# Struct cgmath::Quaternion [−] [src]

```pub struct Quaternion<S> {
pub s: S,
pub v: Vector3<S>,
}```

A quaternion in scalar/vector form.

This type is marked as `#[repr(C, packed)]`.

## Fields

`s: S`

The scalar part of the quaternion.

`v: Vector3<S>`

The vector part of the quaternion.

## Methods

### `impl<S: BaseFloat> Quaternion<S>`[src]

#### `fn new(w: S, xi: S, yj: S, zk: S) -> Quaternion<S>`

Construct a new quaternion from one scalar component and three imaginary components

#### `fn from_sv(s: S, v: Vector3<S>) -> Quaternion<S>`

Construct a new quaternion from a scalar and a vector

#### `fn from_arc(src: Vector3<S>, dst: Vector3<S>, fallback: Option<Vector3<S>>) -> Quaternion<S>`

Construct a new quaternion as a closest arc between two vectors

Return the closest rotation that turns `src` vector into `dst`.

#### `fn conjugate(self) -> Quaternion<S>`

The conjugate of the quaternion.

#### `fn nlerp(self, other: Quaternion<S>, amount: S) -> Quaternion<S>`

Do a normalized linear interpolation with `other`, by `amount`.

#### `fn slerp(self, other: Quaternion<S>, amount: S) -> Quaternion<S>`

Spherical Linear Intoperlation

Return the spherical linear interpolation between the quaternion and `other`. Both quaternions should be normalized first.

# Performance notes

The `acos` operation used in `slerp` is an expensive operation, so unless your quarternions are far away from each other it's generally more advisable to use `nlerp` when you know your rotations are going to be small.

## Trait Implementations

### `impl<S: BaseFloat> From<Matrix3<S>> for Quaternion<S>`[src]

#### `fn from(mat: Matrix3<S>) -> Quaternion<S>`

Convert the matrix to a quaternion

### `impl<S: PartialEq> PartialEq for Quaternion<S>`[src]

#### `fn eq(&self, __arg_0: &Quaternion<S>) -> bool`

This method tests for `self` and `other` values to be equal, and is used by `==`. Read more

#### `fn ne(&self, __arg_0: &Quaternion<S>) -> bool`

This method tests for `!=`.

### `impl<S: Debug> Debug for Quaternion<S>`[src]

#### `fn fmt(&self, __arg_0: &mut Formatter) -> Result`

Formats the value using the given formatter.

### `impl<S: Clone> Clone for Quaternion<S>`[src]

#### `fn clone(&self) -> Quaternion<S>`

Returns a copy of the value. Read more

#### `fn clone_from(&mut self, source: &Self)`1.0.0

Performs copy-assignment from `source`. Read more

### `impl<S: BaseFloat> Zero for Quaternion<S>`[src]

#### `fn zero() -> Quaternion<S>`

Returns the additive identity element of `Self`, `0`. Read more

#### `fn is_zero(&self) -> bool`

Returns `true` if `self` is equal to the additive identity.

### `impl<S: BaseFloat> One for Quaternion<S>`[src]

#### `fn one() -> Quaternion<S>`

Returns the multiplicative identity element of `Self`, `1`. Read more

### `impl<S: BaseFloat> VectorSpace for Quaternion<S>`[src]

#### `type Scalar = S`

The associated scalar.

### `impl<S: BaseFloat> MetricSpace for Quaternion<S>`[src]

#### `type Metric = S`

The metric to be returned by the `distance` function.

#### `fn distance2(self, other: Self) -> S`

Returns the squared distance. Read more

#### `fn distance(self, other: Self) -> Self::Metric`

The distance between two values.

### `impl<S: BaseFloat> InnerSpace for Quaternion<S>`[src]

#### `fn dot(self, other: Quaternion<S>) -> S`

Vector dot (or inner) product.

#### `fn is_perpendicular(self, other: Self) -> bool`

Returns `true` if the vector is perpendicular (at right angles) to the other vector. Read more

#### `fn magnitude2(self) -> Self::Scalar`

Returns the squared magnitude. Read more

#### `fn magnitude(self) -> Self::Scalar`

The distance from the tail to the tip of the vector.

