Struct nalgebra::geometry::Quaternion
source · #[repr(C)]pub struct Quaternion<T> {
pub coords: Vector4<T>,
}
Expand description
A quaternion. See the type alias UnitQuaternion = Unit<Quaternion>
for a quaternion
that may be used as a rotation.
Fields§
§coords: Vector4<T>
This quaternion as a 4D vector of coordinates in the [ x, y, z, w ]
storage order.
Implementations§
source§impl<T: SimdRealField> Quaternion<T>where
T::Element: SimdRealField,
impl<T: SimdRealField> Quaternion<T>where
T::Element: SimdRealField,
sourcepub fn into_owned(self) -> Self
👎Deprecated: This method is a no-op and will be removed in a future release.
pub fn into_owned(self) -> Self
Moves this unit quaternion into one that owns its data.
sourcepub fn clone_owned(&self) -> Self
👎Deprecated: This method is a no-op and will be removed in a future release.
pub fn clone_owned(&self) -> Self
Clones this unit quaternion into one that owns its data.
sourcepub fn normalize(&self) -> Self
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);
sourcepub fn conjugate(&self) -> Self
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);
sourcepub fn lerp(&self, other: &Self, t: T) -> Self
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));
sourcepub fn vector(
&self
) -> MatrixView<'_, T, U3, U1, RStride<T, U4, U1>, CStride<T, U4, U1>>
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);
sourcepub fn scalar(&self) -> T
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);
sourcepub fn as_vector(&self) -> &Vector4<T>
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));
sourcepub fn norm(&self) -> T
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);
sourcepub fn magnitude(&self) -> T
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);
sourcepub fn norm_squared(&self) -> T
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);
sourcepub fn magnitude_squared(&self) -> T
pub fn magnitude_squared(&self) -> T
A synonym for the squared norm of this quaternion.
Aka the squared length.
This is the same as .norm_squared()
§Example
let q = Quaternion::new(1.0, 2.0, 3.0, 4.0);
assert_eq!(q.magnitude_squared(), 30.0);
source§impl<T: SimdRealField> Quaternion<T>where
T::Element: SimdRealField,
impl<T: SimdRealField> Quaternion<T>where
T::Element: SimdRealField,
sourcepub fn try_inverse(&self) -> Option<Self>where
T: RealField,
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());
sourcepub fn simd_try_inverse(&self) -> SimdOption<Self>
pub fn simd_try_inverse(&self) -> SimdOption<Self>
Attempt to inverse this quaternion.
This method also works with SIMD components.
sourcepub fn inner(&self, other: &Self) -> Self
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);
sourcepub fn outer(&self, other: &Self) -> Self
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);
sourcepub fn project(&self, other: &Self) -> Option<Self>where
T: RealField,
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);
sourcepub fn reject(&self, other: &Self) -> Option<Self>where
T: RealField,
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);
sourcepub fn polar_decomposition(&self) -> (T, T, Option<Unit<Vector3<T>>>)where
T: RealField,
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()));
sourcepub fn ln(&self) -> Self
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)
sourcepub fn exp(&self) -> Self
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)
sourcepub fn exp_eps(&self, eps: T) -> Self
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());
sourcepub fn powf(&self, n: T) -> Self
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);
sourcepub fn as_vector_mut(&mut self) -> &mut Vector4<T>
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);
sourcepub fn vector_mut(
&mut self
) -> MatrixViewMut<'_, T, U3, U1, RStride<T, U4, U1>, CStride<T, U4, U1>>
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);
sourcepub fn conjugate_mut(&mut self)
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);
sourcepub fn try_inverse_mut(&mut self) -> T::SimdBool
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());
sourcepub fn normalize_mut(&mut self) -> T
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);
sourcepub fn is_pure(&self) -> bool
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
).
sourcepub fn left_div(&self, other: &Self) -> Option<Self>where
T: RealField,
pub fn left_div(&self, other: &Self) -> Option<Self>where
T: RealField,
Left quaternionic division.
