Struct nalgebra::geometry::Quaternion

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#[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.

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§coords: Vector4<T>

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

Implementations§

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impl<T: SimdRealField> Quaternion<T>

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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.

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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.

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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();
assert_relative_eq!(q_normalized.norm(), 1.0);
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pub fn imag(&self) -> Vector3<T>

The imaginary part of this quaternion.

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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);
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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));
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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);
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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);
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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));
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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);
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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);
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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.norm_squared(), 30.0);
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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);
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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);
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impl<T: SimdRealField> Quaternion<T>

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

Attempt to inverse this quaternion.

This method also works with SIMD components.

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

Calculates square of a quaternion.

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pub fn half(&self) -> Self

Divides quaternion into two.

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pub fn sqrt(&self) -> Self

Calculates square root.

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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).

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pub fn pure(&self) -> Self

Convert quaternion to pure quaternion.

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

Left quaternionic division.

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

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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);
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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);
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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);
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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);
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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);
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pub fn tan(&self) -> Self
where 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);
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pub fn atan(&self) -> Self
where 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);
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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);
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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);
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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);
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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);
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pub fn tanh(&self) -> Self
where 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);
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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);
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impl<T> Quaternion<T>

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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.

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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));
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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));
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impl<T: SimdRealField> Quaternion<T>

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

Constructs a pure quaternion.

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pub fn from_parts<SB>(scalar: T, vector: Vector<T, U3, SB>) -> Self
where 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));
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pub fn from_real(r: T) -> Self

Constructs a real quaternion.

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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);
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impl<T: SimdRealField> Quaternion<T>

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

Creates a new quaternion from its polar decomposition.

Note that axis is assumed to be a unit vector.

Trait Implementations§

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

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type Epsilon = T

Used for specifying relative comparisons.
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fn default_epsilon() -> Self::Epsilon

The default tolerance to use when testing values that are close together. Read more
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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.
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fn abs_diff_ne(&self, other: &Rhs, epsilon: Self::Epsilon) -> bool

The inverse of AbsDiffEq::abs_diff_eq.
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impl<'a, 'b, T: SimdRealField> Add<&'b Quaternion<T>> for &'a Quaternion<T>

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type Output = Quaternion<T>

The resulting type after applying the + operator.
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fn add(self, rhs: &'b Quaternion<T>) -> Self::Output

Performs the + operation. Read more
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impl<'b, T: SimdRealField> Add<&'b Quaternion<T>> for Quaternion<T>

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type Output = Quaternion<T>

The resulting type after applying the + operator.
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fn add(self, rhs: &'b Quaternion<T>) -> Self::Output

Performs the + operation. Read more
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impl<'a, T: SimdRealField> Add<Quaternion<T>> for &'a Quaternion<T>

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type Output = Quaternion<T>

The resulting type after applying the + operator.
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fn add(self, rhs: Quaternion<T>) -> Self::Output

Performs the + operation. Read more
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impl<T: SimdRealField> Add for Quaternion<T>

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type Output = Quaternion<T>

The resulting type after applying the + operator.
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fn add(self, rhs: Quaternion<T>) -> Self::Output

Performs the + operation. Read more
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impl<'b, T: SimdRealField> AddAssign<&'b Quaternion<T>> for Quaternion<T>

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

Performs the += operation. Read more
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impl<T: SimdRealField> AddAssign for Quaternion<T>

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

Performs the += operation. Read more
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impl<T: Clone> Clone for Quaternion<T>

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

Returns a copy of the value. Read more
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fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source. Read more
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impl<T: Debug> Debug for Quaternion<T>

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

Formats the value using the given formatter. Read more
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impl<T: Scalar + Zero> Default for Quaternion<T>

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fn default() -> Self

Returns the “default value” for a type. Read more
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impl<T: Scalar + SimdValue> Deref for Quaternion<T>

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type Target = IJKW<T>

The resulting type after dereferencing.
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fn deref(&self) -> &Self::Target

Dereferences the value.
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impl<T: Scalar + SimdValue> DerefMut for Quaternion<T>

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

Mutably dereferences the value.
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impl<T: RealField + Display> Display for Quaternion<T>

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

Formats the value using the given formatter. Read more
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impl<'a, T: SimdRealField> Div<T> for &'a Quaternion<T>

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type Output = Quaternion<T>

The resulting type after applying the / operator.
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fn div(self, n: T) -> Self::Output

Performs the / operation. Read more
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impl<T: SimdRealField> Div<T> for Quaternion<T>

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type Output = Quaternion<T>

The resulting type after applying the / operator.
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fn div(self, n: T) -> Self::Output