#### `fn angle(self, other: Self) -> Rad<Self::Scalar>`

Returns the angle between two vectors in radians.

#### `fn normalize(self) -> Self`

Returns a vector with the same direction, but with a magnitude of `1`.

#### `fn normalize_to(self, magnitude: Self::Scalar) -> Self`

Returns a vector with the same direction and a given magnitude.

#### `fn lerp(self, other: Self, amount: Self::Scalar) -> Self`

Returns the result of linearly interpolating the magnitude of the vector towards the magnitude of `other` by the specified amount. Read more

### `impl<A> From<Euler<A>> for Quaternion<A::Unitless> where A: Angle + Into<Rad<A::Unitless>>`[src]

#### `fn from(src: Euler<A>) -> Quaternion<A::Unitless>`

Performs the conversion.

### `impl<S: BaseFloat> Neg for Quaternion<S>`[src]

#### `type Output = Quaternion<S>`

The resulting type after applying the `-` operator

#### `fn neg(self) -> Quaternion<S>`

The method for the unary `-` operator

### `impl<'a, S: BaseFloat> Neg for &'a Quaternion<S>`[src]

#### `type Output = Quaternion<S>`

The resulting type after applying the `-` operator

#### `fn neg(self) -> Quaternion<S>`

The method for the unary `-` operator

### `impl<S: BaseFloat> Mul<S> for Quaternion<S>`[src]

#### `type Output = Quaternion<S>`

The resulting type after applying the `*` operator

#### `fn mul(self, other: S) -> Quaternion<S>`

The method for the `*` operator

### `impl<'a, S: BaseFloat> Mul<S> for &'a Quaternion<S>`[src]

#### `type Output = Quaternion<S>`

The resulting type after applying the `*` operator

#### `fn mul(self, other: S) -> Quaternion<S>`

The method for the `*` operator

### `impl<S: BaseFloat + MulAssign<S>> MulAssign<S> for Quaternion<S>`[src]

#### `fn mul_assign(&mut self, scalar: S)`

The method for the `*=` operator

### `impl<S: BaseFloat> Div<S> for Quaternion<S>`[src]

#### `type Output = Quaternion<S>`

The resulting type after applying the `/` operator

#### `fn div(self, other: S) -> Quaternion<S>`

The method for the `/` operator

### `impl<'a, S: BaseFloat> Div<S> for &'a Quaternion<S>`[src]

#### `type Output = Quaternion<S>`

The resulting type after applying the `/` operator

#### `fn div(self, other: S) -> Quaternion<S>`

The method for the `/` operator

### `impl<S: BaseFloat + DivAssign<S>> DivAssign<S> for Quaternion<S>`[src]

#### `fn div_assign(&mut self, scalar: S)`

The method for the `/=` operator

### `impl<S: BaseFloat> Rem<S> for Quaternion<S>`[src]

#### `type Output = Quaternion<S>`

The resulting type after applying the `%` operator

#### `fn rem(self, other: S) -> Quaternion<S>`

The method for the `%` operator

### `impl<'a, S: BaseFloat> Rem<S> for &'a Quaternion<S>`[src]

#### `type Output = Quaternion<S>`

The resulting type after applying the `%` operator

#### `fn rem(self, other: S) -> Quaternion<S>`

The method for the `%` operator

### `impl<S: BaseFloat + RemAssign<S>> RemAssign<S> for Quaternion<S>`[src]

#### `fn rem_assign(&mut self, scalar: S)`

The method for the `%=` operator

### `impl<S: BaseFloat> Mul<Vector3<S>> for Quaternion<S>`[src]

#### `type Output = Vector3<S>`

The resulting type after applying the `*` operator

#### `fn mul(self, other: Vector3<S>) -> Vector3<S>`

The method for the `*` operator

