Struct nalgebra::geometry::Quaternion [−][src]
A quaternion. See the type alias UnitQuaternion = Unit<Quaternion>
for a quaternion
that may be used as a rotation.
Fields
coords: Vector4<N>
This quaternion as a 4D vector of coordinates in the [ x, y, z, w ]
storage order.
Implementations
impl<N: SimdRealField> Quaternion<N> where
N::Element: SimdRealField,
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impl<N: SimdRealField> Quaternion<N> where
N::Element: SimdRealField,
[src]pub fn into_owned(self) -> Self
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This method is a no-op and will be removed in a future release.
Moves this unit quaternion into one that owns its data.
pub fn clone_owned(&self) -> Self
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This method is a no-op and will be removed in a future release.
Clones this unit quaternion into one that owns its data.
#[must_use = "Did you mean to use normalize_mut()?"]pub fn normalize(&self) -> Self
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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);
pub fn imag(&self) -> Vector3<N>
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The imaginary part of this quaternion.
#[must_use = "Did you mean to use conjugate_mut()?"]pub fn conjugate(&self) -> Self
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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);
pub fn lerp(&self, other: &Self, t: N) -> Self
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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));
pub fn vector(
&self
) -> MatrixSlice<'_, N, U3, U1, RStride<N, U4, U1>, CStride<N, U4, U1>>
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&self
) -> MatrixSlice<'_, N, U3, U1, RStride<N, U4, U1>, CStride<N, 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);
pub fn scalar(&self) -> N
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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);
pub fn as_vector(&self) -> &Vector4<N>
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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));
pub fn norm(&self) -> N
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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);
pub fn magnitude(&self) -> N
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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);
pub fn norm_squared(&self) -> N
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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);
pub fn magnitude_squared(&self) -> N
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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);
pub fn dot(&self, rhs: &Self) -> N
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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);
impl<N: SimdRealField> Quaternion<N> where
N::Element: SimdRealField,
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impl<N: SimdRealField> Quaternion<N> where
N::Element: SimdRealField,
[src]#[must_use = "Did you mean to use try_inverse_mut()?"]pub fn try_inverse(&self) -> Option<Self> where
N: RealField,
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N: 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());
#[must_use = "Did you mean to use try_inverse_mut()?"]pub fn simd_try_inverse(&self) -> SimdOption<Self>
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Attempt to inverse this quaternion.
This method also works with SIMD components.
pub fn inner(&self, other: &Self) -> Self
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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);
pub fn outer(&self, other: &Self) -> Self
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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);
pub fn project(&self, other: &Self) -> Option<Self> where
N: RealField,
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N: 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);
pub fn reject(&self, other: &Self) -> Option<Self> where
N: RealField,
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N: 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);
pub fn polar_decomposition(&self) -> (N, N, Option<Unit<Vector3<N>>>) where
N: RealField,
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N: 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()));
pub fn ln(&self) -> Self
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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)
pub fn exp(&self) -> Self
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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)
pub fn exp_eps(&self, eps: N) -> Self
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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());
pub fn powf(&self, n: N) -> Self
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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);
pub fn as_vector_mut(&mut self) -> &mut Vector4<N>
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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);
pub fn vector_mut(
&mut self
) -> MatrixSliceMut<'_, N, U3, U1, RStride<N, U4, U1>, CStride<N, U4, U1>>
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&mut self
) -> MatrixSliceMut<'_, N, U3, U1, RStride<N, U4, U1>, CStride<N, 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);
pub fn conjugate_mut(&mut self)
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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);
pub fn try_inverse_mut(&mut self) -> N::SimdBool
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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());
pub fn normalize_mut(&mut self) -> N
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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);
pub fn squared(&self) -> Self
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Calculates square of a quaternion.
pub fn half(&self) -> Self
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Divides quaternion into two.
pub fn sqrt(&self) -> Self
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Calculates square root.
pub fn is_pure(&self) -> bool
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Check if the quaternion is pure.
