JOGL 2.3.2 · com.jogamp.opengl.math.Quaternion

Modifier and Type	Field and Description
public static final float	ALLOWED_DEVIANCE Quaternion Epsilon, used with equals method to determine if two Quaternions are close enough to be considered equal.
private float	w
private float	x
private float	y
private float	z

Access	Constructor and Description
public	Quaternion()
public	Quaternion(final Quaternion q)
public	Quaternion(final float x, final float y, final float z, final float w)

Method Summary

Modifier and Type	Method and Description
public final Quaternion	Returns: this quaternion for chaining. add(final Quaternion quaternion q) Add a quaternion
public Quaternion	Returns: this quaternion for chaining. conjugate() Conjugates this quaternion `[-x, -y, -z, w]`.
public float[]	Returns: the result column-vector for chaining. copyMatrixColumn(final int the 3x3 rotation matrix column to retrieve from this quaternion (normalized). Must be between 0 and 2. index, final float[] the vector object to store the result in. result, final int resultOffset)
private final float	determinant3f(final float[] m)
public final float	dot(final float x, final float y, final float z, final float w) Returns the dot product of this quaternion with the given x,y,z and w components.
public final float	dot(final Quaternion quat) Returns the dot product of this quaternion with the given quaternion
public boolean	Returns: true if this quaternion and the provided quaternion have roughly the same x, y, z and w values. equals(final Object the object to compare for equality o) Overrides java.lang.Object.equals. Indicates whether some other object is "equal to" this one.
public final float	getW()
public final float	getX()
public final float	getY()
public final float	getZ()
public final int	hashCode() Overrides java.lang.Object.hashCode. Returns a hash code value for this object.
public final Quaternion	Returns: this quaternion for chaining. invert() Invert the quaternion If rotational, will produce a the inverse rotation Implementation Details: `conjugates` if `magnitudeSquared()` is is `equals 1f` using `epsilon`
public final boolean	isIdentity() Returns `true` if this quaternion has identity.
public final boolean	Returns: true if representing a rotational matrix, false otherwise isRotationMatrix3f(final float[] 3x3 column matrix m) Check if the the 3x3 matrix (param) is in fact an affine rotational matrix
public final float	magnitude() Return the magnitude of this quaternion, i.e. sqrt(`magnitude()`) A magnitude of zero shall equal `identity`, as performed by `normalize()`.
public final float	Returns: the squared magnitude of this quaternion. magnitudeSquared() See `magnitude()` for special handling of `epsilon`, which is not applied here.
public final Quaternion	Returns: this quaternion for chaining. mult(final Quaternion a quaternion to multiply with q) Multiply this quaternion by the param quaternion
public final Quaternion	Returns: this quaternion for chaining. normalize() Normalize a quaternion required if to be used as a rotational quaternion.
public Quaternion	Returns: this quaternion for chaining. rotateByAngleNormalAxis(final float in radians angle, final float x-coord of rotation axis axisX, final float y-coord of rotation axis axisY, final float z-coord of rotation axis axisZ) Rotate this quaternion by the given angle and axis.
public Quaternion	Returns: this quaternion for chaining. rotateByAngleX(final float in radians angle) Rotate this quaternion around X axis with the given angle in radians
public Quaternion	Returns: this quaternion for chaining. rotateByAngleY(final float in radians angle) Rotate this quaternion around Y axis with the given angle in radians
public Quaternion	Returns: this quaternion for chaining. rotateByAngleZ(final float in radians angle) Rotate this quaternion around Z axis with the given angle in radians
public final Quaternion	Returns: this quaternion for chaining. rotateByEuler(final float[] euler angel array in radians angradXYZ) Rotates this quaternion from the given Euler rotation array `angradXYZ` in radians.
public final Quaternion	Returns: this quaternion for chaining. rotateByEuler(final float the Euler pitch angle in radians. (rotation about the X axis) bankX, final float the Euler yaw angle in radians. (rotation about the Y axis) headingY, final float the Euler roll angle in radians. (rotation about the Z axis) attitudeZ) Rotates this quaternion from the given Euler rotation angles in radians.
public final float[]	Returns: the given vecOut store for chaining rotateVector(final float[] result float[3] storage for rotated vector, maybe equal to vecIn for in-place rotation vecOut, final int offset in result storage vecOutOffset, final float[] float[3] vector to be rotated vecIn, final int offset in vecIn vecInOffset) Rotate the given vector by this quaternion
public final Quaternion	Returns: this quaternion for chaining. scale(final float a float constant n) Scale this quaternion by a constant
public final Quaternion	Returns: this quaternion for chaining. set(final Quaternion src) Set all values of this quaternion using the given src.
public final Quaternion	Returns: this quaternion for chaining. set(final float x, final float y, final float z, final float w) Set all values of this quaternion using the given components.