### `impl<'a, S: BaseFloat> Mul<&'a Vector3<S>> for Quaternion<S>`[src]

#### `type Output = Vector3<S>`

The resulting type after applying the `*` operator

#### `fn mul(self, other: &'a Vector3<S>) -> Vector3<S>`

The method for the `*` operator

### `impl<'a, S: BaseFloat> Mul<Vector3<S>> for &'a Quaternion<S>`[src]

#### `type Output = Vector3<S>`

The resulting type after applying the `*` operator

#### `fn mul(self, other: Vector3<S>) -> Vector3<S>`

The method for the `*` operator

### `impl<'a, 'b, S: BaseFloat> Mul<&'a Vector3<S>> for &'b Quaternion<S>`[src]

#### `type Output = Vector3<S>`

The resulting type after applying the `*` operator

#### `fn mul(self, other: &'a Vector3<S>) -> Vector3<S>`

The method for the `*` operator

### `impl<S: BaseFloat> Add<Quaternion<S>> for Quaternion<S>`[src]

#### `type Output = Quaternion<S>`

The resulting type after applying the `+` operator

#### `fn add(self, other: Quaternion<S>) -> Quaternion<S>`

The method for the `+` operator

### `impl<'a, S: BaseFloat> Add<&'a Quaternion<S>> for Quaternion<S>`[src]

#### `type Output = Quaternion<S>`

The resulting type after applying the `+` operator

#### `fn add(self, other: &'a Quaternion<S>) -> Quaternion<S>`

The method for the `+` operator

### `impl<'a, S: BaseFloat> Add<Quaternion<S>> for &'a Quaternion<S>`[src]

#### `type Output = Quaternion<S>`

The resulting type after applying the `+` operator

#### `fn add(self, other: Quaternion<S>) -> Quaternion<S>`

The method for the `+` operator

### `impl<'a, 'b, S: BaseFloat> Add<&'a Quaternion<S>> for &'b Quaternion<S>`[src]

#### `type Output = Quaternion<S>`

The resulting type after applying the `+` operator

#### `fn add(self, other: &'a Quaternion<S>) -> Quaternion<S>`

The method for the `+` operator

### `impl<S: BaseFloat + AddAssign<S>> AddAssign<Quaternion<S>> for Quaternion<S>`[src]

#### `fn add_assign(&mut self, other: Quaternion<S>)`

The method for the `+=` operator

### `impl<S: BaseFloat> Sub<Quaternion<S>> for Quaternion<S>`[src]

#### `type Output = Quaternion<S>`

The resulting type after applying the `-` operator

#### `fn sub(self, other: Quaternion<S>) -> Quaternion<S>`

The method for the `-` operator

### `impl<'a, S: BaseFloat> Sub<&'a Quaternion<S>> for Quaternion<S>`[src]

#### `type Output = Quaternion<S>`

The resulting type after applying the `-` operator

#### `fn sub(self, other: &'a Quaternion<S>) -> Quaternion<S>`

The method for the `-` operator

### `impl<'a, S: BaseFloat> Sub<Quaternion<S>> for &'a Quaternion<S>`[src]

#### `type Output = Quaternion<S>`

The resulting type after applying the `-` operator

#### `fn sub(self, other: Quaternion<S>) -> Quaternion<S>`

The method for the `-` operator

### `impl<'a, 'b, S: BaseFloat> Sub<&'a Quaternion<S>> for &'b Quaternion<S>`[src]

#### `type Output = Quaternion<S>`

The resulting type after applying the `-` operator

#### `fn sub(self, other: &'a Quaternion<S>) -> Quaternion<S>`

The method for the `-` operator

### `impl<S: BaseFloat + SubAssign<S>> SubAssign<Quaternion<S>> for Quaternion<S>`[src]

#### `fn sub_assign(&mut self, other: Quaternion<S>)`

The method for the `-=` operator

### `impl<S: BaseFloat> Mul<Quaternion<S>> for Quaternion<S>`[src]

#### `type Output = Quaternion<S>`

The resulting type after applying the `*` operator