Calculates B-1 * A where A = self, B = other.
sourcepub fn right_div(&self, other: &Self) -> Option<Self>where
T: RealField,
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);
sourcepub fn cos(&self) -> Self
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);
sourcepub fn acos(&self) -> Self
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);
sourcepub fn sin(&self) -> Self
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);
sourcepub fn asin(&self) -> Self
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);
sourcepub fn tan(&self) -> Selfwhere
T: RealField,
pub fn tan(&self) -> Selfwhere
T: RealField,
Calculates the quaternionic tangent.
§Example
let input = Quaternion::new(1.0, 2.0, 3.0, 4.0);
let expected = Quaternion::new(0.00003821631725009489, 0.3713971716439371, 0.5570957574659058, 0.7427943432878743);
let result = input.tan();
assert_relative_eq!(expected, result, epsilon = 1.0e-7);
sourcepub fn atan(&self) -> Selfwhere
T: RealField,
pub fn atan(&self) -> Selfwhere
T: RealField,
Calculates the quaternionic arctangent.
§Example
let input = Quaternion::new(1.0, 2.0, 3.0, 4.0);
let result = input.tan().atan();
assert_relative_eq!(input, result, epsilon = 1.0e-7);
sourcepub fn sinh(&self) -> Self
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);
sourcepub fn asinh(&self) -> Self
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);
sourcepub fn cosh(&self) -> Self
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);
sourcepub fn acosh(&self) -> Self
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);
sourcepub fn tanh(&self) -> Selfwhere
T: RealField,
pub fn tanh(&self) -> Selfwhere
T: RealField,
Calculates the hyperbolic quaternionic tangent.
§Example
let input = Quaternion::new(1.0, 2.0, 3.0, 4.0);
let expected = Quaternion::new(1.0248695360556623, -0.10229568178876419, -0.1534435226831464, -0.20459136357752844);
let result = input.tanh();
assert_relative_eq!(expected, result, epsilon = 1.0e-7);
sourcepub fn atanh(&self) -> Self
pub fn atanh(&self) -> Self
Calculates the hyperbolic quaternionic arctangent.
§Example
let input = Quaternion::new(1.0, 2.0, 3.0, 4.0);
let expected = Quaternion::new(0.03230293287000163, 0.5173453683196951, 0.7760180524795426, 1.0346907366393903);
let result = input.atanh();
assert_relative_eq!(expected, result, epsilon = 1.0e-7);
source§impl<T> Quaternion<T>
impl<T> Quaternion<T>
sourcepub const fn from_vector(vector: Vector4<T>) -> Self
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.
sourcepub const fn new(w: T, i: T, j: T, k: T) -> Self
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));
sourcepub fn cast<To>(self) -> Quaternion<To>
pub fn cast<To>(self) -> Quaternion<To>
Cast the components of self
to another type.
§Example
let q = Quaternion::new(1.0f64, 2.0, 3.0, 4.0);
let q2 = q.cast::<f32>();
assert_eq!(q2, Quaternion::new(1.0f32, 2.0, 3.0, 4.0));
source§impl<T: SimdRealField> Quaternion<T>
impl<T: SimdRealField> Quaternion<T>
sourcepub fn from_parts<SB>(scalar: T, vector: Vector<T, U3, SB>) -> Self
pub fn from_parts<SB>(scalar: T, vector: Vector<T, U3, SB>) -> Self
Creates a new quaternion from its scalar and vector parts. Note that the arguments order does not follow the storage order.
The storage order is [ vector, scalar ].