Performs the / operation. Read more
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impl<T: SimdRealField> DivAssign<T> for Quaternion<T>

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fn div_assign(&mut self, n: T)

Performs the /= operation. Read more
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impl<T> From<[Quaternion<<T as SimdValue>::Element>; 16]> for Quaternion<T>

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

Converts to this type from the input type.
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impl<T> From<[Quaternion<<T as SimdValue>::Element>; 2]> for Quaternion<T>

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

Converts to this type from the input type.
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impl<T> From<[Quaternion<<T as SimdValue>::Element>; 4]> for Quaternion<T>

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

Converts to this type from the input type.
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impl<T> From<[Quaternion<<T as SimdValue>::Element>; 8]> for Quaternion<T>

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

Converts to this type from the input type.
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impl<T: Scalar> From<[T; 4]> for Quaternion<T>

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

Converts to this type from the input type.
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impl From<DQuat> for Quaternion<f64>

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fn from(e: DQuat) -> Quaternion<f64>

Converts to this type from the input type.
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impl<T: Scalar> From<Matrix<T, Const<4>, Const<1>, ArrayStorage<T, 4, 1>>> for Quaternion<T>

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

Converts to this type from the input type.
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impl From<Quat> for Quaternion<f32>

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fn from(e: Quat) -> Quaternion<f32>

Converts to this type from the input type.
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impl From<Quaternion<f32>> for Quat

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fn from(e: Quaternion<f32>) -> Quat

Converts to this type from the input type.
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impl From<Quaternion<f64>> for DQuat

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fn from(e: Quaternion<f64>) -> DQuat

Converts to this type from the input type.
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impl<T: Scalar + Hash> Hash for Quaternion<T>

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

Feeds this value into the given Hasher. Read more
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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
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impl<T: Scalar> Index<usize> for Quaternion<T>

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type Output = T

The returned type after indexing.
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fn index(&self, i: usize) -> &Self::Output

Performs the indexing (container[index]) operation. Read more
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impl<T: Scalar> IndexMut<usize> for Quaternion<T>

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

Performs the mutable indexing (container[index]) operation. Read more
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impl<'a, 'b, T: SimdRealField> Mul<&'b Quaternion<T>> for &'a Quaternion<T>

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type Output = Quaternion<T>

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b Quaternion<T>) -> Self::Output

Performs the * operation. Read more
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impl<'b, T: SimdRealField> Mul<&'b Quaternion<T>> for Quaternion<T>

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type Output = Quaternion<T>

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b Quaternion<T>) -> Self::Output

Performs the * operation. Read more
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impl<'b> Mul<&'b Quaternion<f32>> for f32

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type Output = Quaternion<f32>

The resulting type after applying the * operator.
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fn mul(self, right: &'b Quaternion<f32>) -> Self::Output

Performs the * operation. Read more
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impl<'b> Mul<&'b Quaternion<f64>> for f64

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type Output = Quaternion<f64>

The resulting type after applying the * operator.
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fn mul(self, right: &'b Quaternion<f64>) -> Self::Output

Performs the * operation. Read more
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impl<'a, T: SimdRealField> Mul<Quaternion<T>> for &'a Quaternion<T>

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type Output = Quaternion<T>

The resulting type after applying the * operator.
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fn mul(self, rhs: Quaternion<T>) -> Self::Output

Performs the * operation. Read more
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impl Mul<Quaternion<f32>> for f32

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type Output = Quaternion<f32>

The resulting type after applying the * operator.
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fn mul(self, right: Quaternion<f32>) -> Self::Output

Performs the * operation. Read more
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impl Mul<Quaternion<f64>> for f64

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type Output = Quaternion<f64>

The resulting type after applying the * operator.
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fn mul(self, right: Quaternion<f64>) -> Self::Output

Performs the * operation. Read more
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impl<'a, T: SimdRealField> Mul<T> for &'a Quaternion<T>

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type Output = Quaternion<T>

The resulting type after applying the * operator.
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fn mul(self, n: T) -> Self::Output

Performs the * operation. Read more
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impl<T: SimdRealField> Mul<T> for Quaternion<T>

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type Output = Quaternion<T>

The resulting type after applying the * operator.
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fn mul(self, n: T) -> Self::Output

Performs the * operation. Read more
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impl<T: SimdRealField> Mul for Quaternion<T>

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type Output = Quaternion<T>

The resulting type after applying the * operator.
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fn mul(self, rhs: Quaternion<T>) -> Self::Output

Performs the * operation. Read more
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impl<'b, T: SimdRealField> MulAssign<&'b Quaternion<T>> for Quaternion<T>