A quaternion is pure if it has no real part (self.w == 0.0
).
pub fn pure(&self) -> Self
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Convert quaternion to pure quaternion.
pub fn left_div(&self, other: &Self) -> Option<Self> where
N: RealField,
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N: RealField,
Left quaternionic division.
Calculates B-1 * A where A = self, B = other.
pub fn right_div(&self, other: &Self) -> Option<Self> where
N: RealField,
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N: 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);
pub fn cos(&self) -> Self
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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);
pub fn acos(&self) -> Self
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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);
pub fn sin(&self) -> Self
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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);
pub fn asin(&self) -> Self
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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);
pub fn tan(&self) -> Self where
N: RealField,
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N: 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);
pub fn atan(&self) -> Self where
N: RealField,
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N: 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);
pub fn sinh(&self) -> Self
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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);
pub fn asinh(&self) -> Self
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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);
pub fn cosh(&self) -> Self
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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);
pub fn acosh(&self) -> Self
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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);
pub fn tanh(&self) -> Self where
N: RealField,
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N: 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);
pub fn atanh(&self) -> Self
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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);
impl<N: Scalar> Quaternion<N>
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impl<N: Scalar> Quaternion<N>
[src]pub fn from_vector(vector: Vector4<N>) -> Self
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Use ::from
instead.
Creates a quaternion from a 4D vector. The quaternion scalar part corresponds to the w
vector component.
pub fn new(w: N, i: N, j: N, k: N) -> Self
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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));
impl<N: SimdRealField> Quaternion<N>
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impl<N: SimdRealField> Quaternion<N>
[src]pub fn from_imag(vector: Vector3<N>) -> Self
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Constructs a pure quaternion.
pub fn from_parts<SB>(scalar: N, vector: Vector<N, U3, SB>) -> Self where
SB: Storage<N, U3>,
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SB: Storage<N, 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));
pub fn from_real(r: N) -> Self
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Constructs a real quaternion.
pub fn identity() -> Self
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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);
impl<N: SimdRealField> Quaternion<N> where
N::Element: SimdRealField,
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impl<N: SimdRealField> Quaternion<N> where
N::Element: SimdRealField,
[src]Trait Implementations
impl<N: RealField + AbsDiffEq<Epsilon = N>> AbsDiffEq<Quaternion<N>> for Quaternion<N>
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impl<N: RealField + AbsDiffEq<Epsilon = N>> AbsDiffEq<Quaternion<N>> for Quaternion<N>
[src]type Epsilon = N
Used for specifying relative comparisons.
fn default_epsilon() -> Self::Epsilon
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fn abs_diff_eq(&self, other: &Self, epsilon: Self::Epsilon) -> bool
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pub fn abs_diff_ne(&self, other: &Rhs, epsilon: Self::Epsilon) -> bool
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impl<'a, 'b, N: SimdRealField> Add<&'b Quaternion<N>> for &'a Quaternion<N> where
N::Element: SimdRealField,
DefaultAllocator: Allocator<N, U4, U1>,
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impl<'a, 'b, N: SimdRealField> Add<&'b Quaternion<N>> for &'a Quaternion<N> where
N::Element: SimdRealField,
DefaultAllocator: Allocator<N, U4, U1>,
[src]type Output = Quaternion<N>
The resulting type after applying the +
operator.
fn add(self, rhs: &'b Quaternion<N>) -> Self::Output
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impl<'b, N: SimdRealField> Add<&'b Quaternion<N>> for Quaternion<N> where
N::Element: SimdRealField,
DefaultAllocator: Allocator<N, U4, U1>,
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impl<'b, N: SimdRealField> Add<&'b Quaternion<N>> for Quaternion<N> where
N::Element: SimdRealField,
DefaultAllocator: Allocator<N, U4, U1>,
[src]type Output = Quaternion<N>
The resulting type after applying the +
operator.
