Quaternion in nalgebra::geometry - Rust
Description: A quaternion. See the type alias `UnitQuaternion = Unit<Quaternion>` for a quaternion that may be used as a rotation.
Keywords: rust, rustlang, rust-lang, Quaternion

# Struct nalgebra::geometry::Quaternion

source ·

    #[repr(C)]pub struct Quaternion<T> {
        pub coords: Vector4<T>,
    }

Expand description

A quaternion. See the type alias `UnitQuaternion = Unit<Quaternion>` for a quaternion that may be used as a rotation.

## Fields§

§`coords: Vector4<T>`

This quaternion as a 4D vector of coordinates in the `[ x, y, z, w ]` storage order.

## Implementations§

source§

### impl<T: SimdRealField> Quaternion<T>where
T::Element: SimdRealField,

source

#### pub fn into_owned(self) -> Self

👎Deprecated: This method is a no-op and will be removed in a future release.

Moves this unit quaternion into one that owns its data.

source

#### pub fn clone_owned(&self) -> Self

👎Deprecated: This method is a no-op and will be removed in a future release.

Clones this unit quaternion into one that owns its data.

source

#### pub fn normalize(&self) -> Self

Normalizes this quaternion.

##### Example

    let q = Quaternion::new(1.0, 2.0, 3.0, 4.0);
    let q_normalized = q.normalize();
    relative_eq!(q_normalized.norm(), 1.0);

source

#### pub fn imag(&self) -> Vector3<T>

The imaginary part of this quaternion.

source

#### pub fn conjugate(&self) -> Self

The conjugate of this quaternion.

##### Example

    let q = Quaternion::new(1.0, 2.0, 3.0, 4.0);
    let conj = q.conjugate();
    assert!(conj.i == -2.0 && conj.j == -3.0 && conj.k == -4.0 && conj.w == 1.0);

source

#### pub fn lerp(&self, other: &Self, t: T) -> Self

Linear interpolation between two quaternion.

Computes `self * (1 - t) + other * t`.

##### Example

    let q1 = Quaternion::new(1.0, 2.0, 3.0, 4.0);
    let q2 = Quaternion::new(10.0, 20.0, 30.0, 40.0);

    assert_eq!(q1.lerp(&q2, 0.1), Quaternion::new(1.9, 3.8, 5.7, 7.6));

source

#### pub fn vector(
&self
) -> MatrixView<'_, T, U3, U1, RStride<T, U4, U1>, CStride<T, U4, U1>>

The vector part `(i, j, k)` of this quaternion.

##### Example

    let q = Quaternion::new(1.0, 2.0, 3.0, 4.0);
    assert_eq!(q.vector()[0], 2.0);
    assert_eq!(q.vector()[1], 3.0);
    assert_eq!(q.vector()[2], 4.0);

source

#### pub fn scalar(&self) -> T

The scalar part `w` of this quaternion.

##### Example

    let q = Quaternion::new(1.0, 2.0, 3.0, 4.0);
    assert_eq!(q.scalar(), 1.0);

source

#### pub fn as_vector(&self) -> &Vector4<T>

Reinterprets this quaternion as a 4D vector.

##### Example

    let q = Quaternion::new(1.0, 2.0, 3.0, 4.0);
    // Recall that the quaternion is stored internally as (i, j, k, w)
    // while the crate::new constructor takes the arguments as (w, i, j, k).
    assert_eq!(*q.as_vector(), Vector4::new(2.0, 3.0, 4.0, 1.0));

source

#### pub fn norm(&self) -> T

The norm of this quaternion.

##### Example

    let q = Quaternion::new(1.0, 2.0, 3.0, 4.0);
    assert_relative_eq!(q.norm(), 5.47722557, epsilon = 1.0e-6);

source

#### pub fn magnitude(&self) -> T

A synonym for the norm of this quaternion.

Aka the length. This is the same as `.norm()`

##### Example

    let q = Quaternion::new(1.0, 2.0, 3.0, 4.0);
    assert_relative_eq!(q.magnitude(), 5.47722557, epsilon = 1.0e-6);

source

#### pub fn norm_squared(&self) -> T

The squared norm of this quaternion.

##### Example

    let q = Quaternion::new(1.0, 2.0, 3.0, 4.0);
    assert_eq!(q.magnitude_squared(), 30.0);

source

#### pub fn magnitude_squared(&self) -> T

A synonym for the squared norm of this quaternion.

Aka the squared length. This is the same as `.norm_squared()`

##### Example

    let q = Quaternion::new(1.0, 2.0, 3.0, 4.0);
    assert_eq!(q.magnitude_squared(), 30.0);

source

#### pub fn dot(&self, rhs: &Self) -> T

The dot product of two quaternions.

##### Example

    let q1 = Quaternion::new(1.0, 2.0, 3.0, 4.0);
    let q2 = Quaternion::new(5.0, 6.0, 7.0, 8.0);
    assert_eq!(q1.dot(&q2), 70.0);

source§

### impl<T: SimdRealField> Quaternion<T>where
T::Element: SimdRealField,

source

#### pub fn try_inverse(&self) -> Option<Self>where
T: RealField,

Inverts this quaternion if it is not zero.

This method also does not works with SIMD components (see `simd_try_inverse` instead).