§Example
let w = 1.0;
let ijk = Vector3::new(2.0, 3.0, 4.0);
let q = Quaternion::from_parts(w, ijk);
assert!(q.i == 2.0 && q.j == 3.0 && q.k == 4.0 && q.w == 1.0);
assert_eq!(*q.as_vector(), Vector4::new(2.0, 3.0, 4.0, 1.0));
source§impl<T: SimdRealField> Quaternion<T>where
T::Element: SimdRealField,
impl<T: SimdRealField> Quaternion<T>where
T::Element: SimdRealField,
Trait Implementations§
source§impl<T: RealField + AbsDiffEq<Epsilon = T>> AbsDiffEq for Quaternion<T>
impl<T: RealField + AbsDiffEq<Epsilon = T>> AbsDiffEq for Quaternion<T>
source§fn default_epsilon() -> Self::Epsilon
fn default_epsilon() -> Self::Epsilon
source§fn abs_diff_eq(&self, other: &Self, epsilon: Self::Epsilon) -> bool
fn abs_diff_eq(&self, other: &Self, epsilon: Self::Epsilon) -> bool
source§fn abs_diff_ne(&self, other: &Rhs, epsilon: Self::Epsilon) -> bool
fn abs_diff_ne(&self, other: &Rhs, epsilon: Self::Epsilon) -> bool
AbsDiffEq::abs_diff_eq
.source§impl<'a, 'b, T: SimdRealField> Add<&'b Quaternion<T>> for &'a Quaternion<T>where
T::Element: SimdRealField,
impl<'a, 'b, T: SimdRealField> Add<&'b Quaternion<T>> for &'a Quaternion<T>where
T::Element: SimdRealField,
§type Output = Quaternion<T>
type Output = Quaternion<T>
+
operator.source§impl<'b, T: SimdRealField> Add<&'b Quaternion<T>> for Quaternion<T>where
T::Element: SimdRealField,
impl<'b, T: SimdRealField> Add<&'b Quaternion<T>> for Quaternion<T>where
T::Element: SimdRealField,
§type Output = Quaternion<T>
type Output = Quaternion<T>
+
operator.source§impl<'a, T: SimdRealField> Add<Quaternion<T>> for &'a Quaternion<T>where
T::Element: SimdRealField,
impl<'a, T: SimdRealField> Add<Quaternion<T>> for &'a Quaternion<T>where
T::Element: SimdRealField,
§type Output = Quaternion<T>
type Output = Quaternion<T>
+
operator.source§impl<T: SimdRealField> Add for Quaternion<T>where
T::Element: SimdRealField,
impl<T: SimdRealField> Add for Quaternion<T>where
T::Element: SimdRealField,
§type Output = Quaternion<T>
type Output = Quaternion<T>
+
operator.source§impl<'b, T: SimdRealField> AddAssign<&'b Quaternion<T>> for Quaternion<T>where
T::Element: SimdRealField,
impl<'b, T: SimdRealField> AddAssign<&'b Quaternion<T>> for Quaternion<T>where
T::Element: SimdRealField,
source§fn add_assign(&mut self, rhs: &'b Quaternion<T>)
fn add_assign(&mut self, rhs: &'b Quaternion<T>)
+=
operation. Read moresource§impl<T: SimdRealField> AddAssign for Quaternion<T>where
T::Element: SimdRealField,
impl<T: SimdRealField> AddAssign for Quaternion<T>where
T::Element: SimdRealField,
source§fn add_assign(&mut self, rhs: Quaternion<T>)
fn add_assign(&mut self, rhs: Quaternion<T>)
+=
operation. Read moresource§impl<T: Clone> Clone for Quaternion<T>
impl<T: Clone> Clone for Quaternion<T>
source§fn clone(&self) -> Quaternion<T>
fn clone(&self) -> Quaternion<T>
1.0.0 · source§fn clone_from(&mut self, source: &Self)
fn clone_from(&mut self, source: &Self)
source
. Read moresource§impl<T: Debug> Debug for Quaternion<T>
impl<T: Debug> Debug for Quaternion<T>
source§impl<'a, T: SimdRealField> Div<T> for &'a Quaternion<T>where
T::Element: SimdRealField,
impl<'a, T: SimdRealField> Div<T> for &'a Quaternion<T>where
T::Element: SimdRealField,
source§impl<T: SimdRealField> Div<T> for Quaternion<T>where
T::Element: SimdRealField,
