# Module: quat

Quaternion
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### Members

#### (static, constant) equals

Returns whether or not the quaternions have approximately the same elements in the same position.
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#### (static, constant) exactEquals

Returns whether or not the quaternions have exactly the same elements in the same position (when compared with ===)
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#### (static, constant) length

Calculates the length of a quat
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#### (static, constant) rotationTo

Sets a quaternion to represent the shortest rotation from one vector to another. Both vectors are assumed to be unit length.
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#### (static, constant) setAxes

Sets the specified quaternion with values corresponding to the given axes. Each axis is a vec3 and is expected to be unit length and perpendicular to all other specified axes.
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#### (static, constant) sqlerp

Performs a spherical linear interpolation with two control points
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### Methods

#### (static) add(out, a, b) → {quat}

##### Parameters:
Name Type Description
`out` quat the receiving quaternion
`a` quat the first operand
`b` quat the second operand
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out
Type
quat

#### (static) calculateW(out, a) → {quat}

Calculates the W component of a quat from the X, Y, and Z components. Assumes that quaternion is 1 unit in length. Any existing W component will be ignored.
##### Parameters:
Name Type Description
`out` quat the receiving quaternion
`a` quat quat to calculate W component of
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out
Type
quat

#### (static) clone(a) → {quat}

Creates a new quat initialized with values from an existing quaternion
##### Parameters:
Name Type Description
`a` quat quaternion to clone
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a new quaternion
Type
quat

#### (static) conjugate(out, a) → {quat}

Calculates the conjugate of a quat If the quaternion is normalized, this function is faster than quat.inverse and produces the same result.
##### Parameters:
Name Type Description
`out` quat the receiving quaternion
`a` quat quat to calculate conjugate of
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out
Type
quat

#### (static) copy(out, a) → {quat}

Copy the values from one quat to another
##### Parameters:
Name Type Description
`out` quat the receiving quaternion
`a` quat the source quaternion
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out
Type
quat

#### (static) create() → {quat}

Creates a new identity quat
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a new quaternion
Type
quat

#### (static) dot(a, b) → {Number}

Calculates the dot product of two quat's
##### Parameters:
Name Type Description
`a` quat the first operand
`b` quat the second operand
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##### Returns:
dot product of a and b
Type
Number

#### (static) fromEuler(out, Angle, Angle, Angle) → {quat}

Creates a quaternion from the given euler angle x, y, z.
##### Parameters:
Name Type Description
`out` quat the receiving quaternion
`Angle` x to rotate around X axis in degrees.
`Angle` y to rotate around Y axis in degrees.
`Angle` z to rotate around Z axis in degrees.
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out
Type
quat

#### (static) fromMat3(out, m) → {quat}

Creates a quaternion from the given 3x3 rotation matrix. NOTE: The resultant quaternion is not normalized, so you should be sure to renormalize the quaternion yourself where necessary.
##### Parameters:
Name Type Description
`out` quat the receiving quaternion
`m` mat3 rotation matrix
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out
Type
quat

#### (static) fromValues(x, y, z, w) → {quat}

Creates a new quat initialized with the given values
##### Parameters:
Name Type Description
`x` Number X component
`y` Number Y component
`z` Number Z component
`w` Number W component
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a new quaternion
Type
quat

#### (static) getAxisAngle(out_axis, q) → {Number}

Gets the rotation axis and angle for a given quaternion. If a quaternion is created with setAxisAngle, this method will return the same values as providied in the original parameter list OR functionally equivalent values. Example: The quaternion formed by axis [0, 0, 1] and angle -90 is the same as the quaternion formed by [0, 0, 1] and 270. This method favors the latter.
##### Parameters:
Name Type Description
`out_axis` vec3 Vector receiving the axis of rotation
`q` quat Quaternion to be decomposed
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##### Returns:
Angle, in radians, of the rotation
Type
Number

#### (static) identity(out) → {quat}

Set a quat to the identity quaternion
##### Parameters:
Name Type Description
`out` quat the receiving quaternion
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out
Type
quat

#### (static) invert(out, a) → {quat}

Calculates the inverse of a quat
##### Parameters:
Name Type Description
`out` quat the receiving quaternion
`a` quat quat to calculate inverse of
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out
Type
quat

#### (static) len()

Alias for quat.length
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#### (static) lerp(out, a, b, t) → {quat}

Performs a linear interpolation between two quat's
##### Parameters:
Name Type Description
`out` quat the receiving quaternion
`a` quat the first operand
`b` quat the second operand
`t` Number interpolation amount, in the range [0-1], between the two inputs
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out
Type
quat

#### (static) mul()

Alias for quat.multiply
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#### (static) multiply(out, a, b) → {quat}

Multiplies two quat's
##### Parameters:
Name Type Description
`out` quat the receiving quaternion
`a` quat the first operand
`b` quat the second operand
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out
Type
quat

#### (static) normalize(out, a) → {quat}

Normalize a quat
##### Parameters:
Name Type Description
`out` quat the receiving quaternion
`a` quat quaternion to normalize
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out
Type
quat

#### (static) random(out) → {quat}

Generates a random quaternion
##### Parameters:
Name Type Description
`out` quat the receiving quaternion
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out
Type
quat

#### (static) rotateX(out, a, rad) → {quat}

Rotates a quaternion by the given angle about the X axis
##### Parameters:
Name Type Description
`out` quat quat receiving operation result
`a` quat quat to rotate
`rad` number angle (in radians) to rotate
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out
Type
quat

#### (static) rotateY(out, a, rad) → {quat}

Rotates a quaternion by the given angle about the Y axis
##### Parameters:
Name Type Description
`out` quat quat receiving operation result
`a` quat quat to rotate
`rad` number angle (in radians) to rotate
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out
Type
quat

#### (static) rotateZ(out, a, rad) → {quat}

Rotates a quaternion by the given angle about the Z axis
##### Parameters:
Name Type Description
`out` quat quat receiving operation result
`a` quat quat to rotate
`rad` number angle (in radians) to rotate
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out
Type
quat

#### (static) scale(out, a, b) → {quat}

Scales a quat by a scalar number
##### Parameters:
Name Type Description
`out` quat the receiving vector
`a` quat the vector to scale
`b` Number amount to scale the vector by
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out
Type
quat

#### (static) set(out, x, y, z, w) → {quat}

Set the components of a quat to the given values
##### Parameters:
Name Type Description
`out` quat the receiving quaternion
`x` Number X component
`y` Number Y component
`z` Number Z component
`w` Number W component
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out
Type
quat

#### (static) setAxisAngle(out, axis, rad) → {quat}

Sets a quat from the given angle and rotation axis, then returns it.
##### Parameters:
Name Type Description
`out` quat the receiving quaternion
`axis` vec3 the axis around which to rotate
`rad` Number the angle in radians
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out
Type
quat

#### (static) slerp(out, a, b, t) → {quat}

Performs a spherical linear interpolation between two quat
##### Parameters:
Name Type Description
`out` quat the receiving quaternion
`a` quat the first operand
`b` quat the second operand
`t` Number interpolation amount, in the range [0-1], between the two inputs
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out
Type
quat

#### (static) sqrLen()

Alias for quat.squaredLength
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#### (static) squaredLength(a) → {Number}

Calculates the squared length of a quat
##### Parameters:
Name Type Description
`a` quat vector to calculate squared length of
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##### Returns:
squared length of a
Type
Number

#### (static) str(a) → {String}

Returns a string representation of a quatenion
##### Parameters:
Name Type Description
`a` quat vector to represent as a string
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##### Returns:
string representation of the vector
Type
String