[−][src]Struct na::Quaternion
A quaternion. See the type alias UnitQuaternion = Unit<Quaternion>
for a quaternion
that may be used as a rotation.
Fields
coords: Matrix<N, U4, U1, <DefaultAllocator as Allocator<N, U4, U1>>::Buffer>
This quaternion as a 4D vector of coordinates in the [ x, y, z, w ]
storage order.
Implementations
impl<N> Quaternion<N> where
N: SimdRealField,
<N as SimdValue>::Element: SimdRealField,
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N: SimdRealField,
<N as SimdValue>::Element: SimdRealField,
pub fn into_owned(self) -> Quaternion<N>
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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) -> Quaternion<N>
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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) -> Quaternion<N>
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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
) -> Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3, U1>>::Buffer>
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&self
) -> Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3, U1>>::Buffer>
The imaginary part of this quaternion.
#[must_use = "Did you mean to use conjugate_mut()?"]pub fn conjugate(&self) -> Quaternion<N>
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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: &Quaternion<N>, t: N) -> Quaternion<N>
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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
) -> Matrix<N, U3, U1, SliceStorage<'_, N, U3, U1, <<DefaultAllocator as Allocator<N, U4, U1>>::Buffer as Storage<N, U4, U1>>::RStride, <<DefaultAllocator as Allocator<N, U4, U1>>::Buffer as Storage<N, U4, U1>>::CStride>>
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&self
) -> Matrix<N, U3, U1, SliceStorage<'_, N, U3, U1, <<DefaultAllocator as Allocator<N, U4, U1>>::Buffer as Storage<N, U4, U1>>::RStride, <<DefaultAllocator as Allocator<N, U4, U1>>::Buffer as Storage<N, U4, U1>>::CStride>>
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
) -> &Matrix<N, U4, U1, <DefaultAllocator as Allocator<N, U4, U1>>::Buffer>
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&self
) -> &Matrix<N, U4, U1, <DefaultAllocator as Allocator<N, U4, U1>>::Buffer>
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: &Quaternion<N>) -> 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> Quaternion<N> where
N: SimdRealField,
<N as SimdValue>::Element: SimdRealField,
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N: SimdRealField,
<N as SimdValue>::Element: SimdRealField,
#[must_use = "Did you mean to use try_inverse_mut()?"]pub fn try_inverse(&self) -> Option<Quaternion<N>> 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<Quaternion<N>>
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Attempt to inverse this quaternion.
This method also works with SIMD components.
pub fn inner(&self, other: &Quaternion<N>) -> Quaternion<N>
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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: &Quaternion<N>) -> Quaternion<N>
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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: &Quaternion<N>) -> Option<Quaternion<N>> 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: &Quaternion<N>) -> Option<Quaternion<N>> 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<Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3, U1>>::Buffer>>>) where
N: RealField,
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&self
) -> (N, N, Option<Unit<Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3, U1>>::Buffer>>>) where
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) -> Quaternion<N>
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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) -> Quaternion<N>
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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) -> Quaternion<N>
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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) -> Quaternion<N>
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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 Matrix<N, U4, U1, <DefaultAllocator as Allocator<N, U4, U1>>::Buffer>
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&mut self
) -> &mut Matrix<N, U4, U1, <DefaultAllocator as Allocator<N, U4, U1>>::Buffer>
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
) -> Matrix<N, U3, U1, SliceStorageMut<'_, N, U3, U1, <<DefaultAllocator as Allocator<N, U4, U1>>::Buffer as Storage<N, U4, U1>>::RStride, <<DefaultAllocator as Allocator<N, U4, U1>>::Buffer as Storage<N, U4, U1>>::CStride>>
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&mut self
) -> Matrix<N, U3, U1, SliceStorageMut<'_, N, U3, U1, <<DefaultAllocator as Allocator<N, U4, U1>>::Buffer as Storage<N, U4, U1>>::RStride, <<DefaultAllocator as Allocator<N, U4, U1>>::Buffer as Storage<N, U4, U1>>::CStride>>
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 as SimdValue>::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) -> Quaternion<N>
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Calculates square of a quaternion.
pub fn half(&self) -> Quaternion<N>
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Divides quaternion into two.
pub fn sqrt(&self) -> Quaternion<N>
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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) -> Quaternion<N>
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Convert quaternion to pure quaternion.