impl<T: SimdRealField> Div<T> for Quaternion<T>where
T::Element: SimdRealField,
source§impl<T: SimdRealField> DivAssign<T> for Quaternion<T>where
T::Element: SimdRealField,
impl<T: SimdRealField> DivAssign<T> for Quaternion<T>where
T::Element: SimdRealField,
source§fn div_assign(&mut self, n: T)
fn div_assign(&mut self, n: T)
/=
operation. Read moresource§impl<T> From<[Quaternion<<T as SimdValue>::Element>; 16]> for Quaternion<T>
impl<T> From<[Quaternion<<T as SimdValue>::Element>; 16]> for Quaternion<T>
source§impl<T> From<[Quaternion<<T as SimdValue>::Element>; 2]> for Quaternion<T>
impl<T> From<[Quaternion<<T as SimdValue>::Element>; 2]> for Quaternion<T>
source§impl<T> From<[Quaternion<<T as SimdValue>::Element>; 4]> for Quaternion<T>
impl<T> From<[Quaternion<<T as SimdValue>::Element>; 4]> for Quaternion<T>
source§impl<T> From<[Quaternion<<T as SimdValue>::Element>; 8]> for Quaternion<T>
impl<T> From<[Quaternion<<T as SimdValue>::Element>; 8]> for Quaternion<T>
source§impl<T: Scalar> From<Matrix<T, Const<4>, Const<1>, ArrayStorage<T, 4, 1>>> for Quaternion<T>
impl<T: Scalar> From<Matrix<T, Const<4>, Const<1>, ArrayStorage<T, 4, 1>>> for Quaternion<T>
source§impl<'a, 'b, T: SimdRealField> Mul<&'b Quaternion<T>> for &'a Quaternion<T>where
T::Element: SimdRealField,
impl<'a, 'b, T: SimdRealField> Mul<&'b Quaternion<T>> for &'a Quaternion<T>where
T::Element: SimdRealField,
§type Output = Quaternion<T>
type Output = Quaternion<T>
*
operator.source§impl<'b, T: SimdRealField> Mul<&'b Quaternion<T>> for Quaternion<T>where
T::Element: SimdRealField,
impl<'b, T: SimdRealField> Mul<&'b Quaternion<T>> for Quaternion<T>where
T::Element: SimdRealField,
§type Output = Quaternion<T>
type Output = Quaternion<T>
*
operator.source§impl<'a, T: SimdRealField> Mul<Quaternion<T>> for &'a Quaternion<T>where
T::Element: SimdRealField,
impl<'a, T: SimdRealField> Mul<Quaternion<T>> for &'a Quaternion<T>where
T::Element: SimdRealField,
§type Output = Quaternion<T>
type Output = Quaternion<T>
*
operator.source§impl<'a, T: SimdRealField> Mul<T> for &'a Quaternion<T>where
T::Element: SimdRealField,
impl<'a, T: SimdRealField> Mul<T> for &'a Quaternion<T>where
T::Element: SimdRealField,
source§impl<T: SimdRealField> Mul<T> for Quaternion<T>where
T::Element: SimdRealField,
impl<T: SimdRealField> Mul<T> for Quaternion<T>where
T::Element: SimdRealField,
source§impl<T: SimdRealField> Mul for Quaternion<T>where
T::Element: SimdRealField,
impl<T: SimdRealField> Mul for Quaternion<T>where
T::Element: SimdRealField,
§type Output = Quaternion<T>
type Output = Quaternion<T>
*
operator.source§impl<'b, T: SimdRealField> MulAssign<&'b Quaternion<T>> for Quaternion<T>where
T::Element: SimdRealField,
impl<'b, T: SimdRealField> MulAssign<&'b Quaternion<T>> for Quaternion<T>where
T::Element: SimdRealField,
source§fn mul_assign(&mut self, rhs: &'b Quaternion<T>)
fn mul_assign(&mut self, rhs: &'b Quaternion<T>)
*=
operation. Read moresource§impl<T: SimdRealField> MulAssign<T> for Quaternion<T>where
T::Element: SimdRealField,
impl<T: SimdRealField> MulAssign<T> for Quaternion<T>where
T::Element: SimdRealField,
source§fn mul_assign(&mut self, n: T)
fn mul_assign(&mut self, n: T)
*=
operation. Read moresource§impl<T: SimdRealField> MulAssign for Quaternion<T>where