fn add(self, rhs: &'b Quaternion<N>) -> Self::Output
[src]
impl<'a, N: SimdRealField> Add<Quaternion<N>> for &'a Quaternion<N> where
N::Element: SimdRealField,
DefaultAllocator: Allocator<N, U4, U1>,
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impl<'a, N: SimdRealField> Add<Quaternion<N>> for &'a Quaternion<N> where
N::Element: SimdRealField,
DefaultAllocator: Allocator<N, U4, U1>,
[src]type Output = Quaternion<N>
The resulting type after applying the +
operator.
fn add(self, rhs: Quaternion<N>) -> Self::Output
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impl<N: SimdRealField> Add<Quaternion<N>> for Quaternion<N> where
N::Element: SimdRealField,
DefaultAllocator: Allocator<N, U4, U1>,
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impl<N: SimdRealField> Add<Quaternion<N>> for Quaternion<N> where
N::Element: SimdRealField,
DefaultAllocator: Allocator<N, U4, U1>,
[src]type Output = Quaternion<N>
The resulting type after applying the +
operator.
fn add(self, rhs: Quaternion<N>) -> Self::Output
[src]
impl<'b, N: SimdRealField> AddAssign<&'b Quaternion<N>> for Quaternion<N> where
N::Element: SimdRealField,
DefaultAllocator: Allocator<N, U4, U1>,
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impl<'b, N: SimdRealField> AddAssign<&'b Quaternion<N>> for Quaternion<N> where
N::Element: SimdRealField,
DefaultAllocator: Allocator<N, U4, U1>,
[src]fn add_assign(&mut self, rhs: &'b Quaternion<N>)
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impl<N: SimdRealField> AddAssign<Quaternion<N>> for Quaternion<N> where
N::Element: SimdRealField,
DefaultAllocator: Allocator<N, U4, U1>,
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impl<N: SimdRealField> AddAssign<Quaternion<N>> for Quaternion<N> where
N::Element: SimdRealField,
DefaultAllocator: Allocator<N, U4, U1>,
[src]fn add_assign(&mut self, rhs: Quaternion<N>)
[src]
impl<N: Clone + Scalar> Clone for Quaternion<N>
[src]
impl<N: Clone + Scalar> Clone for Quaternion<N>
[src]fn clone(&self) -> Quaternion<N>
[src]
pub fn clone_from(&mut self, source: &Self)
1.0.0[src]
impl<N: Debug + Scalar> Debug for Quaternion<N>
[src]
impl<N: Debug + Scalar> Debug for Quaternion<N>
[src]impl<N: Scalar + SimdValue> Deref for Quaternion<N>
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impl<N: Scalar + SimdValue> Deref for Quaternion<N>
[src]impl<N: Scalar + SimdValue> DerefMut for Quaternion<N>
[src]
impl<N: Scalar + SimdValue> DerefMut for Quaternion<N>
[src]impl<'a, N: Scalar> Deserialize<'a> for Quaternion<N> where
Owned<N, U4>: Deserialize<'a>,
[src]
impl<'a, N: Scalar> Deserialize<'a> for Quaternion<N> where
Owned<N, U4>: Deserialize<'a>,
[src]fn deserialize<Des>(deserializer: Des) -> Result<Self, Des::Error> where
Des: Deserializer<'a>,
[src]
Des: Deserializer<'a>,
impl<N: RealField + Display> Display for Quaternion<N>
[src]
impl<N: RealField + Display> Display for Quaternion<N>
[src]impl<N: SimdRealField> Distribution<Quaternion<N>> for Standard where
Standard: Distribution<N>,
[src]
impl<N: SimdRealField> Distribution<Quaternion<N>> for Standard where
Standard: Distribution<N>,
[src]fn sample<'a, R: Rng + ?Sized>(&self, rng: &'a mut R) -> Quaternion<N>
[src]
pub fn sample_iter<R>(self, rng: R) -> DistIter<Self, R, T> where
R: Rng,
[src]
R: Rng,
impl<N: SimdRealField> Div<N> for Quaternion<N> where
N::Element: SimdRealField,
[src]
impl<N: SimdRealField> Div<N> for Quaternion<N> where
N::Element: SimdRealField,
[src]type Output = Quaternion<N>
The resulting type after applying the /
operator.