public final Quaternion	Returns: this quaternion for chaining. setFromAngleAxis(final float rotation angle (rads) angle, final float[] axis vector not normalized vector, final float[] float[3] temp storage to normalize vector tmpV3f) Initialize this quaternion with given non-normalized axis vector and rotation angle Implementation Details: `setIdentity()` if axis is `is zero` using `epsilon`
public final Quaternion	Returns: this quaternion for chaining. setFromAngleNormalAxis(final float rotation angle (rads) angle, final float[] axis vector normalized vector) Initialize this quaternion with given normalized axis vector and rotation angle Implementation Details: `setIdentity()` if axis is `is zero` using `epsilon`
public final Quaternion	Returns: this quaternion for chaining. setFromAxes(final float[] vector representing the orthogonal x-axis of the coordinate system. xAxis, final float[] vector representing the orthogonal y-axis of the coordinate system. yAxis, final float[] vector representing the orthogonal z-axis of the coordinate system. zAxis) Initializes this quaternion to represent a rotation formed by the given three orthogonal axes.
public final Quaternion	Returns: this quaternion for chaining. setFromEuler(final float[] euler angel array in radians angradXYZ) Initializes this quaternion from the given Euler rotation array `angradXYZ` in radians.
public final Quaternion	Returns: this quaternion for chaining. setFromEuler(final float the Euler pitch angle in radians. (rotation about the X axis) bankX, final float the Euler yaw angle in radians. (rotation about the Y axis) headingY, final float the Euler roll angle in radians. (rotation about the Z axis) attitudeZ) Initializes this quaternion from the given Euler rotation angles in radians.
public final Quaternion	Returns: this quaternion for chaining. setFromMatrix(final float[] 4x4 column matrix m, final int m_off) Initializes this quaternion from a 4x4 column rotation matrix See Graphics Gems Code, MatrixTrace.
public Quaternion	Returns: this quaternion for chaining. setFromMatrix(final float m00, final float m01, final float m02, final float m10, final float m11, final float m12, final float m20, final float m21, final float m22) Compute the quaternion from a 3x3 column rotation matrix See Graphics Gems Code, MatrixTrace.
public final Quaternion	Returns: this quaternion for chaining. setFromNormalVectors(final float[] normalized v1, final float[] normalized v2, final float[] float[3] temp storage for cross product tmpPivotVec) Initialize this quaternion from two normalized vectors q = (s,v) = (v1•v2 , v1 × v2), angle = angle(v1, v2) = v1•v2 axis = v1 x v2
public final Quaternion	Returns: this quaternion for chaining. setFromVectors(final float[] not normalized v1, final float[] not normalized v2, final float[] float[3] temp storage for cross product tmpPivotVec, final float[] float[3] temp storage to normalize vector tmpNormalVec) Initialize this quaternion from two vectors q = (s,v) = (v1•v2 , v1 × v2), angle = angle(v1, v2) = v1•v2 axis = normal(v1 x v2)
public final Quaternion	Returns: this quaternion for chaining. setIdentity() Set this quaternion to identity (x=0,y=0,z=0,w=1)
public Quaternion	Returns: this quaternion for chaining. setLookAt(final float[] where to look at directionIn, final float[] a vector indicating the local up direction. upIn, final float[] vector storing the orthogonal x-axis of the coordinate system. xAxisOut, final float[] vector storing the orthogonal y-axis of the coordinate system. yAxisOut, final float[] vector storing the orthogonal z-axis of the coordinate system. zAxisOut) Set this quaternion to equal the rotation required to point the z-axis at direction and the y-axis to up.
public final Quaternion	Returns: this quaternion for chaining. setSlerp(final Quaternion start quaternion a, final Quaternion end quaternion b, final float float between 0 and 1 representing interpolation. changeAmnt) Set this quaternion to a spherical linear interpolation between the given start and end quaternions by the given change amount.
public final void	setW(final float w)
public final void	setX(final float x)
public final void	setY(final float y)
public final void	setZ(final float z)
public final Quaternion	Returns: this quaternion for chaining. subtract(final Quaternion quaternion q) Subtract a quaternion
public final float	Returns: the rotation angle in radians toAngleAxis(final float[] float[3] storage for computed axis axis) Transform the rotational quaternion to axis based rotation angles
public void	toAxes(final float[] vector representing the orthogonal x-axis of the coordinate system. xAxis, final float[] vector representing the orthogonal y-axis of the coordinate system. yAxis, final float[] vector representing the orthogonal z-axis of the coordinate system. zAxis, final float[] temporary float[4] matrix, used to transform this quaternion to a matrix. tmpMat4) Extracts this quaternion's orthogonal rotation axes.
public float[]	Returns: the double[] array, filled with heading, attitude and bank in that order.. toEuler(final float[] the float[] array storing the computed angles. result) Transform this quaternion to Euler rotation angles in radians (pitchX, yawY and rollZ).
public final float[]	Returns: the given matrix store toMatrix(final float[] float[16] store for the resulting normalized column matrix 4x4 matrix, final int mat_offset) Transform this quaternion to a normalized 4x4 column matrix representing the rotation.
public String	toString() Overrides java.lang.Object.toString. Returns a string representation of the object.