##### Example

    let q = Quaternion::new(1.0, 2.0, 3.0, 4.0);
    let inv_q = q.try_inverse();

    assert!(inv_q.is_some());
    assert_relative_eq!(inv_q.unwrap() * q, Quaternion::identity());

    //Non-invertible case
    let q = Quaternion::new(0.0, 0.0, 0.0, 0.0);
    let inv_q = q.try_inverse();

    assert!(inv_q.is_none());

source

#### pub fn simd_try_inverse(&self) -> SimdOption<Self>

Attempt to inverse this quaternion.

This method also works with SIMD components.

source

#### pub fn inner(&self, other: &Self) -> Self

Calculates the inner product (also known as the dot product). See “Foundations of Game Engine Development, Volume 1: Mathematics” by Lengyel Formula 4.89.

##### Example

    let a = Quaternion::new(0.0, 2.0, 3.0, 4.0);
    let b = Quaternion::new(0.0, 5.0, 2.0, 1.0);
    let expected = Quaternion::new(-20.0, 0.0, 0.0, 0.0);
    let result = a.inner(&b);
    assert_relative_eq!(expected, result, epsilon = 1.0e-5);

source

#### pub fn outer(&self, other: &Self) -> Self

Calculates the outer product (also known as the wedge product). See “Foundations of Game Engine Development, Volume 1: Mathematics” by Lengyel Formula 4.89.

##### Example

    let a = Quaternion::new(0.0, 2.0, 3.0, 4.0);
    let b = Quaternion::new(0.0, 5.0, 2.0, 1.0);
    let expected = Quaternion::new(0.0, -5.0, 18.0, -11.0);
    let result = a.outer(&b);
    assert_relative_eq!(expected, result, epsilon = 1.0e-5);

source

#### pub fn project(&self, other: &Self) -> Option<Self>where
T: RealField,

Calculates the projection of `self` onto `other` (also known as the parallel). See “Foundations of Game Engine Development, Volume 1: Mathematics” by Lengyel Formula 4.94.

##### Example

    let a = Quaternion::new(0.0, 2.0, 3.0, 4.0);
    let b = Quaternion::new(0.0, 5.0, 2.0, 1.0);
    let expected = Quaternion::new(0.0, 3.333333333333333, 1.3333333333333333, 0.6666666666666666);
    let result = a.project(&b).unwrap();
    assert_relative_eq!(expected, result, epsilon = 1.0e-5);

source

#### pub fn reject(&self, other: &Self) -> Option<Self>where
T: RealField,

Calculates the rejection of `self` from `other` (also known as the perpendicular). See “Foundations of Game Engine Development, Volume 1: Mathematics” by Lengyel Formula 4.94.

##### Example

    let a = Quaternion::new(0.0, 2.0, 3.0, 4.0);
    let b = Quaternion::new(0.0, 5.0, 2.0, 1.0);
    let expected = Quaternion::new(0.0, -1.3333333333333333, 1.6666666666666665, 3.3333333333333335);
    let result = a.reject(&b).unwrap();
    assert_relative_eq!(expected, result, epsilon = 1.0e-5);

source

#### pub fn polar_decomposition(&self) -> (T, T, Option<Unit<Vector3<T>>>)where
T: RealField,

The polar decomposition of this quaternion.

Returns, from left to right: the quaternion norm, the half rotation angle, the rotation axis. If the rotation angle is zero, the rotation axis is set to `None`.

##### Example

    let q = Quaternion::new(0.0, 5.0, 0.0, 0.0);
    let (norm, half_ang, axis) = q.polar_decomposition();
    assert_eq!(norm, 5.0);
    assert_eq!(half_ang, f32::consts::FRAC_PI_2);
    assert_eq!(axis, Some(Vector3::x_axis()));

source

#### pub fn ln(&self) -> Self

Compute the natural logarithm of a quaternion.

##### Example

    let q = Quaternion::new(2.0, 5.0, 0.0, 0.0);
    assert_relative_eq!(q.ln(), Quaternion::new(1.683647, 1.190289, 0.0, 0.0), epsilon = 1.0e-6)

source

#### pub fn exp(&self) -> Self

Compute the exponential of a quaternion.

##### Example

    let q = Quaternion::new(1.683647, 1.190289, 0.0, 0.0);
    assert_relative_eq!(q.exp(), Quaternion::new(2.0, 5.0, 0.0, 0.0), epsilon = 1.0e-5)

source

#### pub fn exp_eps(&self, eps: T) -> Self

Compute the exponential of a quaternion. Returns the identity if the vector part of this quaternion has a norm smaller than `eps`.

##### Example

    let q = Quaternion::new(1.683647, 1.190289, 0.0, 0.0);
    assert_relative_eq!(q.exp_eps(1.0e-6), Quaternion::new(2.0, 5.0, 0.0, 0.0), epsilon = 1.0e-5);

    // Singular case.
    let q = Quaternion::new(0.0000001, 0.0, 0.0, 0.0);
    assert_eq!(q.exp_eps(1.0e-6), Quaternion::identity());

source

#### pub fn powf(&self, n: T) -> Self

Raise the quaternion to a given floating power.

##### Example

    let q = Quaternion::new(1.0, 2.0, 3.0, 4.0);
    assert_relative_eq!(q.powf(1.5), Quaternion::new( -6.2576659, 4.1549037, 6.2323556, 8.3098075), epsilon = 1.0e-6);

source

#### pub fn as_vector_mut(&mut self) -> &mut Vector4<T>

Transforms this quaternion into its 4D vector form (Vector part, Scalar part).