#### `fn mul(self, other: Quaternion<S>) -> Quaternion<S>`

The method for the `*` operator

### `impl<'a, S: BaseFloat> Mul<&'a Quaternion<S>> for Quaternion<S>`[src]

#### `type Output = Quaternion<S>`

The resulting type after applying the `*` operator

#### `fn mul(self, other: &'a Quaternion<S>) -> Quaternion<S>`

The method for the `*` operator

### `impl<'a, S: BaseFloat> Mul<Quaternion<S>> for &'a Quaternion<S>`[src]

#### `type Output = Quaternion<S>`

The resulting type after applying the `*` operator

#### `fn mul(self, other: Quaternion<S>) -> Quaternion<S>`

The method for the `*` operator

### `impl<'a, 'b, S: BaseFloat> Mul<&'a Quaternion<S>> for &'b Quaternion<S>`[src]

#### `type Output = Quaternion<S>`

The resulting type after applying the `*` operator

#### `fn mul(self, other: &'a Quaternion<S>) -> Quaternion<S>`

The method for the `*` operator

### `impl<S: BaseFloat> Rotation<Point3<S>> for Quaternion<S>`[src]

#### `fn look_at(dir: Vector3<S>, up: Vector3<S>) -> Quaternion<S>`

Create a rotation to a given direction with an 'up' vector

#### `fn between_vectors(a: Vector3<S>, b: Vector3<S>) -> Quaternion<S>`

Create a shortest rotation to transform vector 'a' into 'b'. Both given vectors are assumed to have unit length. Read more

#### `fn rotate_vector(&self, vec: Vector3<S>) -> Vector3<S>`

Rotate a vector using this rotation.

#### `fn invert(&self) -> Quaternion<S>`

Create a new rotation which "un-does" this rotation. That is, `r * r.invert()` is the identity. Read more

#### `fn rotate_point(&self, point: P) -> P`

Rotate a point using this rotation, by converting it to its representation as a vector. Read more

### `impl<S: BaseFloat> Rotation3<S> for Quaternion<S>`[src]

#### `fn from_axis_angle<A: Into<Rad<S>>>(axis: Vector3<S>, angle: A) -> Quaternion<S>`

Create a rotation using an angle around a given axis. Read more

#### `fn from_angle_x<A: Into<Rad<S>>>(theta: A) -> Self`

Create a rotation from an angle around the `x` axis (pitch).

#### `fn from_angle_y<A: Into<Rad<S>>>(theta: A) -> Self`

Create a rotation from an angle around the `y` axis (yaw).

#### `fn from_angle_z<A: Into<Rad<S>>>(theta: A) -> Self`

Create a rotation from an angle around the `z` axis (roll).

### `impl<S: BaseFloat> Into<[S; 4]> for Quaternion<S>`[src]

#### `fn into(self) -> [S; 4]`

Performs the conversion.

### `impl<S: BaseFloat> AsRef<[S; 4]> for Quaternion<S>`[src]

#### `fn as_ref(&self) -> &[S; 4]`

Performs the conversion.

### `impl<S: BaseFloat> AsMut<[S; 4]> for Quaternion<S>`[src]

#### `fn as_mut(&mut self) -> &mut [S; 4]`

Performs the conversion.

### `impl<S: BaseFloat> From<[S; 4]> for Quaternion<S>`[src]

#### `fn from(v: [S; 4]) -> Quaternion<S>`

Performs the conversion.

### `impl<'a, S: BaseFloat> From<&'a [S; 4]> for &'a Quaternion<S>`[src]

#### `fn from(v: &'a [S; 4]) -> &'a Quaternion<S>`

Performs the conversion.

### `impl<'a, S: BaseFloat> From<&'a mut [S; 4]> for &'a mut Quaternion<S>`[src]

#### `fn from(v: &'a mut [S; 4]) -> &'a mut Quaternion<S>`

Performs the conversion.

### `impl<S: BaseFloat> Into<(S, S, S, S)> for Quaternion<S>`[src]

#### `fn into(self) -> (S, S, S, S)`

Performs the conversion.

### `impl<S: BaseFloat> AsRef<(S, S, S, S)> for Quaternion<S>`[src]

#### `fn as_ref(&self) -> &(S, S, S, S)`

Performs the conversion.