Inherited from java.lang.Object:: clone finalize getClass notify notifyAll wait wait wait

ALLOWED_DEVIANCE	back to summary
public static final float ALLOWED_DEVIANCE Quaternion Epsilon, used with equals method to determine if two Quaternions are close enough to be considered equal. Using , which is ~10 times `FloatUtil#EPSILON`.

w	back to summary
private float w

x	back to summary
private float x

y	back to summary
private float y

z	back to summary
private float z

Quaternion	back to summary
public Quaternion()

Quaternion	back to summary
public Quaternion(final Quaternion q)

Quaternion	back to summary
public Quaternion(final float x, final float y, final float z, final float w)

Method Detail

add	back to summary
public final Quaternion add(final Quaternion q) Add a quaternion Parameters q:Quaternion quaternion Returns:Quaternion this quaternion for chaining. See Also euclideanspace.com-QuaternionAdd

add

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public final Quaternion add(final Quaternion q)

Add a quaternion

Parameters

q:Quaternion: quaternion

Returns:Quaternion

this quaternion for chaining.

See Also

euclideanspace.com-QuaternionAdd

conjugate back to summary

conjugate	back to summary
public Quaternion conjugate() Conjugates this quaternion `[-x, -y, -z, w]`. Returns:Quaternion this quaternion for chaining. See Also Matrix-FAQ Q49

public Quaternion conjugate()

Conjugates this quaternion [-x, -y, -z, w].

Returns:Quaternion: this quaternion for chaining.
See Also: Matrix-FAQ Q49

copyMatrixColumn	back to summary
public float[] copyMatrixColumn(final int index, final float[] result, final int resultOffset) Parameters index:int the 3x3 rotation matrix column to retrieve from this quaternion (normalized). Must be between 0 and 2. result:float[] the vector object to store the result in. Returns:float[] the result column-vector for chaining.

determinant3f	back to summary
private final float determinant3f(final float[] m)

dot	back to summary
public final float dot(final float x, final float y, final float z, final float w) Returns the dot product of this quaternion with the given x,y,z and w components.

dot	back to summary
public final float dot(final Quaternion quat) Returns the dot product of this quaternion with the given quaternion

equals back to summary

equals	back to summary
public boolean equals(final Object o) Overrides java.lang.Object.equals. Doc from java.lang.Object.equals. Indicates whether some other object is "equal to" this one. The `equals` method implements an equivalence relation on non-null object references: It is reflexive: for any non-null reference value `x`, `x.equals(x)` should return `true`. It is symmetric: for any non-null reference values `x` and `y`, `x.equals(y)` should return `true` if and only if `y.equals(x)` returns `true`. It is transitive: for any non-null reference values `x`, `y`, and `z`, if `x.equals(y)` returns `true` and `y.equals(z)` returns `true`, then `x.equals(z)` should return `true`. It is consistent: for any non-null reference values `x` and `y`, multiple invocations of `x.equals(y)` consistently return `true` or consistently return `false`, provided no information used in `equals` comparisons on the objects is modified. For any non-null reference value `x`, `x.equals(null)` should return `false`. An equivalence relation partitions the elements it operates on into equivalence classes; all the members of an equivalence class are equal to each other. Members of an equivalence class are substitutable for each other, at least for some purposes. Parameters o:Object the object to compare for equality Returns:boolean true if this quaternion and the provided quaternion have roughly the same x, y, z and w values. Annotations @Override

public boolean equals(final Object o)

Overrides java.lang.Object.equals.

Doc from java.lang.Object.equals.

Indicates whether some other object is "equal to" this one.

The equals method implements an equivalence relation on non-null object references:

It is reflexive: for any non-null reference value x, x.equals(x) should return true.
It is symmetric: for any non-null reference values x and y, x.equals(y) should return true if and only if y.equals(x) returns true.
It is transitive: for any non-null reference values x, y, and z, if x.equals(y) returns true and y.equals(z) returns true, then x.equals(z) should return true.
It is consistent: for any non-null reference values x and y, multiple invocations of x.equals(y) consistently return true or consistently return false, provided no information used in equals comparisons on the objects is modified.
For any non-null reference value x, x.equals(null) should return false.

An equivalence relation partitions the elements it operates on into equivalence classes; all the members of an equivalence class are equal to each other. Members of an equivalence class are substitutable for each other, at least for some purposes.

Parameters

o:Object: the object to compare for equality

Returns:boolean

true if this quaternion and the provided quaternion have roughly the same x, y, z and w values.

Annotations

@Override

getW	back to summary
public final float getW()

getX	back to summary
public final float getX()

getY	back to summary
public final float getY()

getZ	back to summary
public final float getZ()

hashCode back to summary

hashCode	back to summary
public final int hashCode() Overrides java.lang.Object.hashCode. Doc from java.lang.Object.hashCode. Returns a hash code value for this object. This method is supported for the benefit of hash tables such as those provided by `java.util.HashMap`. The general contract of `hashCode` is: Whenever it is invoked on the same object more than once during an execution of a Java application, the `hashCode` method must consistently return the same integer, provided no information used in `equals` comparisons on the object is modified. This integer need not remain consistent from one execution of an application to another execution of the same application. If two objects are equal according to the `equals` method, then calling the `hashCode` method on each of the two objects must produce the same integer result. It is not required that if two objects are unequal according to the `equals` method, then calling the `hashCode` method on each of the two objects must produce distinct integer results. However, the programmer should be aware that producing distinct integer results for unequal objects may improve the performance of hash tables. Returns:int a hash code value for this object Annotations @Override

public final int hashCode()

Overrides java.lang.Object.hashCode.