T::Element: SimdRealField,
impl<T: SimdRealField> MulAssign for Quaternion<T>where
T::Element: SimdRealField,
source§fn mul_assign(&mut self, rhs: Quaternion<T>)
fn mul_assign(&mut self, rhs: Quaternion<T>)
*=
operation. Read moresource§impl<'a, T: SimdRealField> Neg for &'a Quaternion<T>where
T::Element: SimdRealField,
impl<'a, T: SimdRealField> Neg for &'a Quaternion<T>where
T::Element: SimdRealField,
source§impl<T: SimdRealField> Neg for Quaternion<T>where
T::Element: SimdRealField,
impl<T: SimdRealField> Neg for Quaternion<T>where
T::Element: SimdRealField,
source§impl<T: SimdRealField> Normed for Quaternion<T>
impl<T: SimdRealField> Normed for Quaternion<T>
§type Norm = <T as SimdComplexField>::SimdRealField
type Norm = <T as SimdComplexField>::SimdRealField
source§fn norm(&self) -> T::SimdRealField
fn norm(&self) -> T::SimdRealField
source§fn norm_squared(&self) -> T::SimdRealField
fn norm_squared(&self) -> T::SimdRealField
source§fn unscale_mut(&mut self, n: Self::Norm)
fn unscale_mut(&mut self, n: Self::Norm)
self
by n.source§impl<T: SimdRealField> One for Quaternion<T>where
T::Element: SimdRealField,
impl<T: SimdRealField> One for Quaternion<T>where
T::Element: SimdRealField,
source§impl<T: Scalar> PartialEq for Quaternion<T>
impl<T: Scalar> PartialEq for Quaternion<T>
source§impl<T: RealField + RelativeEq<Epsilon = T>> RelativeEq for Quaternion<T>
impl<T: RealField + RelativeEq<Epsilon = T>> RelativeEq for Quaternion<T>
source§fn default_max_relative() -> Self::Epsilon
fn default_max_relative() -> Self::Epsilon
source§fn relative_eq(
&self,
other: &Self,
epsilon: Self::Epsilon,
max_relative: Self::Epsilon
) -> bool
fn relative_eq( &self, other: &Self, epsilon: Self::Epsilon, max_relative: Self::Epsilon ) -> bool
source§fn relative_ne(
&self,
other: &Rhs,
epsilon: Self::Epsilon,
max_relative: Self::Epsilon
) -> bool
fn relative_ne( &self, other: &Rhs, epsilon: Self::Epsilon, max_relative: Self::Epsilon ) -> bool
RelativeEq::relative_eq
.source§impl<T: Scalar + SimdValue> SimdValue for Quaternion<T>
impl<T: Scalar + SimdValue> SimdValue for Quaternion<T>
§type Element = Quaternion<<T as SimdValue>::Element>
type Element = Quaternion<<T as SimdValue>::Element>
§type SimdBool = <T as SimdValue>::SimdBool
type SimdBool = <T as SimdValue>::SimdBool
self
.source§unsafe fn extract_unchecked(&self, i: usize) -> Self::Element
unsafe fn extract_unchecked(&self, i: usize) -> Self::Element
self
without bound-checking. Read moresource§unsafe fn replace_unchecked(&mut self, i: usize, val: Self::Element)
unsafe fn replace_unchecked(&mut self, i: usize, val: Self::Element)
source§impl<'a, 'b, T: SimdRealField> Sub<&'b Quaternion<T>> for &'a Quaternion<T>where
T::Element: SimdRealField,
impl<'a, 'b, T: SimdRealField> Sub<&'b Quaternion<T>> for &'a Quaternion<T>where
T::Element: SimdRealField,
§type Output = Quaternion<T>
type Output = Quaternion<T>
-
operator.source§impl<'b, T: SimdRealField> Sub<&'b Quaternion<T>> for Quaternion<T>where
T::Element: SimdRealField,
impl<'b, T: SimdRealField> Sub<&'b Quaternion<T>> for Quaternion<T>where
T::Element: SimdRealField,
§type Output = Quaternion<T>
type Output = Quaternion<T>
-
operator.source§impl<'a, T: SimdRealField> Sub<Quaternion<T>> for &'a Quaternion<T>where