fn div(self, n: N) -> Self::Output
[src]
impl<'a, N: SimdRealField> Div<N> for &'a Quaternion<N> where
N::Element: SimdRealField,
[src]
impl<'a, N: SimdRealField> Div<N> for &'a Quaternion<N> where
N::Element: SimdRealField,
[src]type Output = Quaternion<N>
The resulting type after applying the /
operator.
fn div(self, n: N) -> Self::Output
[src]
impl<N: SimdRealField> DivAssign<N> for Quaternion<N> where
N::Element: SimdRealField,
[src]
impl<N: SimdRealField> DivAssign<N> for Quaternion<N> where
N::Element: SimdRealField,
[src]fn div_assign(&mut self, n: N)
[src]
impl<N: Scalar + PrimitiveSimdValue> From<[Quaternion<<N as SimdValue>::Element>; 16]> for Quaternion<N> where
N: From<[<N as SimdValue>::Element; 16]>,
N::Element: Scalar + Copy,
[src]
impl<N: Scalar + PrimitiveSimdValue> From<[Quaternion<<N as SimdValue>::Element>; 16]> for Quaternion<N> where
N: From<[<N as SimdValue>::Element; 16]>,
N::Element: Scalar + Copy,
[src]impl<N: Scalar + PrimitiveSimdValue> From<[Quaternion<<N as SimdValue>::Element>; 2]> for Quaternion<N> where
N: From<[<N as SimdValue>::Element; 2]>,
N::Element: Scalar + Copy,
[src]
impl<N: Scalar + PrimitiveSimdValue> From<[Quaternion<<N as SimdValue>::Element>; 2]> for Quaternion<N> where
N: From<[<N as SimdValue>::Element; 2]>,
N::Element: Scalar + Copy,
[src]impl<N: Scalar + PrimitiveSimdValue> From<[Quaternion<<N as SimdValue>::Element>; 4]> for Quaternion<N> where
N: From<[<N as SimdValue>::Element; 4]>,
N::Element: Scalar + Copy,
[src]
impl<N: Scalar + PrimitiveSimdValue> From<[Quaternion<<N as SimdValue>::Element>; 4]> for Quaternion<N> where
N: From<[<N as SimdValue>::Element; 4]>,
N::Element: Scalar + Copy,
[src]impl<N: Scalar + PrimitiveSimdValue> From<[Quaternion<<N as SimdValue>::Element>; 8]> for Quaternion<N> where
N: From<[<N as SimdValue>::Element; 8]>,
N::Element: Scalar + Copy,
[src]
impl<N: Scalar + PrimitiveSimdValue> From<[Quaternion<<N as SimdValue>::Element>; 8]> for Quaternion<N> where
N: From<[<N as SimdValue>::Element; 8]>,
N::Element: Scalar + Copy,
[src]impl<N: Scalar> From<Matrix<N, U4, U1, <DefaultAllocator as Allocator<N, U4, U1>>::Buffer>> for Quaternion<N>
[src]
impl<N: Scalar> From<Matrix<N, U4, U1, <DefaultAllocator as Allocator<N, U4, U1>>::Buffer>> for Quaternion<N>
[src]impl<N: Hash + Scalar> Hash for Quaternion<N>
[src]
impl<N: Hash + Scalar> Hash for Quaternion<N>
[src]impl<N: Scalar> Index<usize> for Quaternion<N>
[src]
impl<N: Scalar> Index<usize> for Quaternion<N>
[src]impl<N: Scalar> IndexMut<usize> for Quaternion<N>
[src]
impl<N: Scalar> IndexMut<usize> for Quaternion<N>
[src]impl<'a, 'b, N: SimdRealField> Mul<&'b Quaternion<N>> for &'a Quaternion<N> where
N::Element: SimdRealField,
DefaultAllocator: Allocator<N, U4, U1>,
[src]
impl<'a, 'b, N: SimdRealField> Mul<&'b Quaternion<N>> for &'a Quaternion<N> where
N::Element: SimdRealField,
DefaultAllocator: Allocator<N, U4, U1>,
[src]type Output = Quaternion<N>
The resulting type after applying the *
operator.