Doc from java.lang.Object.hashCode.

Returns a hash code value for this object. This method is supported for the benefit of hash tables such as those provided by java.util.HashMap.

The general contract of hashCode is:

Whenever it is invoked on the same object more than once during an execution of a Java application, the hashCode method must consistently return the same integer, provided no information used in equals comparisons on the object is modified. This integer need not remain consistent from one execution of an application to another execution of the same application.
If two objects are equal according to the equals method, then calling the hashCode method on each of the two objects must produce the same integer result.
It is not required that if two objects are unequal according to the equals method, then calling the hashCode method on each of the two objects must produce distinct integer results. However, the programmer should be aware that producing distinct integer results for unequal objects may improve the performance of hash tables.

Returns:int

a hash code value for this object

Annotations

@Override

invert back to summary

invert	back to summary
public final Quaternion invert() Invert the quaternion If rotational, will produce a the inverse rotation Implementation Details: `conjugates` if `magnitudeSquared()` is is `equals 1f` using `epsilon` Returns:Quaternion this quaternion for chaining. See Also Matrix-FAQ Q50

public final Quaternion invert()

Invert the quaternion If rotational, will produce a the inverse rotation

Implementation Details:

conjugates if magnitudeSquared() is is equals 1f using epsilon

Returns:Quaternion: this quaternion for chaining.
See Also: Matrix-FAQ Q50

isIdentity back to summary

isIdentity	back to summary
public final boolean isIdentity() Returns `true` if this quaternion has identity. Implementation uses `epsilon` to compare `W` `against 1f` and `X`, `Y` and `Z` `against zero`.

public final boolean isIdentity()

Returns true if this quaternion has identity.

Implementation uses epsilon to compare W against 1f and X, Y and Z against zero.

isRotationMatrix3f	back to summary
public final boolean isRotationMatrix3f(final float[] m) Check if the the 3x3 matrix (param) is in fact an affine rotational matrix Parameters m:float[] 3x3 column matrix Returns:boolean true if representing a rotational matrix, false otherwise

isRotationMatrix3f

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public final boolean isRotationMatrix3f(final float[] m)

Check if the the 3x3 matrix (param) is in fact an affine rotational matrix

Parameters

m:float[]: 3x3 column matrix

Returns:boolean

true if representing a rotational matrix, false otherwise

magnitude back to summary

magnitude	back to summary
public final float magnitude() Return the magnitude of this quaternion, i.e. sqrt(`magnitude()`) A magnitude of zero shall equal `identity`, as performed by `normalize()`. Implementation Details: returns 0f if `magnitudeSquared()` is `is zero` using `epsilon` returns 1f if `magnitudeSquared()` is `equals 1f` using `epsilon`

public final float magnitude()

Return the magnitude of this quaternion, i.e. sqrt(magnitude())

A magnitude of zero shall equal identity, as performed by normalize().

Implementation Details:

returns 0f if magnitudeSquared() is is zero using epsilon
returns 1f if magnitudeSquared() is equals 1f using epsilon

magnitudeSquared back to summary

magnitudeSquared	back to summary
public final float magnitudeSquared() See `magnitude()` for special handling of `epsilon`, which is not applied here. Returns:float the squared magnitude of this quaternion.

public final float magnitudeSquared()

See magnitude() for special handling of epsilon, which is not applied here.

Returns:float: the squared magnitude of this quaternion.

mult	back to summary
public final Quaternion mult(final Quaternion q) Multiply this quaternion by the param quaternion Parameters q:Quaternion a quaternion to multiply with Returns:Quaternion this quaternion for chaining. See Also Matrix-FAQ Q53, euclideanspace.com-QuaternionMul

mult

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public final Quaternion mult(final Quaternion q)

Multiply this quaternion by the param quaternion

Parameters

q:Quaternion: a quaternion to multiply with

Returns:Quaternion

this quaternion for chaining.

normalize back to summary

normalize	back to summary
public final Quaternion normalize() Normalize a quaternion required if to be used as a rotational quaternion. Implementation Details: `setIdentity()` if `magnitude()` is `is zero` using `epsilon` Returns:Quaternion this quaternion for chaining.

public final Quaternion normalize()

Normalize a quaternion required if to be used as a rotational quaternion.