T::Element: SimdRealField,
impl<'a, T: SimdRealField> Sub<Quaternion<T>> for &'a Quaternion<T>where
T::Element: SimdRealField,
§type Output = Quaternion<T>
type Output = Quaternion<T>
-
operator.source§impl<T: SimdRealField> Sub for Quaternion<T>where
T::Element: SimdRealField,
impl<T: SimdRealField> Sub for Quaternion<T>where
T::Element: SimdRealField,
§type Output = Quaternion<T>
type Output = Quaternion<T>
-
operator.source§impl<'b, T: SimdRealField> SubAssign<&'b Quaternion<T>> for Quaternion<T>where
T::Element: SimdRealField,
impl<'b, T: SimdRealField> SubAssign<&'b Quaternion<T>> for Quaternion<T>where
T::Element: SimdRealField,
source§fn sub_assign(&mut self, rhs: &'b Quaternion<T>)
fn sub_assign(&mut self, rhs: &'b Quaternion<T>)
-=
operation. Read moresource§impl<T: SimdRealField> SubAssign for Quaternion<T>where
T::Element: SimdRealField,
impl<T: SimdRealField> SubAssign for Quaternion<T>where
T::Element: SimdRealField,
source§fn sub_assign(&mut self, rhs: Quaternion<T>)
fn sub_assign(&mut self, rhs: Quaternion<T>)
-=
operation. Read moresource§impl<T1, T2> SubsetOf<Quaternion<T2>> for Quaternion<T1>
impl<T1, T2> SubsetOf<Quaternion<T2>> for Quaternion<T1>
source§fn to_superset(&self) -> Quaternion<T2>
fn to_superset(&self) -> Quaternion<T2>
self
to the equivalent element of its superset.source§fn is_in_subset(q: &Quaternion<T2>) -> bool
fn is_in_subset(q: &Quaternion<T2>) -> bool
element
is actually part of the subset Self
(and can be converted to it).source§fn from_superset_unchecked(q: &Quaternion<T2>) -> Self
fn from_superset_unchecked(q: &Quaternion<T2>) -> Self
self.to_superset
but without any property checks. Always succeeds.source§impl<T: RealField + UlpsEq<Epsilon = T>> UlpsEq for Quaternion<T>
impl<T: RealField + UlpsEq<Epsilon = T>> UlpsEq for Quaternion<T>
source§impl<T: SimdRealField> Zero for Quaternion<T>where
T::Element: SimdRealField,
impl<T: SimdRealField> Zero for Quaternion<T>where
T::Element: SimdRealField,
impl<T: Copy> Copy for Quaternion<T>
impl<T: Scalar + Eq> Eq for Quaternion<T>
Auto Trait Implementations§
impl<T> Freeze for Quaternion<T>where
T: Freeze,
impl<T> RefUnwindSafe for Quaternion<T>where
T: RefUnwindSafe,
impl<T> Send for Quaternion<T>where
T: Send,
impl<T> Sync for Quaternion<T>where
T: Sync,
impl<T> Unpin for Quaternion<T>where
T: Unpin,
impl<T> UnwindSafe for Quaternion<T>where
T: UnwindSafe,
Blanket Implementations§
source§impl<T> BorrowMut<T> for Twhere
T: ?Sized,
impl<T> BorrowMut<T> for Twhere
T: ?Sized,
source§fn borrow_mut(&mut self) -> &mut T
fn borrow_mut(&mut self) -> &mut T
source§impl<SS, SP> SupersetOf<SS> for SPwhere
SS: SubsetOf<SP>,
impl<SS, SP> SupersetOf<SS> for SPwhere
SS: SubsetOf<SP>,
source§fn to_subset(&self) -> Option<SS>
fn to_subset(&self) -> Option<SS>
self
from the equivalent element of its
superset. Read moresource§fn is_in_subset(&self) -> bool
fn is_in_subset(&self) -> bool
self
is actually part of its subset T
(and can be converted to it).source§fn to_subset_unchecked(&self) -> SS
fn to_subset_unchecked(&self) -> SS
self.to_subset
but without any property checks. Always succeeds.source§fn from_subset(element: &SS) -> SP
fn from_subset(element: &SS) -> SP
self
to the equivalent element of its superset.