pub fn left_div(&self, other: &Quaternion<N>) -> Option<Quaternion<N>> 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: &Quaternion<N>) -> Option<Quaternion<N>> 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) -> Quaternion<N>
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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) -> Quaternion<N>
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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) -> Quaternion<N>
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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) -> Quaternion<N>
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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) -> Quaternion<N> 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) -> Quaternion<N> 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) -> Quaternion<N>
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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) -> Quaternion<N>
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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) -> Quaternion<N>
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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) -> Quaternion<N>
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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) -> Quaternion<N> 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) -> Quaternion<N>
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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> Quaternion<N> where
N: Scalar + SimdValue,
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N: Scalar + SimdValue,
pub fn from_vector(
vector: Matrix<N, U4, U1, <DefaultAllocator as Allocator<N, U4, U1>>::Buffer>
) -> Quaternion<N>
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vector: Matrix<N, U4, U1, <DefaultAllocator as Allocator<N, U4, U1>>::Buffer>
) -> Quaternion<N>
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) -> Quaternion<N>
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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> Quaternion<N> where
N: SimdRealField,
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N: SimdRealField,
pub fn from_imag(
vector: Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3, U1>>::Buffer>
) -> Quaternion<N>
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vector: Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3, U1>>::Buffer>
) -> Quaternion<N>
Constructs a pure quaternion.
pub fn from_parts<SB>(scalar: N, vector: Matrix<N, U3, U1, SB>) -> Quaternion<N> where
SB: Storage<N, U3, U1>,
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SB: Storage<N, U3, U1>,
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) -> Quaternion<N>
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Constructs a real quaternion.
pub fn identity() -> Quaternion<N>
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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> Quaternion<N> where
N: SimdRealField,
<N as SimdValue>::Element: SimdRealField,
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N: SimdRealField,
<N as SimdValue>::Element: SimdRealField,
pub fn from_polar_decomposition<SB>(
scale: N,
theta: N,
axis: Unit<Matrix<N, U3, U1, SB>>
) -> Quaternion<N> where
SB: Storage<N, U3, U1>,
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scale: N,
theta: N,
axis: Unit<Matrix<N, U3, U1, SB>>
) -> Quaternion<N> where
SB: Storage<N, U3, U1>,
Creates a new quaternion from its polar decomposition.
Note that axis
is assumed to be a unit vector.
Trait Implementations
impl<N> AbsDiffEq<Quaternion<N>> for Quaternion<N> where
N: AbsDiffEq<N, Epsilon = N> + RealField,
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N: AbsDiffEq<N, Epsilon = N> + RealField,
type Epsilon = N
Used for specifying relative comparisons.
fn default_epsilon() -> <Quaternion<N> as AbsDiffEq<Quaternion<N>>>::Epsilon
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fn abs_diff_eq(
&self,
other: &Quaternion<N>,
epsilon: <Quaternion<N> as AbsDiffEq<Quaternion<N>>>::Epsilon
) -> bool
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&self,
other: &Quaternion<N>,
epsilon: <Quaternion<N> as AbsDiffEq<Quaternion<N>>>::Epsilon
) -> bool
fn abs_diff_ne(&self, other: &Rhs, epsilon: Self::Epsilon) -> bool
impl<'b, N> Add<&'b Quaternion<N>> for Quaternion<N> where
N: SimdRealField,
<N as SimdValue>::Element: SimdRealField,
DefaultAllocator: Allocator<N, U4, U1>,
DefaultAllocator: Allocator<N, U4, U1>,
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N: SimdRealField,
<N as SimdValue>::Element: SimdRealField,
DefaultAllocator: Allocator<N, U4, U1>,
DefaultAllocator: Allocator<N, U4, U1>,
type Output = Quaternion<N>
The resulting type after applying the +
operator.
fn add(
self,
rhs: &'b Quaternion<N>
) -> <Quaternion<N> as Add<&'b Quaternion<N>>>::Output
[src]
self,
rhs: &'b Quaternion<N>
) -> <Quaternion<N> as Add<&'b Quaternion<N>>>::Output
impl<'a, 'b, N> Add<&'b Quaternion<N>> for &'a Quaternion<N> where
N: SimdRealField,
<N as SimdValue>::Element: SimdRealField,
DefaultAllocator: Allocator<N, U4, U1>,
DefaultAllocator: Allocator<N, U4, U1>,
[src]
N: SimdRealField,
<N as SimdValue>::Element: SimdRealField,
DefaultAllocator: Allocator<N, U4, U1>,
DefaultAllocator: Allocator<N, U4, U1>,
type Output = Quaternion<N>
The resulting type after applying the +
operator.
fn add(
self,
rhs: &'b Quaternion<N>
) -> <&'a Quaternion<N> as Add<&'b Quaternion<N>>>::Output
[src]
self,
rhs: &'b Quaternion<N>
) -> <&'a Quaternion<N> as Add<&'b Quaternion<N>>>::Output
impl<'a, N> Add<Quaternion<N>> for &'a Quaternion<N> where
N: SimdRealField,
<N as SimdValue>::Element: SimdRealField,
DefaultAllocator: Allocator<N, U4, U1>,
DefaultAllocator: Allocator<N, U4, U1>,
[src]
N: SimdRealField,
<N as SimdValue>::Element: SimdRealField,
DefaultAllocator: Allocator<N, U4, U1>,
DefaultAllocator: Allocator<N, U4, U1>,
type Output = Quaternion<N>
The resulting type after applying the +
operator.