Implementation Details:

setIdentity() if magnitude() is is zero using epsilon

Returns:Quaternion: this quaternion for chaining.

rotateByAngleNormalAxis	back to summary
public Quaternion rotateByAngleNormalAxis(final float angle, final float axisX, final float axisY, final float axisZ) Rotate this quaternion by the given angle and axis. The axis must be a normalized vector. A rotational quaternion is made from the given angle and axis. Parameters angle:float in radians axisX:float x-coord of rotation axis axisY:float y-coord of rotation axis axisZ:float z-coord of rotation axis Returns:Quaternion this quaternion for chaining.

rotateByAngleNormalAxis

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public Quaternion rotateByAngleNormalAxis(final float angle, final float axisX, final float axisY, final float axisZ)

Rotate this quaternion by the given angle and axis.

The axis must be a normalized vector.

A rotational quaternion is made from the given angle and axis.

Parameters

angle:float: in radians
axisX:float: x-coord of rotation axis
axisY:float: y-coord of rotation axis
axisZ:float: z-coord of rotation axis

Returns:Quaternion

this quaternion for chaining.

rotateByAngleX	back to summary
public Quaternion rotateByAngleX(final float angle) Rotate this quaternion around X axis with the given angle in radians Parameters angle:float in radians Returns:Quaternion this quaternion for chaining.

rotateByAngleX

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public Quaternion rotateByAngleX(final float angle)

Rotate this quaternion around X axis with the given angle in radians

Parameters

angle:float: in radians

Returns:Quaternion

this quaternion for chaining.

rotateByAngleY	back to summary
public Quaternion rotateByAngleY(final float angle) Rotate this quaternion around Y axis with the given angle in radians Parameters angle:float in radians Returns:Quaternion this quaternion for chaining.

rotateByAngleY

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public Quaternion rotateByAngleY(final float angle)

Rotate this quaternion around Y axis with the given angle in radians

Parameters

angle:float: in radians

Returns:Quaternion

this quaternion for chaining.

rotateByAngleZ	back to summary
public Quaternion rotateByAngleZ(final float angle) Rotate this quaternion around Z axis with the given angle in radians Parameters angle:float in radians Returns:Quaternion this quaternion for chaining.

rotateByAngleZ

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public Quaternion rotateByAngleZ(final float angle)

Rotate this quaternion around Z axis with the given angle in radians

Parameters

angle:float: in radians

Returns:Quaternion

this quaternion for chaining.

rotateByEuler back to summary

rotateByEuler	back to summary
public final Quaternion rotateByEuler(final float[] angradXYZ) Rotates this quaternion from the given Euler rotation array `angradXYZ` in radians. The `angradXYZ` array is laid out in natural order: x - bank y - heading z - attitude For details see `rotateByEuler(float, float, float)`. Parameters angradXYZ:float[] euler angel array in radians Returns:Quaternion this quaternion for chaining. See Also `rotateByEuler(float, float, float)`

public final Quaternion rotateByEuler(final float[] angradXYZ)

Rotates this quaternion from the given Euler rotation array angradXYZ in radians.

The angradXYZ array is laid out in natural order:

x - bank
y - heading
z - attitude

For details see rotateByEuler(float, float, float).

Parameters

angradXYZ:float[]: euler angel array in radians

Returns:Quaternion

this quaternion for chaining.

See Also

rotateByEuler(float, float, float)

rotateByEuler back to summary

rotateByEuler	back to summary
public final Quaternion rotateByEuler(final float bankX, final float headingY, final float attitudeZ) Rotates this quaternion from the given Euler rotation angles in radians. The rotations are applied in the given order and using chained rotation per axis: y - heading - `rotateByAngleY(float)` z - attitude - `rotateByAngleZ(float)` x - bank - `rotateByAngleX(float)` Implementation Details: NOP if all angles are `is zero` using `epsilon` result is `normalize()`ed Parameters bankX:float the Euler pitch angle in radians. (rotation about the X axis) headingY:float the Euler yaw angle in radians. (rotation about the Y axis) attitudeZ:float the Euler roll angle in radians. (rotation about the Z axis) Returns:Quaternion this quaternion for chaining. See Also `rotateByAngleY(float)`, `rotateByAngleZ(float)`, `rotateByAngleX(float)`, `setFromEuler(float, float, float)`

public final Quaternion rotateByEuler(final float bankX, final float headingY, final float attitudeZ)

Rotates this quaternion from the given Euler rotation angles in radians.

The rotations are applied in the given order and using chained rotation per axis:

Implementation Details:

NOP if all angles are is zero using epsilon
result is normalize()ed

Parameters

bankX:float: the Euler pitch angle in radians. (rotation about the X axis)
headingY:float: the Euler yaw angle in radians. (rotation about the Y axis)
attitudeZ:float: the Euler roll angle in radians. (rotation about the Z axis)

Returns:Quaternion

this quaternion for chaining.

rotateVector	back to summary
public final float[] rotateVector(final float[] vecOut, final int vecOutOffset, final float[] vecIn, final int vecInOffset) Rotate the given vector by this quaternion Parameters vecOut:float[] result float[3] storage for rotated vector, maybe equal to vecIn for in-place rotation vecOutOffset:int offset in result storage vecIn:float[] float[3] vector to be rotated vecInOffset:int offset in vecIn Returns:float[] the given vecOut store for chaining See Also Matrix-FAQ Q63

rotateVector

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public final float[] rotateVector(final float[] vecOut, final int vecOutOffset, final float[] vecIn, final int vecInOffset)