fn mul(self, rhs: &'b Quaternion<N>) -> Self::Output
[src]
impl<'b, N: SimdRealField> Mul<&'b Quaternion<N>> for Quaternion<N> where
N::Element: SimdRealField,
DefaultAllocator: Allocator<N, U4, U1>,
[src]
impl<'b, N: SimdRealField> Mul<&'b Quaternion<N>> for Quaternion<N> where
N::Element: SimdRealField,
DefaultAllocator: Allocator<N, U4, U1>,
[src]type Output = Quaternion<N>
The resulting type after applying the *
operator.
fn mul(self, rhs: &'b Quaternion<N>) -> Self::Output
[src]
impl<'b> Mul<&'b Quaternion<f32>> for f32
[src]
impl<'b> Mul<&'b Quaternion<f32>> for f32
[src]type Output = Quaternion<f32>
The resulting type after applying the *
operator.
fn mul(self, right: &'b Quaternion<f32>) -> Self::Output
[src]
impl<'b> Mul<&'b Quaternion<f64>> for f64
[src]
impl<'b> Mul<&'b Quaternion<f64>> for f64
[src]type Output = Quaternion<f64>
The resulting type after applying the *
operator.
fn mul(self, right: &'b Quaternion<f64>) -> Self::Output
[src]
impl<N: SimdRealField> Mul<N> for Quaternion<N> where
N::Element: SimdRealField,
[src]
impl<N: SimdRealField> Mul<N> for Quaternion<N> where
N::Element: SimdRealField,
[src]type Output = Quaternion<N>
The resulting type after applying the *
operator.
fn mul(self, n: N) -> Self::Output
[src]
impl<'a, N: SimdRealField> Mul<N> for &'a Quaternion<N> where
N::Element: SimdRealField,
[src]
impl<'a, N: SimdRealField> Mul<N> for &'a Quaternion<N> where
N::Element: SimdRealField,
[src]type Output = Quaternion<N>
The resulting type after applying the *
operator.
fn mul(self, n: N) -> Self::Output
[src]
impl<'a, N: SimdRealField> Mul<Quaternion<N>> for &'a Quaternion<N> where
N::Element: SimdRealField,
DefaultAllocator: Allocator<N, U4, U1>,
[src]
impl<'a, N: SimdRealField> Mul<Quaternion<N>> for &'a Quaternion<N> where
N::Element: SimdRealField,
DefaultAllocator: Allocator<N, U4, U1>,
[src]type Output = Quaternion<N>
The resulting type after applying the *
operator.
fn mul(self, rhs: Quaternion<N>) -> Self::Output
[src]
impl<N: SimdRealField> Mul<Quaternion<N>> for Quaternion<N> where
N::Element: SimdRealField,
DefaultAllocator: Allocator<N, U4, U1>,
[src]
impl<N: SimdRealField> Mul<Quaternion<N>> for Quaternion<N> where
N::Element: SimdRealField,
DefaultAllocator: Allocator<N, U4, U1>,
[src]type Output = Quaternion<N>
The resulting type after applying the *
operator.
fn mul(self, rhs: Quaternion<N>) -> Self::Output
[src]
impl Mul<Quaternion<f32>> for f32
[src]
impl Mul<Quaternion<f32>> for f32
[src]type Output = Quaternion<f32>
The resulting type after applying the *
operator.
fn mul(self, right: Quaternion<f32>) -> Self::Output
[src]
impl Mul<Quaternion<f64>> for f64
[src]
impl Mul<Quaternion<f64>> for f64
[src]type Output = Quaternion<f64>
The resulting type after applying the *
operator.