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

Performs the *= operation. Read more
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impl<T: SimdRealField> MulAssign<T> for Quaternion<T>

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fn mul_assign(&mut self, n: T)

Performs the *= operation. Read more
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impl<T: SimdRealField> MulAssign for Quaternion<T>

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

Performs the *= operation. Read more
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impl<'a, T: SimdRealField> Neg for &'a Quaternion<T>

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type Output = Quaternion<T>

The resulting type after applying the - operator.
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fn neg(self) -> Self::Output

Performs the unary - operation. Read more
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impl<T: SimdRealField> Neg for Quaternion<T>

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type Output = Quaternion<T>

The resulting type after applying the - operator.
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fn neg(self) -> Self::Output

Performs the unary - operation. Read more
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impl<T: SimdRealField> Normed for Quaternion<T>

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type Norm = <T as SimdComplexField>::SimdRealField

The type of the norm.
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fn norm(&self) -> T::SimdRealField

Computes the norm.
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fn norm_squared(&self) -> T::SimdRealField

Computes the squared norm.
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fn scale_mut(&mut self, n: Self::Norm)

Multiply self by n.
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fn unscale_mut(&mut self, n: Self::Norm)

Divides self by n.
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impl<T: SimdRealField> One for Quaternion<T>

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fn one() -> Self

Returns the multiplicative identity element of Self, 1. Read more
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fn set_one(&mut self)

Sets self to the multiplicative identity element of Self, 1.
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fn is_one(&self) -> bool
where Self: PartialEq,

Returns true if self is equal to the multiplicative identity. Read more
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impl<T: Scalar> PartialEq for Quaternion<T>

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

This method tests for self and other values to be equal, and is used by ==.
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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.
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impl<T: RealField + RelativeEq<Epsilon = T>> RelativeEq for Quaternion<T>

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fn default_max_relative() -> Self::Epsilon

The default relative tolerance for testing values that are far-apart. Read more
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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.
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fn relative_ne( &self, other: &Rhs, epsilon: Self::Epsilon, max_relative: Self::Epsilon ) -> bool

The inverse of RelativeEq::relative_eq.
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impl<T: Scalar + SimdValue> SimdValue for Quaternion<T>
where T::Element: Scalar,

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const LANES: usize = T::LANES

The number of lanes of this SIMD value.
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type Element = Quaternion<<T as SimdValue>::Element>

The type of the elements of each lane of this SIMD value.
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type SimdBool = <T as SimdValue>::SimdBool

Type of the result of comparing two SIMD values like self.
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fn splat(val: Self::Element) -> Self

Initializes an SIMD value with each lanes set to val.
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fn extract(&self, i: usize) -> Self::Element

Extracts the i-th lane of self. Read more
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unsafe fn extract_unchecked(&self, i: usize) -> Self::Element

Extracts the i-th lane of self without bound-checking. Read more
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fn replace(&mut self, i: usize, val: Self::Element)

Replaces the i-th lane of self by val. Read more
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unsafe fn replace_unchecked(&mut self, i: usize, val: Self::Element)

Replaces the i-th lane of self by val without bound-checking. Read more
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fn select(self, cond: Self::SimdBool, other: Self) -> Self

Merges self and other depending on the lanes of cond. Read more
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fn map_lanes(self, f: impl Fn(Self::Element) -> Self::Element) -> Self
where Self: Clone,

Applies a function to each lane of self. Read more
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fn zip_map_lanes( self, b: Self, f: impl Fn(Self::Element, Self::Element) -> Self::Element ) -> Self
where Self: Clone,

Applies a function to each lane of self paired with the corresponding lane of b. Read more
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impl<'a, 'b, T: SimdRealField> Sub<&'b Quaternion<T>> for &'a Quaternion<T>

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type Output = Quaternion<T>

The resulting type after applying the - operator.
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fn sub(self, rhs: &'b Quaternion<T>) -> Self::Output

Performs the - operation. Read more
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impl<'b, T: SimdRealField> Sub<&'b Quaternion<T>> for Quaternion<T>

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type Output = Quaternion<T>

The resulting type after applying the - operator.
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fn sub(self, rhs: &'b Quaternion<T>) -> Self::Output

Performs the - operation. Read more
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impl<'a, T: SimdRealField> Sub<Quaternion<T>> for &'a Quaternion<T>

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type Output = Quaternion<T>

The resulting type after applying the - operator.
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fn sub(self, rhs: Quaternion<T>) -> Self::Output

Performs the - operation. Read more
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impl<T: SimdRealField> Sub for Quaternion<T>

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type Output = Quaternion<T>

The resulting type after applying the - operator.
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fn sub(self, rhs: Quaternion<T>) -> Self::Output