Rotate the given vector by this quaternion

Parameters

vecOut:float[]: result float[3] storage for rotated vector, maybe equal to vecIn for in-place rotation
vecOutOffset:int: offset in result storage
vecIn:float[]: float[3] vector to be rotated
vecInOffset:int: offset in vecIn

Returns:float[]

the given vecOut store for chaining

See Also

Matrix-FAQ Q63

scale	back to summary
public final Quaternion scale(final float n) Scale this quaternion by a constant Parameters n:float a float constant Returns:Quaternion this quaternion for chaining. See Also euclideanspace.com-QuaternionScale

scale

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public final Quaternion scale(final float n)

Scale this quaternion by a constant

Parameters

n:float: a float constant

Returns:Quaternion

this quaternion for chaining.

See Also

euclideanspace.com-QuaternionScale

set	back to summary
public final Quaternion set(final Quaternion src) Set all values of this quaternion using the given src. Returns:Quaternion this quaternion for chaining.

set

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public final Quaternion set(final Quaternion src)

Set all values of this quaternion using the given src.

Returns:Quaternion: this quaternion for chaining.

set	back to summary
public final Quaternion set(final float x, final float y, final float z, final float w) Set all values of this quaternion using the given components. Returns:Quaternion this quaternion for chaining.

set

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public final Quaternion set(final float x, final float y, final float z, final float w)

Set all values of this quaternion using the given components.

Returns:Quaternion: this quaternion for chaining.

setFromAngleAxis back to summary

setFromAngleAxis	back to summary
public final Quaternion setFromAngleAxis(final float angle, final float[] vector, final float[] tmpV3f) Initialize this quaternion with given non-normalized axis vector and rotation angle Implementation Details: `setIdentity()` if axis is `is zero` using `epsilon` Parameters angle:float rotation angle (rads) vector:float[] axis vector not normalized tmpV3f:float[] float[3] temp storage to normalize vector Returns:Quaternion this quaternion for chaining. See Also Matrix-FAQ Q56, `toAngleAxis(float[])`

public final Quaternion setFromAngleAxis(final float angle, final float[] vector, final float[] tmpV3f)

Initialize this quaternion with given non-normalized axis vector and rotation angle

Implementation Details:

setIdentity() if axis is is zero using epsilon

Parameters

angle:float: rotation angle (rads)
vector:float[]: axis vector not normalized
tmpV3f:float[]: float[3] temp storage to normalize vector

Returns:Quaternion

this quaternion for chaining.

See Also

Matrix-FAQ Q56, toAngleAxis(float[])

setFromAngleNormalAxis back to summary

setFromAngleNormalAxis	back to summary
public final Quaternion setFromAngleNormalAxis(final float angle, final float[] vector) Initialize this quaternion with given normalized axis vector and rotation angle Implementation Details: `setIdentity()` if axis is `is zero` using `epsilon` Parameters angle:float rotation angle (rads) vector:float[] axis vector normalized Returns:Quaternion this quaternion for chaining. See Also Matrix-FAQ Q56, `toAngleAxis(float[])`

public final Quaternion setFromAngleNormalAxis(final float angle, final float[] vector)

Initialize this quaternion with given normalized axis vector and rotation angle

Implementation Details:

setIdentity() if axis is is zero using epsilon

Parameters

angle:float: rotation angle (rads)
vector:float[]: axis vector normalized

Returns:Quaternion

this quaternion for chaining.

See Also

Matrix-FAQ Q56, toAngleAxis(float[])

setFromAxes	back to summary
public final Quaternion setFromAxes(final float[] xAxis, final float[] yAxis, final float[] zAxis) Initializes this quaternion to represent a rotation formed by the given three orthogonal axes. No validation whether the axes are orthogonal is performed. Parameters xAxis:float[] vector representing the orthogonal x-axis of the coordinate system. yAxis:float[] vector representing the orthogonal y-axis of the coordinate system. zAxis:float[] vector representing the orthogonal z-axis of the coordinate system. Returns:Quaternion this quaternion for chaining.

setFromAxes

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public final Quaternion setFromAxes(final float[] xAxis, final float[] yAxis, final float[] zAxis)

Initializes this quaternion to represent a rotation formed by the given three orthogonal axes.

No validation whether the axes are orthogonal is performed.

Parameters

xAxis:float[]: vector representing the orthogonal x-axis of the coordinate system.
yAxis:float[]: vector representing the orthogonal y-axis of the coordinate system.
zAxis:float[]: vector representing the orthogonal z-axis of the coordinate system.