fn mul(self, right: Quaternion<f64>) -> Self::Output
[src]
impl<'b, N: SimdRealField> MulAssign<&'b Quaternion<N>> for Quaternion<N> where
N::Element: SimdRealField,
DefaultAllocator: Allocator<N, U4, U1>,
[src]
impl<'b, N: SimdRealField> MulAssign<&'b Quaternion<N>> for Quaternion<N> where
N::Element: SimdRealField,
DefaultAllocator: Allocator<N, U4, U1>,
[src]fn mul_assign(&mut self, rhs: &'b Quaternion<N>)
[src]
impl<N: SimdRealField> MulAssign<N> for Quaternion<N> where
N::Element: SimdRealField,
[src]
impl<N: SimdRealField> MulAssign<N> for Quaternion<N> where
N::Element: SimdRealField,
[src]fn mul_assign(&mut self, n: N)
[src]
impl<N: SimdRealField> MulAssign<Quaternion<N>> for Quaternion<N> where
N::Element: SimdRealField,
DefaultAllocator: Allocator<N, U4, U1>,
[src]
impl<N: SimdRealField> MulAssign<Quaternion<N>> for Quaternion<N> where
N::Element: SimdRealField,
DefaultAllocator: Allocator<N, U4, U1>,
[src]fn mul_assign(&mut self, rhs: Quaternion<N>)
[src]
impl<N: SimdRealField> Neg for Quaternion<N> where
N::Element: SimdRealField,
[src]
impl<N: SimdRealField> Neg for Quaternion<N> where
N::Element: SimdRealField,
[src]type Output = Quaternion<N>
The resulting type after applying the -
operator.
fn neg(self) -> Self::Output
[src]
impl<'a, N: SimdRealField> Neg for &'a Quaternion<N> where
N::Element: SimdRealField,
[src]
impl<'a, N: SimdRealField> Neg for &'a Quaternion<N> where
N::Element: SimdRealField,
[src]type Output = Quaternion<N>
The resulting type after applying the -
operator.
fn neg(self) -> Self::Output
[src]
impl<N: SimdRealField> Normed for Quaternion<N>
[src]
impl<N: SimdRealField> Normed for Quaternion<N>
[src]type Norm = N::SimdRealField
The type of the norm.
fn norm(&self) -> N::SimdRealField
[src]
fn norm_squared(&self) -> N::SimdRealField
[src]
fn scale_mut(&mut self, n: Self::Norm)
[src]
fn unscale_mut(&mut self, n: Self::Norm)
[src]
impl<N: SimdRealField> One for Quaternion<N> where
N::Element: SimdRealField,
[src]
impl<N: SimdRealField> One for Quaternion<N> where
N::Element: SimdRealField,
[src]impl<N: PartialEq + Scalar> PartialEq<Quaternion<N>> for Quaternion<N>
[src]
impl<N: PartialEq + Scalar> PartialEq<Quaternion<N>> for Quaternion<N>
[src]fn eq(&self, other: &Quaternion<N>) -> bool
[src]
fn ne(&self, other: &Quaternion<N>) -> bool
[src]
impl<N: RealField + RelativeEq<Epsilon = N>> RelativeEq<Quaternion<N>> for Quaternion<N>
[src]
impl<N: RealField + RelativeEq<Epsilon = N>> RelativeEq<Quaternion<N>> for Quaternion<N>
[src]fn default_max_relative() -> Self::Epsilon
[src]
fn relative_eq(
&self,
other: &Self,
epsilon: Self::Epsilon,
max_relative: Self::Epsilon
) -> bool
[src]
&self,
other: &Self,
epsilon: Self::Epsilon,
max_relative: Self::Epsilon
) -> bool
pub fn relative_ne(
&self,
other: &Rhs,
epsilon: Self::Epsilon,
max_relative: Self::Epsilon
) -> bool
[src]
&self,
other: &Rhs,
epsilon: Self::Epsilon,
max_relative: Self::Epsilon
) -> bool
impl<N: Scalar + SimdValue> SimdValue for Quaternion<N> where
N::Element: Scalar,
[src]
impl<N: Scalar + SimdValue> SimdValue for Quaternion<N> where
N::Element: Scalar,
[src]type Element = Quaternion<N::Element>
The type of the elements of each lane of this SIMD value.