##### Example

    let mut q = Quaternion::identity();
    *q.as_vector_mut() = Vector4::new(1.0, 2.0, 3.0, 4.0);
    assert!(q.i == 1.0 && q.j == 2.0 && q.k == 3.0 && q.w == 4.0);

source

#### pub fn vector_mut(
&mut self
) -> MatrixViewMut<'_, T, U3, U1, RStride<T, U4, U1>, CStride<T, U4, U1>>

The mutable vector part `(i, j, k)` of this quaternion.

##### Example

    let mut q = Quaternion::identity();
    {
        let mut v = q.vector_mut();
        v[0] = 2.0;
        v[1] = 3.0;
        v[2] = 4.0;
    }
    assert!(q.i == 2.0 && q.j == 3.0 && q.k == 4.0 && q.w == 1.0);

source

#### pub fn conjugate_mut(&mut self)

Replaces this quaternion by its conjugate.

##### Example

    let mut q = Quaternion::new(1.0, 2.0, 3.0, 4.0);
    q.conjugate_mut();
    assert!(q.i == -2.0 && q.j == -3.0 && q.k == -4.0 && q.w == 1.0);

source

#### pub fn try_inverse_mut(&mut self) -> T::SimdBool

Inverts this quaternion in-place if it is not zero.

##### Example

    let mut q = Quaternion::new(1.0f32, 2.0, 3.0, 4.0);

    assert!(q.try_inverse_mut());
    assert_relative_eq!(q * Quaternion::new(1.0, 2.0, 3.0, 4.0), Quaternion::identity());

    //Non-invertible case
    let mut q = Quaternion::new(0.0f32, 0.0, 0.0, 0.0);
    assert!(!q.try_inverse_mut());

source

#### pub fn normalize_mut(&mut self) -> T

Normalizes this quaternion.

##### Example

    let mut q = Quaternion::new(1.0, 2.0, 3.0, 4.0);
    q.normalize_mut();
    assert_relative_eq!(q.norm(), 1.0);

source

#### pub fn squared(&self) -> Self

Calculates square of a quaternion.

source

#### pub fn half(&self) -> Self

Divides quaternion into two.

source

#### pub fn sqrt(&self) -> Self

Calculates square root.

source

#### pub fn is_pure(&self) -> bool

Check if the quaternion is pure.

A quaternion is pure if it has no real part (`self.w == 0.0`).

source

#### pub fn pure(&self) -> Self

Convert quaternion to pure quaternion.

source

#### pub fn left_div(&self, other: &Self) -> Option<Self>where
T: RealField,

Left quaternionic division.

Calculates B-1 * A where A = self, B = other.

source

#### pub fn right_div(&self, other: &Self) -> Option<Self>where
T: RealField,

Right quaternionic division.

Calculates A * B-1 where A = self, B = other.

##### Example

    let a = Quaternion::new(0.0, 1.0, 2.0, 3.0);
    let b = Quaternion::new(0.0, 5.0, 2.0, 1.0);
    let result = a.right_div(&b).unwrap();
    let expected = Quaternion::new(0.4, 0.13333333333333336, -0.4666666666666667, 0.26666666666666666);
    assert_relative_eq!(expected, result, epsilon = 1.0e-7);

source

#### pub fn cos(&self) -> Self

Calculates the quaternionic cosinus.

##### Example

    let input = Quaternion::new(1.0, 2.0, 3.0, 4.0);
    let expected = Quaternion::new(58.93364616794395, -34.086183690465596, -51.1292755356984, -68.17236738093119);
    let result = input.cos();
    assert_relative_eq!(expected, result, epsilon = 1.0e-7);

source

#### pub fn acos(&self) -> Self

Calculates the quaternionic arccosinus.

##### Example

    let input = Quaternion::new(1.0, 2.0, 3.0, 4.0);
    let result = input.cos().acos();
    assert_relative_eq!(input, result, epsilon = 1.0e-7);

source

#### pub fn sin(&self) -> Self

Calculates the quaternionic sinus.

##### Example

    let input = Quaternion::new(1.0, 2.0, 3.0, 4.0);
    let expected = Quaternion::new(91.78371578403467, 21.886486853029176, 32.82973027954377, 43.77297370605835);
    let result = input.sin();
    assert_relative_eq!(expected, result, epsilon = 1.0e-7);

source

#### pub fn asin(&self) -> Self

Calculates the quaternionic arcsinus.

##### Example

    let input = Quaternion::new(1.0, 2.0, 3.0, 4.0);
    let result = input.sin().asin();
    assert_relative_eq!(input, result, epsilon = 1.0e-7);

source

#### pub fn tan(&self) -> Selfwhere
T: RealField,

Calculates the quaternionic tangent.

##### Example

    let input = Quaternion::new(1.0, 2.0, 3.0, 4.0);
    let expected = Quaternion::new(0.00003821631725009489, 0.3713971716439371, 0.5570957574659058, 0.7427943432878743);
    let result = input.tan();
    assert_relative_eq!(expected, result, epsilon = 1.0e-7);

source

#### pub fn atan(&self) -> Selfwhere
T: RealField,

Calculates the quaternionic arctangent.

##### Example

    let input = Quaternion::new(1.0, 2.0, 3.0, 4.0);
    let result = input.tan().atan();
    assert_relative_eq!(input, result, epsilon = 1.0e-7);

source

#### pub fn sinh(&self) -> Self

Calculates the hyperbolic quaternionic sinus.