fn add(
self,
rhs: Quaternion<N>
) -> <&'a Quaternion<N> as Add<Quaternion<N>>>::Output
[src]
self,
rhs: Quaternion<N>
) -> <&'a Quaternion<N> as Add<Quaternion<N>>>::Output
impl<N> Add<Quaternion<N>> for Quaternion<N> where
N: SimdRealField,
<N as SimdValue>::Element: SimdRealField,
DefaultAllocator: Allocator<N, U4, U1>,
DefaultAllocator: Allocator<N, U4, U1>,
[src]
N: SimdRealField,
<N as SimdValue>::Element: SimdRealField,
DefaultAllocator: Allocator<N, U4, U1>,
DefaultAllocator: Allocator<N, U4, U1>,
type Output = Quaternion<N>
The resulting type after applying the +
operator.
fn add(
self,
rhs: Quaternion<N>
) -> <Quaternion<N> as Add<Quaternion<N>>>::Output
[src]
self,
rhs: Quaternion<N>
) -> <Quaternion<N> as Add<Quaternion<N>>>::Output
impl<'b, N> AddAssign<&'b Quaternion<N>> for Quaternion<N> where
N: SimdRealField,
<N as SimdValue>::Element: SimdRealField,
DefaultAllocator: Allocator<N, U4, U1>,
DefaultAllocator: Allocator<N, U4, U1>,
[src]
N: SimdRealField,
<N as SimdValue>::Element: SimdRealField,
DefaultAllocator: Allocator<N, U4, U1>,
DefaultAllocator: Allocator<N, U4, U1>,
fn add_assign(&mut self, rhs: &'b Quaternion<N>)
[src]
impl<N> AddAssign<Quaternion<N>> for Quaternion<N> where
N: SimdRealField,
<N as SimdValue>::Element: SimdRealField,
DefaultAllocator: Allocator<N, U4, U1>,
DefaultAllocator: Allocator<N, U4, U1>,
[src]
N: SimdRealField,
<N as SimdValue>::Element: SimdRealField,
DefaultAllocator: Allocator<N, U4, U1>,
DefaultAllocator: Allocator<N, U4, U1>,
fn add_assign(&mut self, rhs: Quaternion<N>)
[src]
impl<N> Clone for Quaternion<N> where
N: Scalar + SimdValue,
[src]
N: Scalar + SimdValue,
fn clone(&self) -> Quaternion<N>
[src]
fn clone_from(&mut self, source: &Self)
1.0.0[src]
impl<N> Copy for Quaternion<N> where
N: Scalar + Copy + SimdValue,
[src]
N: Scalar + Copy + SimdValue,
impl<N> Debug for Quaternion<N> where
N: Scalar + Debug + SimdValue,
[src]
N: Scalar + Debug + SimdValue,
impl<N> Default for Quaternion<N> where
N: RealField,
[src]
N: RealField,
fn default() -> Quaternion<N>
[src]
impl<N> Deref for Quaternion<N> where
N: Scalar + SimdValue,
[src]
N: Scalar + SimdValue,
type Target = IJKW<N>
The resulting type after dereferencing.
fn deref(&self) -> &<Quaternion<N> as Deref>::Target
[src]
impl<N> DerefMut for Quaternion<N> where
N: Scalar + SimdValue,
[src]
N: Scalar + SimdValue,
fn deref_mut(&mut self) -> &mut <Quaternion<N> as Deref>::Target
[src]
impl<N> Display for Quaternion<N> where
N: Display + RealField,
[src]
N: Display + RealField,
impl<'a, N> Div<N> for &'a Quaternion<N> where
N: SimdRealField,
<N as SimdValue>::Element: SimdRealField,
[src]
N: SimdRealField,
<N as SimdValue>::Element: SimdRealField,
type Output = Quaternion<N>
The resulting type after applying the /
operator.
fn div(self, n: N) -> <&'a Quaternion<N> as Div<N>>::Output
[src]
impl<N> Div<N> for Quaternion<N> where
N: SimdRealField,
<N as SimdValue>::Element: SimdRealField,
[src]
N: SimdRealField,
<N as SimdValue>::Element: SimdRealField,
type Output = Quaternion<N>
The resulting type after applying the /
operator.