type SimdBool = N::SimdBool
Type of the result of comparing two SIMD values like self
.
fn lanes() -> usize
[src]
fn splat(val: Self::Element) -> Self
[src]
fn extract(&self, i: usize) -> Self::Element
[src]
unsafe fn extract_unchecked(&self, i: usize) -> Self::Element
[src]
fn replace(&mut self, i: usize, val: Self::Element)
[src]
unsafe fn replace_unchecked(&mut self, i: usize, val: Self::Element)
[src]
fn select(self, cond: Self::SimdBool, other: Self) -> Self
[src]
pub fn map_lanes(self, f: impl Fn(Self::Element) -> Self::Element) -> Self where
Self: Clone,
[src]
Self: Clone,
pub fn zip_map_lanes(
self,
b: Self,
f: impl Fn(Self::Element, Self::Element) -> Self::Element
) -> Self where
Self: Clone,
[src]
self,
b: Self,
f: impl Fn(Self::Element, Self::Element) -> Self::Element
) -> Self where
Self: Clone,
impl<'a, 'b, N: SimdRealField> Sub<&'b Quaternion<N>> for &'a Quaternion<N> where
N::Element: SimdRealField,
DefaultAllocator: Allocator<N, U4, U1>,
[src]
impl<'a, 'b, N: SimdRealField> Sub<&'b Quaternion<N>> for &'a Quaternion<N> where
N::Element: SimdRealField,
DefaultAllocator: Allocator<N, U4, U1>,
[src]type Output = Quaternion<N>
The resulting type after applying the -
operator.
fn sub(self, rhs: &'b Quaternion<N>) -> Self::Output
[src]
impl<'b, N: SimdRealField> Sub<&'b Quaternion<N>> for Quaternion<N> where
N::Element: SimdRealField,
DefaultAllocator: Allocator<N, U4, U1>,
[src]
impl<'b, N: SimdRealField> Sub<&'b Quaternion<N>> for Quaternion<N> where
N::Element: SimdRealField,
DefaultAllocator: Allocator<N, U4, U1>,
[src]type Output = Quaternion<N>
The resulting type after applying the -
operator.
fn sub(self, rhs: &'b Quaternion<N>) -> Self::Output
[src]
impl<'a, N: SimdRealField> Sub<Quaternion<N>> for &'a Quaternion<N> where
N::Element: SimdRealField,
DefaultAllocator: Allocator<N, U4, U1>,
[src]
impl<'a, N: SimdRealField> Sub<Quaternion<N>> for &'a Quaternion<N> where
N::Element: SimdRealField,
DefaultAllocator: Allocator<N, U4, U1>,
[src]type Output = Quaternion<N>
The resulting type after applying the -
operator.
fn sub(self, rhs: Quaternion<N>) -> Self::Output
[src]
impl<N: SimdRealField> Sub<Quaternion<N>> for Quaternion<N> where
N::Element: SimdRealField,
DefaultAllocator: Allocator<N, U4, U1>,
[src]
impl<N: SimdRealField> Sub<Quaternion<N>> for Quaternion<N> where
N::Element: SimdRealField,
DefaultAllocator: Allocator<N, U4, U1>,
[src]type Output = Quaternion<N>
The resulting type after applying the -
operator.