##### Example

    let input = Quaternion::new(1.0, 2.0, 3.0, 4.0);
    let expected = Quaternion::new(0.7323376060463428, -0.4482074499805421, -0.6723111749708133, -0.8964148999610843);
    let result = input.sinh();
    assert_relative_eq!(expected, result, epsilon = 1.0e-7);

source

#### pub fn asinh(&self) -> Self

Calculates the hyperbolic quaternionic arcsinus.

##### Example

    let input = Quaternion::new(1.0, 2.0, 3.0, 4.0);
    let expected = Quaternion::new(2.385889902585242, 0.514052600662788, 0.7710789009941821, 1.028105201325576);
    let result = input.asinh();
    assert_relative_eq!(expected, result, epsilon = 1.0e-7);

source

#### pub fn cosh(&self) -> Self

Calculates the hyperbolic quaternionic cosinus.

##### Example

    let input = Quaternion::new(1.0, 2.0, 3.0, 4.0);
    let expected = Quaternion::new(0.9615851176369566, -0.3413521745610167, -0.5120282618415251, -0.6827043491220334);
    let result = input.cosh();
    assert_relative_eq!(expected, result, epsilon = 1.0e-7);

source

#### pub fn acosh(&self) -> Self

Calculates the hyperbolic quaternionic arccosinus.

##### Example

    let input = Quaternion::new(1.0, 2.0, 3.0, 4.0);
    let expected = Quaternion::new(2.4014472020074007, 0.5162761016176176, 0.7744141524264264, 1.0325522032352352);
    let result = input.acosh();
    assert_relative_eq!(expected, result, epsilon = 1.0e-7);

source

#### pub fn tanh(&self) -> Selfwhere
T: RealField,

Calculates the hyperbolic quaternionic tangent.

##### Example

    let input = Quaternion::new(1.0, 2.0, 3.0, 4.0);
    let expected = Quaternion::new(1.0248695360556623, -0.10229568178876419, -0.1534435226831464, -0.20459136357752844);
    let result = input.tanh();
    assert_relative_eq!(expected, result, epsilon = 1.0e-7);

source

#### pub fn atanh(&self) -> Self

Calculates the hyperbolic quaternionic arctangent.

##### Example

    let input = Quaternion::new(1.0, 2.0, 3.0, 4.0);
    let expected = Quaternion::new(0.03230293287000163, 0.5173453683196951, 0.7760180524795426, 1.0346907366393903);
    let result = input.atanh();
    assert_relative_eq!(expected, result, epsilon = 1.0e-7);

source§

### impl<T> Quaternion<T>

source

#### pub const fn from_vector(vector: Vector4<T>) -> Self

Creates a quaternion from a 4D vector. The quaternion scalar part corresponds to the `w` vector component.

source

#### pub const fn new(w: T, i: T, j: T, k: T) -> Self

Creates a new quaternion from its individual components. Note that the arguments order does not follow the storage order.

The storage order is `[ i, j, k, w ]` while the arguments for this functions are in the order `(w, i, j, k)`.

##### Example

    let q = Quaternion::new(1.0, 2.0, 3.0, 4.0);
    assert!(q.i == 2.0 && q.j == 3.0 && q.k == 4.0 && q.w == 1.0);
    assert_eq!(*q.as_vector(), Vector4::new(2.0, 3.0, 4.0, 1.0));

source

#### pub fn cast<To>(self) -> Quaternion<To>where
T: Scalar,
To: SupersetOf<T> + Scalar,

Cast the components of `self` to another type.

##### Example

    let q = Quaternion::new(1.0f64, 2.0, 3.0, 4.0);
    let q2 = q.cast::<f32>();
    assert_eq!(q2, Quaternion::new(1.0f32, 2.0, 3.0, 4.0));

source§

### impl<T: SimdRealField> Quaternion<T>

source

#### pub fn from_imag(vector: Vector3<T>) -> Self

Constructs a pure quaternion.

source

#### pub fn from_parts<SB>(scalar: T, vector: Vector<T, U3, SB>) -> Selfwhere
SB: Storage<T, U3>,

Creates a new quaternion from its scalar and vector parts. Note that the arguments order does not follow the storage order.

The storage order is [ vector, scalar ].

##### Example

    let w = 1.0;
    let ijk = Vector3::new(2.0, 3.0, 4.0);
    let q = Quaternion::from_parts(w, ijk);
    assert!(q.i == 2.0 && q.j == 3.0 && q.k == 4.0 && q.w == 1.0);
    assert_eq!(*q.as_vector(), Vector4::new(2.0, 3.0, 4.0, 1.0));

source

#### pub fn from_real(r: T) -> Self

Constructs a real quaternion.

source

#### pub fn identity() -> Self

The quaternion multiplicative identity.

##### Example

    let q = Quaternion::identity();
    let q2 = Quaternion::new(1.0, 2.0, 3.0, 4.0);

    assert_eq!(q * q2, q2);
    assert_eq!(q2 * q, q2);

source§

### impl<T: SimdRealField> Quaternion<T>where
T::Element: SimdRealField,

source

#### pub fn from_polar_decomposition<SB>(
scale: T,
theta: T,
axis: Unit<Vector<T, U3, SB>>
) -> Selfwhere
SB: Storage<T, U3>,

Creates a new quaternion from its polar decomposition.

Note that `axis` is assumed to be a unit vector.