fn div(self, n: N) -> <Quaternion<N> as Div<N>>::Output
[src]
impl<N> DivAssign<N> for Quaternion<N> where
N: SimdRealField,
<N as SimdValue>::Element: SimdRealField,
[src]
N: SimdRealField,
<N as SimdValue>::Element: SimdRealField,
fn div_assign(&mut self, n: N)
[src]
impl<N> Eq for Quaternion<N> where
N: Eq + SimdRealField,
<N as SimdValue>::Element: SimdRealField,
[src]
N: Eq + SimdRealField,
<N as SimdValue>::Element: SimdRealField,
impl<N> From<[Quaternion<<N as SimdValue>::Element>; 16]> for Quaternion<N> where
N: Scalar + PrimitiveSimdValue + From<[<N as SimdValue>::Element; 16]>,
<N as SimdValue>::Element: Scalar,
<N as SimdValue>::Element: Copy,
[src]
N: Scalar + PrimitiveSimdValue + From<[<N as SimdValue>::Element; 16]>,
<N as SimdValue>::Element: Scalar,
<N as SimdValue>::Element: Copy,
fn from(arr: [Quaternion<<N as SimdValue>::Element>; 16]) -> Quaternion<N>
[src]
impl<N> From<[Quaternion<<N as SimdValue>::Element>; 2]> for Quaternion<N> where
N: Scalar + PrimitiveSimdValue + From<[<N as SimdValue>::Element; 2]>,
<N as SimdValue>::Element: Scalar,
<N as SimdValue>::Element: Copy,
[src]
N: Scalar + PrimitiveSimdValue + From<[<N as SimdValue>::Element; 2]>,
<N as SimdValue>::Element: Scalar,
<N as SimdValue>::Element: Copy,
fn from(arr: [Quaternion<<N as SimdValue>::Element>; 2]) -> Quaternion<N>
[src]
impl<N> From<[Quaternion<<N as SimdValue>::Element>; 4]> for Quaternion<N> where
N: Scalar + PrimitiveSimdValue + From<[<N as SimdValue>::Element; 4]>,
<N as SimdValue>::Element: Scalar,
<N as SimdValue>::Element: Copy,
[src]
N: Scalar + PrimitiveSimdValue + From<[<N as SimdValue>::Element; 4]>,
<N as SimdValue>::Element: Scalar,
<N as SimdValue>::Element: Copy,
fn from(arr: [Quaternion<<N as SimdValue>::Element>; 4]) -> Quaternion<N>
[src]
impl<N> From<[Quaternion<<N as SimdValue>::Element>; 8]> for Quaternion<N> where
N: Scalar + PrimitiveSimdValue + From<[<N as SimdValue>::Element; 8]>,
<N as SimdValue>::Element: Scalar,
<N as SimdValue>::Element: Copy,
[src]
N: Scalar + PrimitiveSimdValue + From<[<N as SimdValue>::Element; 8]>,
<N as SimdValue>::Element: Scalar,
<N as SimdValue>::Element: Copy,
fn from(arr: [Quaternion<<N as SimdValue>::Element>; 8]) -> Quaternion<N>
[src]
impl<N> From<Matrix<N, U4, U1, <DefaultAllocator as Allocator<N, U4, U1>>::Buffer>> for Quaternion<N> where
N: Scalar + SimdValue,
[src]
N: Scalar + SimdValue,
fn from(
coords: Matrix<N, U4, U1, <DefaultAllocator as Allocator<N, U4, U1>>::Buffer>
) -> Quaternion<N>
[src]
coords: Matrix<N, U4, U1, <DefaultAllocator as Allocator<N, U4, U1>>::Buffer>
) -> Quaternion<N>
impl<N> Hash for Quaternion<N> where
N: Hash + SimdRealField,
[src]
N: Hash + SimdRealField,
fn hash<H>(&self, state: &mut H) where
H: Hasher,
[src]
H: Hasher,
fn hash_slice<H>(data: &[Self], state: &mut H) where
H: Hasher,
1.3.0[src]
H: Hasher,
impl<N> Index<usize> for Quaternion<N> where
N: SimdRealField,
[src]
N: SimdRealField,
type Output = N
The returned type after indexing.
fn index(&self, i: usize) -> &<Quaternion<N> as Index<usize>>::Output
[src]
impl<N> IndexMut<usize> for Quaternion<N> where
N: SimdRealField,
[src]
N: SimdRealField,
impl<'b, N> Mul<&'b Quaternion<N>> for Quaternion<N> where
N: SimdRealField,
<N as SimdValue>::Element: SimdRealField,
DefaultAllocator: Allocator<N, U4, U1>,
DefaultAllocator: Allocator<N, U4, U1>,
[src]
N: SimdRealField,
<N as SimdValue>::Element: SimdRealField,
DefaultAllocator: Allocator<N, U4, U1>,
DefaultAllocator: Allocator<N, U4, U1>,
type Output = Quaternion<N>
The resulting type after applying the *
operator.