fn sub(self, rhs: Quaternion<N>) -> Self::Output
[src]
impl<'b, N: SimdRealField> SubAssign<&'b Quaternion<N>> for Quaternion<N> where
N::Element: SimdRealField,
DefaultAllocator: Allocator<N, U4, U1>,
[src]
impl<'b, N: SimdRealField> SubAssign<&'b Quaternion<N>> for Quaternion<N> where
N::Element: SimdRealField,
DefaultAllocator: Allocator<N, U4, U1>,
[src]fn sub_assign(&mut self, rhs: &'b Quaternion<N>)
[src]
impl<N: SimdRealField> SubAssign<Quaternion<N>> for Quaternion<N> where
N::Element: SimdRealField,
DefaultAllocator: Allocator<N, U4, U1>,
[src]
impl<N: SimdRealField> SubAssign<Quaternion<N>> for Quaternion<N> where
N::Element: SimdRealField,
DefaultAllocator: Allocator<N, U4, U1>,
[src]fn sub_assign(&mut self, rhs: Quaternion<N>)
[src]
impl<N1, N2> SubsetOf<Quaternion<N2>> for Quaternion<N1> where
N1: SimdRealField,
N2: SimdRealField + SupersetOf<N1>,
[src]
impl<N1, N2> SubsetOf<Quaternion<N2>> for Quaternion<N1> where
N1: SimdRealField,
N2: SimdRealField + SupersetOf<N1>,
[src]fn to_superset(&self) -> Quaternion<N2>
[src]
fn is_in_subset(q: &Quaternion<N2>) -> bool
[src]
fn from_superset_unchecked(q: &Quaternion<N2>) -> Self
[src]
pub fn from_superset(element: &T) -> Option<Self>
[src]
impl<N: RealField + UlpsEq<Epsilon = N>> UlpsEq<Quaternion<N>> for Quaternion<N>
[src]
impl<N: RealField + UlpsEq<Epsilon = N>> UlpsEq<Quaternion<N>> for Quaternion<N>
[src]impl<N: SimdRealField> Zero for Quaternion<N> where
N::Element: SimdRealField,
[src]
impl<N: SimdRealField> Zero for Quaternion<N> where
N::Element: SimdRealField,
[src]impl<N: Copy + Scalar> Copy for Quaternion<N>
[src]
impl<N: Eq + Scalar> Eq for Quaternion<N>
[src]
impl<N: Scalar> StructuralEq for Quaternion<N>
[src]
impl<N: Scalar> StructuralPartialEq for Quaternion<N>
[src]
Auto Trait Implementations
impl<N> RefUnwindSafe for Quaternion<N> where
N: RefUnwindSafe,
N: RefUnwindSafe,
impl<N> Send for Quaternion<N> where
N: Send,
N: Send,
impl<N> Sync for Quaternion<N> where
N: Sync,
N: Sync,
impl<N> Unpin for Quaternion<N> where
N: Unpin,
N: Unpin,
impl<N> UnwindSafe for Quaternion<N> where
N: UnwindSafe,
N: UnwindSafe,
Blanket Implementations
impl<SS, SP> SupersetOf<SS> for SP where
SS: SubsetOf<SP>,
[src]
impl<SS, SP> SupersetOf<SS> for SP where
SS: SubsetOf<SP>,
[src]pub fn to_subset(&self) -> Option<SS>
[src]
pub fn is_in_subset(&self) -> bool
[src]
pub fn to_subset_unchecked(&self) -> SS
[src]
pub fn from_subset(element: &SS) -> SP
[src]
impl<T, Right> ClosedAdd<Right> for T where
T: Add<Right, Output = T> + AddAssign<Right>,
[src]
T: Add<Right, Output = T> + AddAssign<Right>,
impl<T, Right> ClosedDiv<Right> for T where
T: Div<Right, Output = T> + DivAssign<Right>,
[src]
T: Div<Right, Output = T> + DivAssign<Right>,
impl<T, Right> ClosedMul<Right> for T where
T: Mul<Right, Output = T> + MulAssign<Right>,
[src]
T: Mul<Right, Output = T> + MulAssign<Right>,
impl<T> ClosedNeg for T where
T: Neg<Output = T>,
[src]
T: Neg<Output = T>,
impl<T, Right> ClosedSub<Right> for T where
T: Sub<Right, Output = T> + SubAssign<Right>,
[src]
T: Sub<Right, Output = T> + SubAssign<Right>,
impl<T> DeserializeOwned for T where
T: for<'de> Deserialize<'de>,
[src]
T: for<'de> Deserialize<'de>,