## Trait Implementations§

source§

### impl<T: RealField + AbsDiffEq<Epsilon = T>> AbsDiffEq<Quaternion<T>> for Quaternion<T>

§

#### type Epsilon = T

Used for specifying relative comparisons.
source§

#### fn default_epsilon() -> Self::Epsilon

The default tolerance to use when testing values that are close together. Read more
source§

#### fn abs_diff_eq(&self, other: &Self, epsilon: Self::Epsilon) -> bool

A test for equality that uses the absolute difference to compute the approximate equality of two numbers. Read more
source§

#### fn abs_diff_ne(&self, other: &Rhs, epsilon: Self::Epsilon) -> bool

The inverse of `AbsDiffEq::abs_diff_eq`.
source§

### impl<'a, 'b, T: SimdRealField> Add<&'b Quaternion<T>> for &'a Quaternion<T>where
T::Element: SimdRealField,

§

#### type Output = Quaternion<T>

The resulting type after applying the `+` operator.
source§

#### fn add(self, rhs: &'b Quaternion<T>) -> Self::Output

Performs the `+` operation. Read more
source§

### impl<'b, T: SimdRealField> Add<&'b Quaternion<T>> for Quaternion<T>where
T::Element: SimdRealField,

§

#### type Output = Quaternion<T>

The resulting type after applying the `+` operator.
source§

#### fn add(self, rhs: &'b Quaternion<T>) -> Self::Output

Performs the `+` operation. Read more
source§

### impl<'a, T: SimdRealField> Add<Quaternion<T>> for &'a Quaternion<T>where
T::Element: SimdRealField,

§

#### type Output = Quaternion<T>

The resulting type after applying the `+` operator.
source§

#### fn add(self, rhs: Quaternion<T>) -> Self::Output

Performs the `+` operation. Read more
source§

### impl<T: SimdRealField> Add<Quaternion<T>> for Quaternion<T>where
T::Element: SimdRealField,

§

#### type Output = Quaternion<T>

The resulting type after applying the `+` operator.
source§

#### fn add(self, rhs: Quaternion<T>) -> Self::Output

Performs the `+` operation. Read more
source§

### impl<'b, T: SimdRealField> AddAssign<&'b Quaternion<T>> for Quaternion<T>where
T::Element: SimdRealField,

source§

#### fn add_assign(&mut self, rhs: &'b Quaternion<T>)

Performs the `+=` operation. Read more
source§

### impl<T: SimdRealField> AddAssign<Quaternion<T>> for Quaternion<T>where
T::Element: SimdRealField,

source§

#### fn add_assign(&mut self, rhs: Quaternion<T>)

Performs the `+=` operation. Read more
source§

### impl<T: Clone> Clone for Quaternion<T>

source§

#### fn clone(&self) -> Quaternion<T>

Returns a copy of the value. Read more
1.0.0 · source§

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

Performs copy-assignment from `source`. Read more
source§

### impl<T: Debug> Debug for Quaternion<T>

source§

#### fn fmt(&self, formatter: &mut Formatter<'_>) -> Result<(), Error>

Formats the value using the given formatter. Read more
source§

### impl<T: Scalar + Zero> Default for Quaternion<T>

source§

#### fn default() -> Self

Returns the “default value” for a type. Read more
source§

### impl<T: Scalar + SimdValue> Deref for Quaternion<T>

§

#### type Target = IJKW<T>

The resulting type after dereferencing.
source§

#### fn deref(&self) -> &Self::Target

Dereferences the value.
source§

### impl<T: Scalar + SimdValue> DerefMut for Quaternion<T>

source§

#### fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.
source§

### impl<T: RealField + Display> Display for Quaternion<T>

source§

#### fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter. Read more
source§

### impl<'a, T: SimdRealField> Div<T> for &'a Quaternion<T>where
T::Element: SimdRealField,

§

#### type Output = Quaternion<T>

The resulting type after applying the `/` operator.
source§

#### fn div(self, n: T) -> Self::Output

Performs the `/` operation. Read more
source§

### impl<T: SimdRealField> Div<T> for Quaternion<T>where
T::Element: SimdRealField,

§

#### type Output = Quaternion<T>

The resulting type after applying the `/` operator.
source§

#### fn div(self, n: T) -> Self::Output

Performs the `/` operation. Read more
source§

### impl<T: SimdRealField> DivAssign<T> for Quaternion<T>where
T::Element: SimdRealField,

source§

#### fn div_assign(&mut self, n: T)

Performs the `/=` operation. Read more
source§

### impl<T> From<[Quaternion<<T as SimdValue>::Element>; 16]> for Quaternion<T>where
T: From<[<T as SimdValue>::Element; 16]> + Scalar + PrimitiveSimdValue,
T::Element: Scalar + Copy,

source§

#### fn from(arr: [Quaternion<T::Element>; 16]) -> Self

Converts to this type from the input type.
source§

### impl<T> From<[Quaternion<<T as SimdValue>::Element>; 2]> for Quaternion<T>where
T: From<[<T as SimdValue>::Element; 2]> + Scalar + PrimitiveSimdValue,
T::Element: Scalar + Copy,

source§

#### fn from(arr: [Quaternion<T::Element>; 2]) -> Self

Converts to this type from the input type.
source§

### impl<T> From<[Quaternion<<T as SimdValue>::Element>; 4]> for Quaternion<T>where
T: From<[<T as SimdValue>::Element; 4]> + Scalar + PrimitiveSimdValue,
T::Element: Scalar + Copy,

source§

#### fn from(arr: [Quaternion<T::Element>; 4]) -> Self

Converts to this type from the input type.
source§

### impl<T> From<[Quaternion<<T as SimdValue>::Element>; 8]> for Quaternion<T>where
T: From<[<T as SimdValue>::Element; 8]> + Scalar + PrimitiveSimdValue,
T::Element: Scalar + Copy,