fn mul(
self,
rhs: &'b Quaternion<N>
) -> <Quaternion<N> as Mul<&'b Quaternion<N>>>::Output
[src]
self,
rhs: &'b Quaternion<N>
) -> <Quaternion<N> as Mul<&'b Quaternion<N>>>::Output
impl<'a, 'b, N> Mul<&'b Quaternion<N>> for &'a Quaternion<N> where
N: SimdRealField,
<N as SimdValue>::Element: SimdRealField,
DefaultAllocator: Allocator<N, U4, U1>,
DefaultAllocator: Allocator<N, U4, U1>,
[src]
N: SimdRealField,
<N as SimdValue>::Element: SimdRealField,
DefaultAllocator: Allocator<N, U4, U1>,
DefaultAllocator: Allocator<N, U4, U1>,
type Output = Quaternion<N>
The resulting type after applying the *
operator.
fn mul(
self,
rhs: &'b Quaternion<N>
) -> <&'a Quaternion<N> as Mul<&'b Quaternion<N>>>::Output
[src]
self,
rhs: &'b Quaternion<N>
) -> <&'a Quaternion<N> as Mul<&'b Quaternion<N>>>::Output
impl<'a, N> Mul<N> for &'a Quaternion<N> where
N: SimdRealField,
<N as SimdValue>::Element: SimdRealField,
[src]
N: SimdRealField,
<N as SimdValue>::Element: SimdRealField,
type Output = Quaternion<N>
The resulting type after applying the *
operator.
fn mul(self, n: N) -> <&'a Quaternion<N> as Mul<N>>::Output
[src]
impl<N> Mul<N> for Quaternion<N> where
N: SimdRealField,
<N as SimdValue>::Element: SimdRealField,
[src]
N: SimdRealField,
<N as SimdValue>::Element: SimdRealField,
type Output = Quaternion<N>
The resulting type after applying the *
operator.
fn mul(self, n: N) -> <Quaternion<N> as Mul<N>>::Output
[src]
impl<'a, N> Mul<Quaternion<N>> for &'a Quaternion<N> where
N: SimdRealField,
<N as SimdValue>::Element: SimdRealField,
DefaultAllocator: Allocator<N, U4, U1>,
DefaultAllocator: Allocator<N, U4, U1>,
[src]
N: SimdRealField,
<N as SimdValue>::Element: SimdRealField,
DefaultAllocator: Allocator<N, U4, U1>,
DefaultAllocator: Allocator<N, U4, U1>,
type Output = Quaternion<N>
The resulting type after applying the *
operator.
fn mul(
self,
rhs: Quaternion<N>
) -> <&'a Quaternion<N> as Mul<Quaternion<N>>>::Output
[src]
self,
rhs: Quaternion<N>
) -> <&'a Quaternion<N> as Mul<Quaternion<N>>>::Output
impl<N> Mul<Quaternion<N>> for Quaternion<N> where
N: SimdRealField,
<N as SimdValue>::Element: SimdRealField,
DefaultAllocator: Allocator<N, U4, U1>,
DefaultAllocator: Allocator<N, U4, U1>,
[src]
N: SimdRealField,
<N as SimdValue>::Element: SimdRealField,
DefaultAllocator: Allocator<N, U4, U1>,
DefaultAllocator: Allocator<N, U4, U1>,
type Output = Quaternion<N>
The resulting type after applying the *
operator.
fn mul(
self,
rhs: Quaternion<N>
) -> <Quaternion<N> as Mul<Quaternion<N>>>::Output
[src]
self,
rhs: Quaternion<N>
) -> <Quaternion<N> as Mul<Quaternion<N>>>::Output
impl<'b, N> MulAssign<&'b Quaternion<N>> for Quaternion<N> where
N: SimdRealField,
<N as SimdValue>::Element: SimdRealField,
DefaultAllocator: Allocator<N, U4, U1>,
DefaultAllocator: Allocator<N, U4, U1>,
[src]
N: SimdRealField,
<N as SimdValue>::Element: SimdRealField,
DefaultAllocator: Allocator<N, U4, U1>,
DefaultAllocator: Allocator<N, U4, U1>,
fn mul_assign(&mut self, rhs: &'b Quaternion<N>)
[src]
impl<N> MulAssign<N> for Quaternion<N> where
N: SimdRealField,
<N as SimdValue>::Element: SimdRealField,
[src]
N: SimdRealField,
<N as SimdValue>::Element: SimdRealField,
fn mul_assign(&mut self, n: N)
[src]
impl<N> MulAssign<Quaternion<N>> for Quaternion<N> where
N: SimdRealField,
<N as SimdValue>::Element: SimdRealField,
DefaultAllocator: Allocator<N, U4, U1>,
DefaultAllocator: Allocator<N, U4, U1>,
[src]
N: SimdRealField,
<N as SimdValue>::Element: SimdRealField,
DefaultAllocator: Allocator<N, U4, U1>,
DefaultAllocator: Allocator<N, U4, U1>,
fn mul_assign(&mut self, rhs: Quaternion<N>)
[src]
impl<'a, N> Neg for &'a Quaternion<N> where
N: SimdRealField,
<N as SimdValue>::Element: SimdRealField,
[src]
N: SimdRealField,
<N as SimdValue>::Element: SimdRealField,
type Output = Quaternion<N>
The resulting type after applying the -
operator.