Returns:Quaternion

this quaternion for chaining.

setFromEuler back to summary

setFromEuler	back to summary
public final Quaternion setFromEuler(final float[] angradXYZ) Initializes this quaternion from the given Euler rotation array `angradXYZ` in radians. The `angradXYZ` array is laid out in natural order: x - bank y - heading z - attitude For details see `setFromEuler(float, float, float)`. Parameters angradXYZ:float[] euler angel array in radians Returns:Quaternion this quaternion for chaining. See Also `setFromEuler(float, float, float)`

public final Quaternion setFromEuler(final float[] angradXYZ)

Initializes this quaternion from the given Euler rotation array angradXYZ in radians.

The angradXYZ array is laid out in natural order:

x - bank
y - heading
z - attitude

For details see setFromEuler(float, float, float).

Parameters

angradXYZ:float[]: euler angel array in radians

Returns:Quaternion

this quaternion for chaining.

See Also

setFromEuler(float, float, float)

setFromEuler back to summary

setFromEuler	back to summary
public final Quaternion setFromEuler(final float bankX, final float headingY, final float attitudeZ) Initializes this quaternion from the given Euler rotation angles in radians. The rotations are applied in the given order: y - heading z - attitude x - bank Implementation Details: `setIdentity()` if all angles are `is zero` using `epsilon` result is `normalize()`ed Parameters bankX:float the Euler pitch angle in radians. (rotation about the X axis) headingY:float the Euler yaw angle in radians. (rotation about the Y axis) attitudeZ:float the Euler roll angle in radians. (rotation about the Z axis) Returns:Quaternion this quaternion for chaining. See Also Matrix-FAQ Q60, Gems, euclideanspace.com-eulerToQuaternion, `toEuler(float[])`

public final Quaternion setFromEuler(final float bankX, final float headingY, final float attitudeZ)

Initializes this quaternion from the given Euler rotation angles in radians.

The rotations are applied in the given order:

y - heading
z - attitude
x - bank

Implementation Details:

setIdentity() if all angles are is zero using epsilon
result is normalize()ed

Parameters

bankX:float: the Euler pitch angle in radians. (rotation about the X axis)
headingY:float: the Euler yaw angle in radians. (rotation about the Y axis)
attitudeZ:float: the Euler roll angle in radians. (rotation about the Z axis)

Returns:Quaternion

this quaternion for chaining.

setFromMatrix back to summary

setFromMatrix	back to summary
public final Quaternion setFromMatrix(final float[] m, final int m_off) Initializes this quaternion from a 4x4 column rotation matrix See Graphics Gems Code, MatrixTrace. Buggy Matrix-FAQ Q55 Parameters m:float[] 4x4 column matrix Returns:Quaternion this quaternion for chaining. See Also `toMatrix(float[], int)`

public final Quaternion setFromMatrix(final float[] m, final int m_off)

Initializes this quaternion from a 4x4 column rotation matrix

See Graphics Gems Code,
MatrixTrace.

Buggy Matrix-FAQ Q55

Parameters

m:float[]: 4x4 column matrix

Returns:Quaternion

this quaternion for chaining.

See Also

toMatrix(float[], int)

setFromMatrix back to summary

setFromMatrix	back to summary
public Quaternion setFromMatrix(final float m00, final float m01, final float m02, final float m10, final float m11, final float m12, final float m20, final float m21, final float m22) Compute the quaternion from a 3x3 column rotation matrix See Graphics Gems Code, MatrixTrace. Buggy Matrix-FAQ Q55 Returns:Quaternion this quaternion for chaining. See Also `toMatrix(float[], int)`

public Quaternion setFromMatrix(final float m00, final float m01, final float m02, final float m10, final float m11, final float m12, final float m20, final float m21, final float m22)

Compute the quaternion from a 3x3 column rotation matrix

See Graphics Gems Code,
MatrixTrace.

Buggy Matrix-FAQ Q55

Returns:Quaternion: this quaternion for chaining.
See Also: toMatrix(float[], int)

setFromNormalVectors back to summary

setFromNormalVectors	back to summary
public final Quaternion setFromNormalVectors(final float[] v1, final float[] v2, final float[] tmpPivotVec) Initialize this quaternion from two normalized vectors q = (s,v) = (v1•v2 , v1 × v2), angle = angle(v1, v2) = v1•v2 axis = v1 x v2 Implementation Details: `setIdentity()` if square vector-length is `is zero` using `epsilon` Parameters v1:float[] normalized v2:float[] normalized tmpPivotVec:float[] float[3] temp storage for cross product Returns:Quaternion this quaternion for chaining.

public final Quaternion setFromNormalVectors(final float[] v1, final float[] v2, final float[] tmpPivotVec)

Initialize this quaternion from two normalized vectors

  q = (s,v) = (v1•v2 , v1 × v2),
    angle = angle(v1, v2) = v1•v2
     axis = v1 x v2

Implementation Details:

setIdentity() if square vector-length is is zero using epsilon

Parameters

v1:float[]: normalized
v2:float[]: normalized
tmpPivotVec:float[]: float[3] temp storage for cross product

Returns:Quaternion

this quaternion for chaining.