source§

#### fn from(arr: [Quaternion<T::Element>; 8]) -> Self

Converts to this type from the input type.
source§

### impl<T: Scalar> From<[T; 4]> for Quaternion<T>

source§

#### fn from(coords: [T; 4]) -> Self

Converts to this type from the input type.
source§

### impl<T: Scalar> From<Matrix<T, Const<4>, Const<1>, ArrayStorage<T, 4, 1>>> for Quaternion<T>

source§

#### fn from(coords: Vector4<T>) -> Self

Converts to this type from the input type.
source§

### impl<T: Scalar + Hash> Hash for Quaternion<T>

source§

#### fn hash<H: Hasher>(&self, state: &mut H)

Feeds this value into the given `Hasher`. Read more
1.3.0 · source§

#### fn hash_slice<H>(data: &[Self], state: &mut H)where
H: Hasher,
Self: Sized,

Feeds a slice of this type into the given `Hasher`. Read more
source§

### impl<T: Scalar> Index<usize> for Quaternion<T>

§

#### type Output = T

The returned type after indexing.
source§

#### fn index(&self, i: usize) -> &Self::Output

Performs the indexing (`container[index]`) operation. Read more
source§

### impl<T: Scalar> IndexMut<usize> for Quaternion<T>

source§

#### fn index_mut(&mut self, i: usize) -> &mut T

Performs the mutable indexing (`container[index]`) operation. Read more
source§

### impl<'a, 'b, T: SimdRealField> Mul<&'b Quaternion<T>> for &'a Quaternion<T>where
T::Element: SimdRealField,

§

#### type Output = Quaternion<T>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, rhs: &'b Quaternion<T>) -> Self::Output

Performs the `*` operation. Read more
source§

### impl<'b, T: SimdRealField> Mul<&'b Quaternion<T>> for Quaternion<T>where
T::Element: SimdRealField,

§

#### type Output = Quaternion<T>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, rhs: &'b Quaternion<T>) -> Self::Output

Performs the `*` operation. Read more
source§

### impl<'b> Mul<&'b Quaternion<f32>> for f32

§

#### type Output = Quaternion<f32>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, right: &'b Quaternion<f32>) -> Self::Output

Performs the `*` operation. Read more
source§

### impl<'b> Mul<&'b Quaternion<f64>> for f64

§

#### type Output = Quaternion<f64>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, right: &'b Quaternion<f64>) -> Self::Output

Performs the `*` operation. Read more
source§

### impl<'a, T: SimdRealField> Mul<Quaternion<T>> for &'a Quaternion<T>where
T::Element: SimdRealField,

§

#### type Output = Quaternion<T>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, rhs: Quaternion<T>) -> Self::Output

Performs the `*` operation. Read more
source§

### impl<T: SimdRealField> Mul<Quaternion<T>> for Quaternion<T>where
T::Element: SimdRealField,

§

#### type Output = Quaternion<T>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, rhs: Quaternion<T>) -> Self::Output

Performs the `*` operation. Read more
source§

### impl Mul<Quaternion<f32>> for f32

§

#### type Output = Quaternion<f32>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, right: Quaternion<f32>) -> Self::Output

Performs the `*` operation. Read more
source§

### impl Mul<Quaternion<f64>> for f64

§

#### type Output = Quaternion<f64>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, right: Quaternion<f64>) -> Self::Output

Performs the `*` operation. Read more
source§

### impl<'a, T: SimdRealField> Mul<T> for &'a Quaternion<T>where
T::Element: SimdRealField,

§

#### type Output = Quaternion<T>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, n: T) -> Self::Output

Performs the `*` operation. Read more
source§

### impl<T: SimdRealField> Mul<T> for Quaternion<T>where
T::Element: SimdRealField,

§

#### type Output = Quaternion<T>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, n: T) -> Self::Output

Performs the `*` operation. Read more
source§

### impl<'b, T: SimdRealField> MulAssign<&'b Quaternion<T>> for Quaternion<T>where
T::Element: SimdRealField,

source§

#### fn mul_assign(&mut self, rhs: &'b Quaternion<T>)

Performs the `*=` operation. Read more
source§

### impl<T: SimdRealField> MulAssign<Quaternion<T>> for Quaternion<T>where
T::Element: SimdRealField,

source§

#### fn mul_assign(&mut self, rhs: Quaternion<T>)

Performs the `*=` operation. Read more
source§

### impl<T: SimdRealField> MulAssign<T> for Quaternion<T>where
T::Element: SimdRealField,

source§

#### fn mul_assign(&mut self, n: T)

Performs the `*=` operation. Read more
source§

### impl<'a, T: SimdRealField> Neg for &'a Quaternion<T>where
T::Element: SimdRealField,

§

#### type Output = Quaternion<T>

The resulting type after applying the `-` operator.
source§

#### fn neg(self) -> Self::Output

Performs the unary `-` operation. Read more
source§

### impl<T: SimdRealField> Neg for Quaternion<T>where
T::Element: SimdRealField,

§

#### type Output = Quaternion<T>

The resulting type after applying the `-` operator.
source§

#### fn neg(self) -> Self::Output

Performs the unary `-` operation. Read more
source§

### impl<T: SimdRealField> Normed for Quaternion<T>

§

#### type Norm = <T as SimdComplexField>::SimdRealField

The type of the norm.
source§

#### fn norm(&self) -> T::SimdRealField

Computes the norm.
source§

#### fn norm_squared(&self) -> T::SimdRealField

Computes the squared norm.
source§

#### fn scale_mut(&mut self, n: Self::Norm)

Multiply `self` by n.
source§

#### fn unscale_mut(&mut self, n: Self::Norm)

Divides `self` by n.
source§

### impl<T: SimdRealField> One for Quaternion<T>where
T::Element: SimdRealField,

source§

#### fn one() -> Self

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

#### fn set_one(&mut self)

Sets `self` to the multiplicative identity element of `Self`, `1`.
source§

#### fn is_one(&self) -> bool where
Self: PartialEq<Self>,

Returns `true` if `self` is equal to the multiplicative identity. Read more
source§