fn neg(self) -> <&'a Quaternion<N> as Neg>::Output
[src]
impl<N> Neg for Quaternion<N> where
N: SimdRealField,
<N as SimdValue>::Element: SimdRealField,
[src]
N: SimdRealField,
<N as SimdValue>::Element: SimdRealField,
type Output = Quaternion<N>
The resulting type after applying the -
operator.
fn neg(self) -> <Quaternion<N> as Neg>::Output
[src]
impl<N> Normed for Quaternion<N> where
N: SimdRealField,
[src]
N: SimdRealField,
type Norm = <N as SimdComplexField>::SimdRealField
The type of the norm.
fn norm(&self) -> <N as SimdComplexField>::SimdRealField
[src]
fn norm_squared(&self) -> <N as SimdComplexField>::SimdRealField
[src]
fn scale_mut(&mut self, n: <Quaternion<N> as Normed>::Norm)
[src]
fn unscale_mut(&mut self, n: <Quaternion<N> as Normed>::Norm)
[src]
impl<N> One for Quaternion<N> where
N: SimdRealField,
<N as SimdValue>::Element: SimdRealField,
[src]
N: SimdRealField,
<N as SimdValue>::Element: SimdRealField,
fn one() -> Quaternion<N>
[src]
fn set_one(&mut self)
[src]
fn is_one(&self) -> bool where
Self: PartialEq<Self>,
[src]
Self: PartialEq<Self>,
impl<N> PartialEq<Quaternion<N>> for Quaternion<N> where
N: SimdRealField,
<N as SimdValue>::Element: SimdRealField,
[src]
N: SimdRealField,
<N as SimdValue>::Element: SimdRealField,
fn eq(&self, rhs: &Quaternion<N>) -> bool
[src]
#[must_use]fn ne(&self, other: &Rhs) -> bool
1.0.0[src]
impl<N> RelativeEq<Quaternion<N>> for Quaternion<N> where
N: RelativeEq<N, Epsilon = N> + RealField,
[src]
N: RelativeEq<N, Epsilon = N> + RealField,
fn default_max_relative(
) -> <Quaternion<N> as AbsDiffEq<Quaternion<N>>>::Epsilon
[src]
) -> <Quaternion<N> as AbsDiffEq<Quaternion<N>>>::Epsilon
fn relative_eq(
&self,
other: &Quaternion<N>,
epsilon: <Quaternion<N> as AbsDiffEq<Quaternion<N>>>::Epsilon,
max_relative: <Quaternion<N> as AbsDiffEq<Quaternion<N>>>::Epsilon
) -> bool
[src]
&self,
other: &Quaternion<N>,
epsilon: <Quaternion<N> as AbsDiffEq<Quaternion<N>>>::Epsilon,
max_relative: <Quaternion<N> as AbsDiffEq<Quaternion<N>>>::Epsilon
) -> bool
fn relative_ne(
&self,
other: &Rhs,
epsilon: Self::Epsilon,
max_relative: Self::Epsilon
) -> bool
&self,
other: &Rhs,
epsilon: Self::Epsilon,
max_relative: Self::Epsilon
) -> bool
impl<N> SimdValue for Quaternion<N> where
N: Scalar + SimdValue,
<N as SimdValue>::Element: Scalar,
[src]
N: Scalar + SimdValue,
<N as SimdValue>::Element: Scalar,
type Element = Quaternion<<N as SimdValue>::Element>
The type of the elements of each lane of this SIMD value.
type SimdBool = <N as SimdValue>::SimdBool
Type of the result of comparing two SIMD values like self
.
fn lanes() -> usize
[src]
fn splat(val: <Quaternion<N> as SimdValue>::Element) -> Quaternion<N>
[src]
fn extract(&self, i: usize) -> <Quaternion<N> as SimdValue>::Element
[src]
unsafe fn extract_unchecked(
&self,
i: usize
) -> <Quaternion<N> as SimdValue>::Element
[src]
&self,
i: usize
) -> <Quaternion<N> as SimdValue>::Element
fn replace(&mut self, i: usize, val: <Quaternion<N> as SimdValue>::Element)
[src]
unsafe fn replace_unchecked(
&mut self,
i: usize,
val: <Quaternion<N> as SimdValue>::Element
)
[src]
&mut self,
i: usize,
val: <Quaternion<N> as SimdValue>::Element
)
fn select(
self,
cond: <Quaternion<N> as SimdValue>::SimdBool,
other: Quaternion<N>
) -> Quaternion<N>
[src]
self,
cond: <Quaternion<N> as SimdValue>::SimdBool,
other: Quaternion<N>
) -> Quaternion<N>
fn map_lanes(self, f: impl Fn(Self::Element) -> Self::Element) -> Self where
Self: Clone,
[src]
Self: Clone,
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<'b, N> Sub<&'b Quaternion<N>> for Quaternion<N> where
N: SimdRealField,
<N as SimdValue>::Element: SimdRealField,
DefaultAllocator: Allocator<N, U4, U1>,
DefaultAllocator: Allocator<N, U4, U1>,
[src]
N: SimdRealField,
<N as SimdValue>::Element: SimdRealField,
DefaultAllocator: Allocator<N, U4, U1>,
DefaultAllocator: Allocator<N, U4, U1>,
type Output = Quaternion<N>
The resulting type after applying the -
operator.