### `impl<S: BaseFloat> AsMut<(S, S, S, S)> for Quaternion<S>`[src]

#### `fn as_mut(&mut self) -> &mut (S, S, S, S)`

Performs the conversion.

### `impl<S: BaseFloat> From<(S, S, S, S)> for Quaternion<S>`[src]

#### `fn from(v: (S, S, S, S)) -> Quaternion<S>`

Performs the conversion.

### `impl<'a, S: BaseFloat> From<&'a (S, S, S, S)> for &'a Quaternion<S>`[src]

#### `fn from(v: &'a (S, S, S, S)) -> &'a Quaternion<S>`

Performs the conversion.

### `impl<'a, S: BaseFloat> From<&'a mut (S, S, S, S)> for &'a mut Quaternion<S>`[src]

#### `fn from(v: &'a mut (S, S, S, S)) -> &'a mut Quaternion<S>`

Performs the conversion.

### `impl<S: BaseFloat> Index<usize> for Quaternion<S>`[src]

#### `type Output = S`

The returned type after indexing

#### `fn index<'a>(&'a self, i: usize) -> &'a S`

The method for the indexing (`Foo[Bar]`) operation

### `impl<S: BaseFloat> IndexMut<usize> for Quaternion<S>`[src]

#### `fn index_mut<'a>(&'a mut self, i: usize) -> &'a mut S`

The method for the indexing (`Foo[Bar]`) operation

### `impl<S: BaseFloat> Index<Range<usize>> for Quaternion<S>`[src]

#### `type Output = [S]`

The returned type after indexing

#### `fn index<'a>(&'a self, i: Range<usize>) -> &'a [S]`

The method for the indexing (`Foo[Bar]`) operation

### `impl<S: BaseFloat> IndexMut<Range<usize>> for Quaternion<S>`[src]

#### `fn index_mut<'a>(&'a mut self, i: Range<usize>) -> &'a mut [S]`

The method for the indexing (`Foo[Bar]`) operation

### `impl<S: BaseFloat> Index<RangeTo<usize>> for Quaternion<S>`[src]

#### `type Output = [S]`

The returned type after indexing

#### `fn index<'a>(&'a self, i: RangeTo<usize>) -> &'a [S]`

The method for the indexing (`Foo[Bar]`) operation

### `impl<S: BaseFloat> IndexMut<RangeTo<usize>> for Quaternion<S>`[src]

#### `fn index_mut<'a>(&'a mut self, i: RangeTo<usize>) -> &'a mut [S]`

The method for the indexing (`Foo[Bar]`) operation

### `impl<S: BaseFloat> Index<RangeFrom<usize>> for Quaternion<S>`[src]

#### `type Output = [S]`

The returned type after indexing

#### `fn index<'a>(&'a self, i: RangeFrom<usize>) -> &'a [S]`

The method for the indexing (`Foo[Bar]`) operation

### `impl<S: BaseFloat> IndexMut<RangeFrom<usize>> for Quaternion<S>`[src]

#### `fn index_mut<'a>(&'a mut self, i: RangeFrom<usize>) -> &'a mut [S]`

The method for the indexing (`Foo[Bar]`) operation

### `impl<S: BaseFloat> Index<RangeFull> for Quaternion<S>`[src]

#### `type Output = [S]`

The returned type after indexing

#### `fn index<'a>(&'a self, i: RangeFull) -> &'a [S]`

The method for the indexing (`Foo[Bar]`) operation

### `impl<S: BaseFloat> IndexMut<RangeFull> for Quaternion<S>`[src]

#### `fn index_mut<'a>(&'a mut self, i: RangeFull) -> &'a mut [S]`

The method for the indexing (`Foo[Bar]`) operation

### `impl<S: BaseFloat + Rand> Rand for Quaternion<S>`[src]

#### `fn rand<R: Rng>(rng: &mut R) -> Quaternion<S>`

Generates a random instance of this type using the specified source of randomness. Read more

### `impl<S: BaseFloat> From<Basis3<S>> for Quaternion<S>`[src]

#### `fn from(b: Basis3<S>) -> Quaternion<S>`

Performs the conversion.