### impl<T: Scalar> PartialEq<Quaternion<T>> for Quaternion<T>

source§

#### fn eq(&self, right: &Self) -> bool

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

#### fn ne(&self, other: &Rhs) -> bool

This method tests for `!=`. The default implementation is almost always sufficient, and should not be overridden without very good reason. Read more
source§

### impl<T: RealField + RelativeEq<Epsilon = T>> RelativeEq<Quaternion<T>> for Quaternion<T>

source§

#### fn default_max_relative() -> Self::Epsilon

The default relative tolerance for testing values that are far-apart. Read more
source§

#### fn relative_eq(
&self,
other: &Self,
epsilon: Self::Epsilon,
max_relative: Self::Epsilon
) -> bool

A test for equality that uses a relative comparison if the values are far apart.
source§

#### fn relative_ne(
&self,
other: &Rhs,
epsilon: Self::Epsilon,
max_relative: Self::Epsilon
) -> bool

The inverse of `RelativeEq::relative_eq`.
source§

### impl<T: Scalar + SimdValue> SimdValue for Quaternion<T>where
T::Element: Scalar,

§

#### type Element = Quaternion<<T as SimdValue>::Element>

The type of the elements of each lane of this SIMD value.
§

#### type SimdBool = <T as SimdValue>::SimdBool

Type of the result of comparing two SIMD values like `self`.
source§

#### fn lanes() -> usize

The number of lanes of this SIMD value.
source§

#### fn splat(val: Self::Element) -> Self

Initializes an SIMD value with each lanes set to `val`.
source§

#### fn extract(&self, i: usize) -> Self::Element

Extracts the i-th lane of `self`. Read more
source§

#### unsafe fn extract_unchecked(&self, i: usize) -> Self::Element

Extracts the i-th lane of `self` without bound-checking.
source§

#### fn replace(&mut self, i: usize, val: Self::Element)

Replaces the i-th lane of `self` by `val`. Read more
source§

#### unsafe fn replace_unchecked(&mut self, i: usize, val: Self::Element)

Replaces the i-th lane of `self` by `val` without bound-checking.
source§

#### fn select(self, cond: Self::SimdBool, other: Self) -> Self

Merges `self` and `other` depending on the lanes of `cond`. Read more
source§

#### fn map_lanes(self, f: impl Fn(Self::Element) -> Self::Element) -> Selfwhere
Self: Clone,

Applies a function to each lane of `self`. Read more
source§

#### fn zip_map_lanes(
self,
b: Self,
f: impl Fn(Self::Element, Self::Element) -> Self::Element
) -> Selfwhere
Self: Clone,

Applies a function to each lane of `self` paired with the corresponding lane of `b`. Read more
source§

### impl<'a, 'b, T: SimdRealField> Sub<&'b Quaternion<T>> for &'a Quaternion<T>where
T::Element: SimdRealField,

§

#### type Output = Quaternion<T>

The resulting type after applying the `-` operator.
source§

#### fn sub(self, rhs: &'b Quaternion<T>) -> Self::Output

Performs the `-` operation. Read more
source§

### impl<'b, T: SimdRealField> Sub<&'b Quaternion<T>> for Quaternion<T>where
T::Element: SimdRealField,

§

#### type Output = Quaternion<T>

The resulting type after applying the `-` operator.
source§

#### fn sub(self, rhs: &'b Quaternion<T>) -> Self::Output

Performs the `-` operation. Read more
source§

### impl<'a, T: SimdRealField> Sub<Quaternion<T>> for &'a Quaternion<T>where
T::Element: SimdRealField,

§

#### type Output = Quaternion<T>

The resulting type after applying the `-` operator.
source§

#### fn sub(self, rhs: Quaternion<T>) -> Self::Output

Performs the `-` operation. Read more
source§

### impl<T: SimdRealField> Sub<Quaternion<T>> for Quaternion<T>where
T::Element: SimdRealField,

§

#### type Output = Quaternion<T>

The resulting type after applying the `-` operator.
source§

#### fn sub(self, rhs: Quaternion<T>) -> Self::Output

Performs the `-` operation. Read more
source§

### impl<'b, T: SimdRealField> SubAssign<&'b Quaternion<T>> for Quaternion<T>where
T::Element: SimdRealField,

source§

#### fn sub_assign(&mut self, rhs: &'b Quaternion<T>)

Performs the `-=` operation. Read more
source§

### impl<T: SimdRealField> SubAssign<Quaternion<T>> for Quaternion<T>where
T::Element: SimdRealField,

source§

#### fn sub_assign(&mut self, rhs: Quaternion<T>)

Performs the `-=` operation. Read more
source§

### impl<T1, T2> SubsetOf<Quaternion<T2>> for Quaternion<T1>where
T1: Scalar,
T2: Scalar + SupersetOf<T1>,

source§

#### fn to_superset(&self) -> Quaternion<T2>

The inclusion map: converts `self` to the equivalent element of its superset.
source§