fn sub(
self,
rhs: &'b Quaternion<N>
) -> <Quaternion<N> as Sub<&'b Quaternion<N>>>::Output
[src]
self,
rhs: &'b Quaternion<N>
) -> <Quaternion<N> as Sub<&'b Quaternion<N>>>::Output
impl<'a, 'b, N> Sub<&'b Quaternion<N>> for &'a Quaternion<N> where
N: SimdRealField,
<N as SimdValue>::Element: SimdRealField,
DefaultAllocator: Allocator<N, U4, U1>,
DefaultAllocator: Allocator<N, U4, U1>,
[src]
N: SimdRealField,
<N as SimdValue>::Element: SimdRealField,
DefaultAllocator: Allocator<N, U4, U1>,
DefaultAllocator: Allocator<N, U4, U1>,
type Output = Quaternion<N>
The resulting type after applying the -
operator.
fn sub(
self,
rhs: &'b Quaternion<N>
) -> <&'a Quaternion<N> as Sub<&'b Quaternion<N>>>::Output
[src]
self,
rhs: &'b Quaternion<N>
) -> <&'a Quaternion<N> as Sub<&'b Quaternion<N>>>::Output
impl<N> Sub<Quaternion<N>> for Quaternion<N> where
N: SimdRealField,
<N as SimdValue>::Element: SimdRealField,
DefaultAllocator: Allocator<N, U4, U1>,
DefaultAllocator: Allocator<N, U4, U1>,
[src]
N: SimdRealField,
<N as SimdValue>::Element: SimdRealField,
DefaultAllocator: Allocator<N, U4, U1>,
DefaultAllocator: Allocator<N, U4, U1>,
type Output = Quaternion<N>
The resulting type after applying the -
operator.
fn sub(
self,
rhs: Quaternion<N>
) -> <Quaternion<N> as Sub<Quaternion<N>>>::Output
[src]
self,
rhs: Quaternion<N>
) -> <Quaternion<N> as Sub<Quaternion<N>>>::Output
impl<'a, N> Sub<Quaternion<N>> for &'a Quaternion<N> where
N: SimdRealField,
<N as SimdValue>::Element: SimdRealField,
DefaultAllocator: Allocator<N, U4, U1>,
DefaultAllocator: Allocator<N, U4, U1>,
[src]
N: SimdRealField,
<N as SimdValue>::Element: SimdRealField,
DefaultAllocator: Allocator<N, U4, U1>,
DefaultAllocator: Allocator<N, U4, U1>,
type Output = Quaternion<N>
The resulting type after applying the -
operator.
fn sub(
self,
rhs: Quaternion<N>
) -> <&'a Quaternion<N> as Sub<Quaternion<N>>>::Output
[src]
self,
rhs: Quaternion<N>
) -> <&'a Quaternion<N> as Sub<Quaternion<N>>>::Output
impl<'b, N> SubAssign<&'b Quaternion<N>> for Quaternion<N> where
N: SimdRealField,
<N as SimdValue>::Element: SimdRealField,
DefaultAllocator: Allocator<N, U4, U1>,
DefaultAllocator: Allocator<N, U4, U1>,
[src]
N: SimdRealField,
<N as SimdValue>::Element: SimdRealField,
DefaultAllocator: Allocator<N, U4, U1>,
DefaultAllocator: Allocator<N, U4, U1>,
fn sub_assign(&mut self, rhs: &'b Quaternion<N>)
[src]
impl<N> SubAssign<Quaternion<N>> for Quaternion<N> where
N: SimdRealField,
<N as SimdValue>::Element: SimdRealField,
DefaultAllocator: Allocator<N, U4, U1>,
DefaultAllocator: Allocator<N, U4, U1>,
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N: SimdRealField,
<N as SimdValue>::Element: SimdRealField,
DefaultAllocator: Allocator<N, U4, U1>,
DefaultAllocator: Allocator<N, U4, U1>,
fn sub_assign(&mut self, rhs: Quaternion<N>)
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impl<N1, N2> SubsetOf<Quaternion<N2>> for Quaternion<N1> where
N1: SimdRealField,
N2: SimdRealField + SupersetOf<N1>,
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N1: SimdRealField,
N2: SimdRealField + SupersetOf<N1>,
fn to_superset(&self) -> Quaternion<N2>
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fn is_in_subset(q: &Quaternion<N2>) -> bool
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fn from_superset_unchecked(q: &Quaternion<N2>) -> Quaternion<N1>
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fn from_superset(element: &T) -> Option<Self>
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impl<N> UlpsEq<Quaternion<N>> for Quaternion<N> where
N: UlpsEq<N, Epsilon = N> + RealField,
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N: UlpsEq<N, Epsilon = N> + RealField,
fn default_max_ulps() -> u32
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fn ulps_eq(
&self,
other: &Quaternion<N>,
epsilon: <Quaternion<N> as AbsDiffEq<Quaternion<N>>>::Epsilon,
max_ulps: u32
) -> bool
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&self,
other: &Quaternion<N>,
epsilon: <Quaternion<N> as AbsDiffEq<Quaternion<N>>>::Epsilon,
max_ulps: u32
) -> bool
fn ulps_ne(&self, other: &Rhs, epsilon: Self::Epsilon, max_ulps: u32) -> bool
impl<N> Zero for Quaternion<N> where
N: SimdRealField,
<N as SimdValue>::Element: SimdRealField,
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N: SimdRealField,
