectors, the angle is defined between 0 and PI. See DV-MATHS_100

Since:

1.0

See Also:

Vector3D.angle(Vector3D, Vector3D)

Preconditions :

either the first vector or the second one should have non zero norm.

getOrientedAngleBetween2Vector2D

public static double getOrientedAngleBetween2Vector2D(Vector2D vector1,
                                                      Vector2D vector2)

Computes the oriented angle between 2 vectors 2D.

Parameters:

vector1 - the first vector

vector2 - the second vector

Returns:

double angle = the value of the oriented angle between the two vectors, the angle is defined between -2 PI and 2 PI. See DV-MATHS_100 .

Throws:

MathIllegalArgumentException - if at least one norm is zero

MathIllegalArgumentException - if at least one norm is infinity

Since:

1.0

Preconditions :

either the first vector or the second one should have finite coordinate values and non zero norm.

getOrientedAngleBewteen2Vector3D

public static double getOrientedAngleBewteen2Vector3D(Vector3D vector1,
                                                      Vector3D vector2,
                                                      Vector3D vector3)

Computes the oriented angle between 2 vectors 3D.

Parameters:

vector1 - the first vector

vector2 - the second vector

vector3 - the third vector which defines the orientation

Returns:

double angle = the value of the oriented angle between the two vectors, the angle is defined between -PI and PI. See DV-MATHS_100 .

Throws:

IllegalArgumentException - if the cross product is wrong

Since:

1.0

Preconditions :

either the first vector or the second one or the third one should have non zero norm. The third vector should be perpendicular to the plane formed by the formers.

getAngleFromCosineAndSine

public static double getAngleFromCosineAndSine(double cos,
                                               double sin)

Computes an angle from the sine and the cosine

Parameters:

cos - : the cosine of the angle we want to know the value

sin - : the sine of the angle we want to know the value

Returns:

double angle = the angle given by sine and cosine between -PI and PI See DV-MATHS_100 .

Since:

1.0

Preconditions :

the sine and the cosine should be of the same angle ie cos²+sin² is lower than 1.

angleInInterval

public static double angleInInterval(double angle,
                                     AngleInterval interval)

Computes the angle in the given interval modulo 2pi. There are particular cases : numerical quality issue solving in the following cases : - the interval is of the form [a, a + 2PI[ If angle is lower than lower bound and angle + 2Pi larger than higher bound : lower bound is returned - the interval is of the form ]a, a + 2PI] If angle is larger than larger bound and angle - 2Pi lower than lower bound : larger bound is returned These cases occur because of the non-identical repartition of doubles around the two interval boundaries.

Parameters:

angle - angle to be expressed inside the given interval

interval - interval of expression

Returns:

the angle expressed in the interval

Throws:

MathIllegalArgumentException - the angle is'nt in the interval modulo 2PI

Since:

1.0

Preconditions :

the interval can represent the given angle ([0, pi[ doesn't contain -pi/2 modulo 2pi)

equal

public static boolean equal(double alpha,
                            double beta,
                            AngleInterval interval)

Tests the equality of two angles after expressing them in the same interval.

Parameters:

alpha - one angle

beta - one angle

interval - the interval to express the angles

Returns:

boolean : true if equal

Throws:

MathIllegalArgumentException - if one angle is'nt in the interval, modulo 2PI

Since:

1.0

Preconditions :

both angles must be in the given interval modulo 2PI

lowerOrEqual

public static boolean lowerOrEqual(double alpha,
                                   double beta,
                                   AngleInterval interval)

Tests if one angle is lower or equal to another after expressing them in the same interval.

Parameters:

alpha - one angle

beta - one angle

interval - the interval to express the angles

Returns:

boolean : true if lower or equal

Throws:

MathIllegalArgumentException - if one angle is'nt in the interval, modulo 2PI

Since:

1.0

Preconditions :

both angles must be in the given interval modulo 2PI

lowerStrict

public static boolean lowerStrict(double alpha,
                                  double beta,
                                  AngleInterval interval)

Tests if one angle is strictly lower than another after expressing them in the same interval.

Parameters:

alpha - : one angle

beta - : one angle

interval - the interval to express the angles

Returns:

boolean : true if lower

Throws:

MathIllegalArgumentException - if one angle is'nt in the interval, modulo 2PI

Since:

1.0

Preconditions :

both angles must be in the given interval modulo 2PI

greaterOrEqual

public static boolean greaterOrEqual(double alpha,
                                     double beta,
                                     AngleInterval interval)

Tests if one angle is greater or equal to another after expressing them in the same interval.

Parameters:

alpha - : one angle

beta - : one angle

interval - the interval to express the angles

Returns:

boolean : true is greater or equal

Throws:

MathIllegalArgumentException - if one angle is'nt in the interval, modulo 2PI

Since:

1.0

Preconditions :

both angles must be in the given interval modulo 2PI

greaterStrict

public static boolean greaterStrict(double alpha,
                                    double beta,
                                    AngleInterval interval)

Tests if one angle is strictly greater than another after expressing them in the same interval.

Parameters:

alpha - : one angle

beta - : one angle

interval - the interval to express the angles

Returns:

boolean : true is greater

Throws:

MathIllegalArgumentException - if one angle is'nt in the interval, modulo 2PI

Since:

1.0

Preconditions :

both angles must be in the given interval modulo 2PI

supplementaryAngle

public static double supplementaryAngle(double angle,
                                        AngleInterval interval)

Computes the supplementary (PI - angle) of the input angle, and then tries to express it in the input interval.

Parameters:

angle - the angle to get the supplementary

interval - the interval to express the result

Returns:

double : supplementary angle

Throws:

MathIllegalArgumentException - if the resulting angle is'nt in the interval, modulo 2PI See DV-MATHS_80 .

Since:

1.0

complementaryAngle

public static double complementaryAngle(double angle,
                                        AngleInterval interval)

Computes the complementary (PI/2 - angle) of the input angle, and then tries to express it in the input interval.

Parameters:

angle - the angle to get the complementary

interval - the interval to express the result

Returns:

double : complementary angle

Throws:

MathIllegalArgumentException - if the resulting angle is'nt in the interval, modulo 2PI See DV-MATHS_80 .

Since:

1.0

oppositeAngle

public static double oppositeAngle(double angle,
                                   AngleInterval interval)

Computes the opposite of the input angle, and then tries to express it in the input interval.

Parameters:

angle - the angle to get the complementary

interval - the interval to express the result

Returns:

double : opposite angle

Throws:

MathIllegalArgumentException - if the resulting angle is'nt in the interval, modulo 2PI See DV-MATHS_80 .

Since:

1.0