#### fn is_in_subset(q: &Quaternion<T2>) -> bool

Checks if `element` is actually part of the subset `Self` (and can be converted to it).
source§

#### fn from_superset_unchecked(q: &Quaternion<T2>) -> Self

Use with care! Same as `self.to_superset` but without any property checks. Always succeeds.
source§

#### fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct `self` from the equivalent element of its superset. Read more
source§

### impl<T: RealField + UlpsEq<Epsilon = T>> UlpsEq<Quaternion<T>> for Quaternion<T>

source§

#### fn default_max_ulps() -> u32

The default ULPs to tolerate when testing values that are far-apart. Read more
source§

#### fn ulps_eq(&self, other: &Self, epsilon: Self::Epsilon, max_ulps: u32) -> bool

A test for equality that uses units in the last place (ULP) if the values are far apart.
source§

#### fn ulps_ne(&self, other: &Rhs, epsilon: Self::Epsilon, max_ulps: u32) -> bool

The inverse of `UlpsEq::ulps_eq`.
source§

### impl<T: SimdRealField> Zero for Quaternion<T>where
T::Element: SimdRealField,

source§

#### fn zero() -> Self

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

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

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

#### fn set_zero(&mut self)

Sets `self` to the additive identity element of `Self`, `0`.
source§

### impl<T: Copy> Copy for Quaternion<T>

source§

### impl<T: Scalar + Eq> Eq for Quaternion<T>

## Auto Trait Implementations§

§

### impl<T> RefUnwindSafe for Quaternion<T>where
T: RefUnwindSafe,

§

### impl<T> Send for Quaternion<T>where
T: Send,

§

### impl<T> Sync for Quaternion<T>where
T: Sync,

§

### impl<T> Unpin for Quaternion<T>where
T: Unpin,

§

### impl<T> UnwindSafe for Quaternion<T>where
T: UnwindSafe,

## Blanket Implementations§

source§

### impl<T> Any for Twhere
T: 'static + ?Sized,

source§

#### fn type_id(&self) -> TypeId

Gets the `TypeId` of `self`. Read more
source§

### impl<T> Borrow<T> for Twhere
T: ?Sized,

const: unstable · source§

#### fn borrow(&self) -> &T

Immutably borrows from an owned value. Read more
source§

### impl<T> BorrowMut<T> for Twhere
T: ?Sized,

const: unstable · source§

#### fn borrow_mut(&mut self) -> &mut T

Mutably borrows from an owned value. Read more
source§

### impl<T> From<T> for T

const: unstable · source§

#### fn from(t: T) -> T

Returns the argument unchanged.

source§

### impl<T, U> Into<U> for Twhere
U: From<T>,

const: unstable · source§

#### fn into(self) -> U

Calls `U::from(self)`.

That is, this conversion is whatever the implementation of `From<T> for U` chooses to do.

source§

### impl<T> Same<T> for T

§

#### type Output = T

Should always be `Self`
source§

### impl<SS, SP> SupersetOf<SS> for SPwhere
SS: SubsetOf<SP>,

source§

#### fn to_subset(&self) -> Option<SS>

The inverse inclusion map: attempts to construct `self` from the equivalent element of its superset. Read more
source§

#### fn is_in_subset(&self) -> bool

Checks if `self` is actually part of its subset `T` (and can be converted to it).
source§

#### fn to_subset_unchecked(&self) -> SS

Use with care! Same as `self.to_subset` but without any property checks. Always succeeds.
source§

#### fn from_subset(element: &SS) -> SP

The inclusion map: converts `self` to the equivalent element of its superset.
source§

### impl<T> ToOwned for Twhere
T: Clone,

§

#### type Owned = T

The resulting type after obtaining ownership.
source§

#### fn to_owned(&self) -> T

Creates owned data from borrowed data, usually by cloning. Read more
source§

#### fn clone_into(&self, target: &mut T)

Uses borrowed data to replace owned data, usually by cloning. Read more
source§

### impl<T> ToString for Twhere
T: Display + ?Sized,

source§

#### default fn to_string(&self) -> String

Converts the given value to a `String`. Read more
source§

### impl<T, U> TryFrom<U> for Twhere
U: Into<T>,

§

#### type Error = Infallible

The type returned in the event of a conversion error.
const: unstable · source§

#### fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::Error>

Performs the conversion.
source§

### impl<T, U> TryInto<U> for Twhere
U: TryFrom<T>,

§

#### type Error = <U as TryFrom<T>>::Error

The type returned in the event of a conversion error.
const: unstable · source§

#### fn try_into(self) -> Result<U, <U as TryFrom<T>>::Error>

Performs the conversion.
source§

### impl<T, Right> ClosedAdd<Right> for Twhere
T: Add<Right, Output = T> + AddAssign<Right>,

source§

### impl<T, Right> ClosedDiv<Right> for Twhere
T: Div<Right, Output = T> + DivAssign<Right>,

source§

### impl<T, Right> ClosedMul<Right> for Twhere
T: Mul<Right, Output = T> + MulAssign<Right>,

source§

### impl<T> ClosedNeg for Twhere
T: Neg<Output = T>,

source§

### impl<T, Right> ClosedSub<Right> for Twhere
T: Sub<Right, Output = T> + SubAssign<Right>,