setFromVectors back to summary

setFromVectors	back to summary
public final Quaternion setFromVectors(final float[] v1, final float[] v2, final float[] tmpPivotVec, final float[] tmpNormalVec) Initialize this quaternion from two vectors q = (s,v) = (v1•v2 , v1 × v2), angle = angle(v1, v2) = v1•v2 axis = normal(v1 x v2) Implementation Details: `setIdentity()` if square vector-length is `is zero` using `epsilon` Parameters v1:float[] not normalized v2:float[] not normalized tmpPivotVec:float[] float[3] temp storage for cross product tmpNormalVec:float[] float[3] temp storage to normalize vector Returns:Quaternion this quaternion for chaining.

public final Quaternion setFromVectors(final float[] v1, final float[] v2, final float[] tmpPivotVec, final float[] tmpNormalVec)

Initialize this quaternion from two vectors

  q = (s,v) = (v1•v2 , v1 × v2),
    angle = angle(v1, v2) = v1•v2
     axis = normal(v1 x v2)

Implementation Details:

setIdentity() if square vector-length is is zero using epsilon

Parameters

v1:float[]: not normalized
v2:float[]: not normalized
tmpPivotVec:float[]: float[3] temp storage for cross product
tmpNormalVec:float[]: float[3] temp storage to normalize vector

Returns:Quaternion

this quaternion for chaining.

setIdentity	back to summary
public final Quaternion setIdentity() Set this quaternion to identity (x=0,y=0,z=0,w=1) Returns:Quaternion this quaternion for chaining.

setIdentity

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public final Quaternion setIdentity()

Set this quaternion to identity (x=0,y=0,z=0,w=1)

Returns:Quaternion: this quaternion for chaining.

setLookAt back to summary

public Quaternion setLookAt(final float[] directionIn, final float[] upIn, final float[] xAxisOut, final float[] yAxisOut, final float[] zAxisOut)

Set this quaternion to equal the rotation required to point the z-axis at direction and the y-axis to up.

Implementation generates a 3x3 matrix and is equal with ProjectFloat's lookAt(..).

Implementation Details:

result is normalize()ed

Parameters

directionIn:float[]: where to look at
upIn:float[]: a vector indicating the local up direction.
xAxisOut:float[]: vector storing the orthogonal x-axis of the coordinate system.
yAxisOut:float[]: vector storing the orthogonal y-axis of the coordinate system.
zAxisOut:float[]: vector storing the orthogonal z-axis of the coordinate system.

Returns:Quaternion

this quaternion for chaining.

See Also

euclideanspace.com-LookUp

setSlerp

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public final Quaternion setSlerp(final Quaternion a, final Quaternion b, final float changeAmnt)

Set this quaternion to a spherical linear interpolation between the given start and end quaternions by the given change amount.

Note

Method does not normalize this quaternion!

Parameters

a:Quaternion: start quaternion
b:Quaternion: end quaternion
changeAmnt:float: float between 0 and 1 representing interpolation.

Returns:Quaternion

this quaternion for chaining.

See Also

euclideanspace.com-QuaternionSlerp

setW	back to summary
public final void setW(final float w)

setX	back to summary
public final void setX(final float x)

setY	back to summary
public final void setY(final float y)

setZ	back to summary
public final void setZ(final float z)

subtract

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public final Quaternion subtract(final Quaternion q)

Subtract a quaternion

Parameters

q:Quaternion: quaternion

Returns:Quaternion

this quaternion for chaining.

See Also

euclideanspace.com-QuaternionAdd

toAngleAxis back to summary

public final float toAngleAxis(final float[] axis)

Transform the rotational quaternion to axis based rotation angles

Parameters

axis:float[]: float[3] storage for computed axis

Returns:float

the rotation angle in radians

toAxes

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public void toAxes(final float[] xAxis, final float[] yAxis, final float[] zAxis, final float[] tmpMat4)

Extracts this quaternion's orthogonal rotation axes.

Parameters

xAxis:float[]: vector representing the orthogonal x-axis of the coordinate system.
yAxis:float[]: vector representing the orthogonal y-axis of the coordinate system.
zAxis:float[]: vector representing the orthogonal z-axis of the coordinate system.
tmpMat4:float[]: temporary float[4] matrix, used to transform this quaternion to a matrix.

toEuler back to summary

public float[] toEuler(final float[] result)

Transform this quaternion to Euler rotation angles in radians (pitchX, yawY and rollZ).

Parameters

result:float[]: the float[] array storing the computed angles.

Returns:float[]

the double[] array, filled with heading, attitude and bank in that order..

toMatrix back to summary

public final float[] toMatrix(final float[] matrix, final int mat_offset)

Transform this quaternion to a normalized 4x4 column matrix representing the rotation.

Implementation Details:

makes identity matrix if magnitudeSquared() is is zero using epsilon

Parameters

matrix:float[]: float[16] store for the resulting normalized column matrix 4x4

Returns:float[]

the given matrix store

toString

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public String toString()

Overrides java.lang.Object.toString.

Doc from java.lang.Object.toString.

Returns a string representation of the object.

Returns:String: a string representation of the object

public Class Quaternion

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