<N as SimdValue>::Element: SimdRealField,
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<T> Any for T where
T: 'static + ?Sized,
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T: 'static + ?Sized,
impl<T> Borrow<T> for T where
T: ?Sized,
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T: ?Sized,
impl<T> BorrowMut<T> for T where
T: ?Sized,
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T: ?Sized,
fn borrow_mut(&mut self) -> &mut T
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impl<T, Right> ClosedAdd<Right> for T where
T: Add<Right, Output = T> + AddAssign<Right>,
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T: Add<Right, Output = T> + AddAssign<Right>,
impl<T, Right> ClosedDiv<Right> for T where
T: Div<Right, Output = T> + DivAssign<Right>,
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T: Div<Right, Output = T> + DivAssign<Right>,
impl<T, Right> ClosedMul<Right> for T where
T: Mul<Right, Output = T> + MulAssign<Right>,
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T: Mul<Right, Output = T> + MulAssign<Right>,
impl<T> ClosedNeg for T where
T: Neg<Output = T>,
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T: Neg<Output = T>,
impl<T, Right> ClosedSub<Right> for T where
T: Sub<Right, Output = T> + SubAssign<Right>,
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T: Sub<Right, Output = T> + SubAssign<Right>,
impl<T> From<T> for T
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impl<T, U> Into<U> for T where
U: From<T>,
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U: From<T>,
impl<T> IntoPnt<Point<T, U2>> for T where
T: Scalar,
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T: Scalar,
impl<T> IntoPnt<Point<T, U3>> for T where
T: Scalar,
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T: Scalar,
impl<T> IntoPnt<Point<T, U4>> for T where
T: Scalar,
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T: Scalar,
impl<V> IntoPnt<V> for V
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impl<V> IntoVec<V> for V
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impl<T> JoinPnt<T, Point<T, U2>> for T where
T: Scalar,
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T: Scalar,
impl<T> JoinPnt<T, Point<T, U3>> for T where
T: Scalar,
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T: Scalar,
impl<T> JoinPnt<T, T> for T where
T: Scalar,
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T: Scalar,
impl<T> Same<T> for T
type Output = T
Should always be Self
impl<T> Scalar for T where
T: PartialEq<T> + Copy + Any + Debug,
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T: PartialEq<T> + Copy + Any + Debug,
impl<SS, SP> SupersetOf<SS> for SP where
SS: SubsetOf<SP>,
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SS: SubsetOf<SP>,
fn to_subset(&self) -> Option<SS>
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fn is_in_subset(&self) -> bool
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fn to_subset_unchecked(&self) -> SS
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fn from_subset(element: &SS) -> SP
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impl<T> ToOwned for T where
T: Clone,
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T: Clone,
type Owned = T
The resulting type after obtaining ownership.
fn to_owned(&self) -> T
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fn clone_into(&self, target: &mut T)
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impl<T> ToString for T where
T: Display + ?Sized,
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T: Display + ?Sized,
impl<T, U> TryFrom<U> for T where
U: Into<T>,
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U: Into<T>,
type Error = Infallible
The type returned in the event of a conversion error.
fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::Error>
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impl<T, U> TryInto<U> for T where
U: TryFrom<T>,
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U: TryFrom<T>,
type Error = <U as TryFrom<T>>::Error
The type returned in the event of a conversion error.
fn try_into(self) -> Result<U, <U as TryFrom<T>>::Error>
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impl<V, T> VZip<V> for T where
V: MultiLane<T>,
V: MultiLane<T>,