Performs the - operation. Read more
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impl<'b, T: SimdRealField> SubAssign<&'b Quaternion<T>> for Quaternion<T>

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

Performs the -= operation. Read more
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impl<T: SimdRealField> SubAssign for Quaternion<T>

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

Performs the -= operation. Read more
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impl<T1, T2> SubsetOf<Quaternion<T2>> for Quaternion<T1>
where T1: Scalar, T2: Scalar + SupersetOf<T1>,

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

The inclusion map: converts self to the equivalent element of its superset.
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fn is_in_subset(q: &Quaternion<T2>) -> bool

Checks if element is actually part of the subset Self (and can be converted to it).
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fn from_superset_unchecked(q: &Quaternion<T2>) -> Self

Use with care! Same as self.to_superset but without any property checks. Always succeeds.
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fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset. Read more
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impl<T: RealField + UlpsEq<Epsilon = T>> UlpsEq for Quaternion<T>

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fn default_max_ulps() -> u32

The default ULPs to tolerate when testing values that are far-apart. Read more
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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.
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fn ulps_ne(&self, other: &Rhs, epsilon: Self::Epsilon, max_ulps: u32) -> bool

The inverse of UlpsEq::ulps_eq.
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impl<T: SimdRealField> Zero for Quaternion<T>

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fn zero() -> Self

Returns the additive identity element of Self, 0. Read more
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fn is_zero(&self) -> bool

Returns true if self is equal to the additive identity.
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fn set_zero(&mut self)

Sets self to the additive identity element of Self, 0.
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impl<T: Copy> Copy for Quaternion<T>

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

Auto Trait Implementations§

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impl<T> Freeze for Quaternion<T>
where T: Freeze,

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

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

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

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

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

Blanket Implementations§

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

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fn type_id(&self) -> TypeId

Gets the TypeId of self. Read more
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impl<T> Borrow<T> for T
where T: ?Sized,

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fn borrow(&self) -> &T

Immutably borrows from an owned value. Read more
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impl<T> BorrowMut<T> for T
where T: ?Sized,

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

Mutably borrows from an owned value. Read more
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impl<T> From<T> for T

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fn from(t: T) -> T

Returns the argument unchanged.

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impl<T, U> Into<U> for T
where U: From<T>,

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fn into(self) -> U

Calls U::from(self).

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

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impl<T> Same for T

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type Output = T

Should always be Self
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impl<SS, SP> SupersetOf<SS> for SP
where SS: SubsetOf<SP>,

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

The inverse inclusion map: attempts to construct self from the equivalent element of its superset. Read more
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fn is_in_subset(&self) -> bool

Checks if self is actually part of its subset T (and can be converted to it).
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fn to_subset_unchecked(&self) -> SS

Use with care! Same as self.to_subset but without any property checks. Always succeeds.
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fn from_subset(element: &SS) -> SP

The inclusion map: converts self to the equivalent element of its superset.
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impl<T> ToOwned for T
where T: Clone,

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type Owned = T

The resulting type after obtaining ownership.
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fn to_owned(&self) -> T

Creates owned data from borrowed data, usually by cloning. Read more
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fn clone_into(&self, target: &mut T)

Uses borrowed data to replace owned data, usually by cloning. Read more
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impl<T> ToString for T
where T: Display + ?Sized,

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default fn to_string(&self) -> String

Converts the given value to a String. Read more
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impl<T, U> TryFrom<U> for T
where U: Into<T>,

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type Error = Infallible

The type returned in the event of a conversion error.
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fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::Error>

Performs the conversion.
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impl<T, U> TryInto<U> for T
where U: TryFrom<T>,

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

The type returned in the event of a conversion error.
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fn try_into(self) -> Result<U, <U as TryFrom<T>>::Error>

Performs the conversion.
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impl<T, Right> ClosedAdd<Right> for T
where T: Add<Right, Output = T> + AddAssign<Right>,

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impl<T, Right> ClosedAddAssign<Right> for T
where T: ClosedAdd<Right> + AddAssign<Right>,

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

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impl<T, Right> ClosedDivAssign<Right> for T
where T: ClosedDiv<Right> + DivAssign<Right>,

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

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impl<T, Right> ClosedMulAssign<Right> for T
where T: ClosedMul<Right> + MulAssign<Right>,

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impl<T> ClosedNeg for T
where T: Neg<Output = T>,

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

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impl<T, Right> ClosedSubAssign<Right> for T
where T: ClosedSub<Right> + SubAssign<Right>,

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impl<T> Scalar for T
where T: 'static + Clone + PartialEq + Debug,