# Quaternion Class

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Holds a Quaternion object which can be used to manipulate rotations in various ways. Quaternions can be constructed using a few different ways to describe the initial rotation:

```# From Euler Angles
q = tdu.Quaternion(tdu.Vector(30, 5, -5))
# From an angle and a rotation axis
q = tdu.Quaternion(30, tdu.Vector(0, 1, 0))
# From two vectors, rotate from the first vector to the second vector
q = tdu.Quaternion(tdu.Vector(1, 0, 0), tdu.Vector(0, 1, 0))
# From a set of 4 quaternion values
q = tdu.Quaternion(x, y, z, w)
```

See also Transform CHOP which accepts, manipulates and outputs quaternions as sets of CHOP channels.

## Members

`x``float` :

Get or set the x component of the quaternion.

`y``float` :

Get or set the y component of the quaternion.

`z``float` :

Get or set the z component of the quaternion.

`w``float` :

Get or set the w component of the quaternion.

## Methods

`lerp(q2, factor)``quaternion`:

Returns the linear interpolation of the quaternion with another quaternion and an interpolation factor.

The quaternion argument can be anything from which a quaternion can be derived ie. (x,y,z,w), Matrix, etc. The interpolation factor must be between 0 and 1.

```q3 = q.lerp(q2, factor)
```

`length()``float`:

Returns the length of the quaternion.

```l = q.length()
```

`cross(q2)``vector`:

Returns the cross product of the quaternion and argument.

The quaternion argument can be anything from which a quaternion can be derived ie. (x,y,z,w), Matrix, etc.

```l = q.cross(q2)
```

`rotate(vec)``vector`:

Rotates a vector using the current quaternion. Returns a new vector.

```v2 = q.rotate(v1)
```

`slerp(q2, factor)``quaternion`:

Returns the spherical interpolation of the quaternion with another quaternion and an interpolation factor.

The quaternion argument can be anything from which a quaternion can be derived ie. (x,y,z,w), Matrix, etc.

```q3 = q.slerp(q2, factor)
```

`eulerAngles(order='xyz')``tuple`:

Returns euler angles in degrees as a tuple (i.e. pitch as x, yaw as y, roll as z) from current quaternion and a rotation order. The 'order' argument can be set to any valid rotation order which by default is set to 'xyz'.

```r = q.eulerAngles(order='xyz')
```

`fromEuler(order='xyz')``tuple`:

Returns and set the current quaternion from euler angles in degrees as a 3 inputs argument (i.e. pitch as x, yaw as y, roll as z). The 'order' argument can be set to any valid rotation order which by default is set to 'xyz'.

```r = q.fromEuler(order='xyz')
```

`axis()``vector`:

Returns the rotation axis vector of the quaternion.

```v = q.axis()
```

`dot(q2)``float`:

Returns the dot product of the quaternion and the argument.

The quaternion argument can be anything from which a quaternion can be derived ie. (x,y,z,w), Matrix, etc.

```l = q.dot(q2)
```

`exp()``quaternion`:

Returns the exponential of the quaternion as a new quaternion.

```q2 = q.exp()
```

`copy()``quaternion`:

Creates a copy of the quaternion with separate values.

`log()``quaternion`:

Returns the natural logarithm of the current quaternion as a new quaternion.

```l = q.log()
```

`inverse()``None`:

Invert the quaternion in place.

```q.inverse()
```

`angle()``float`:

Returns the rotation angle (in degrees) of the quaternion.

```a = q.angle()
```

### Special Functions

`Quaternion *= Quaternion``Quaternion`:

Applies the rotation of one quaternion to another quaternion.

```# apply rotation of q2 to q1
q1 *= q2
```

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