[][src]Struct bno055::Quaternion

#[repr(C)]
pub struct Quaternion<N> where
    N: Real, 
{ pub coords: Matrix<N, U4, U1, <DefaultAllocator as Allocator<N, U4, U1>>::Buffer>, }

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.

Methods

impl<N> Quaternion<N> where
    N: Real, 
[src]

pub fn into_owned(self) -> Quaternion<N>[src]

Deprecated:

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

Moves this unit quaternion into one that owns its data.

pub fn clone_owned(&self) -> Quaternion<N>[src]

Deprecated:

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

Clones this unit quaternion into one that owns its data.

pub fn normalize(&self) -> Quaternion<N>[src]

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 conjugate(&self) -> Quaternion<N>[src]

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 try_inverse(&self) -> Option<Quaternion<N>>[src]

Inverts this quaternion if it is not zero.

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());

pub fn lerp(&self, other: &Quaternion<N>, t: N) -> Quaternion<N>[src]

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>>
[src]

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[src]

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>
[src]

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 ::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[src]

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[src]

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[src]

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[src]

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[src]

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);

pub fn polar_decomposition(
    &self
) -> (N, N, Option<Unit<Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3, U1>>::Buffer>>>)
[src]

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>[src]

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>[src]

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>[src]

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>[src]

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>
[src]

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>>
[src]

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)[src]

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) -> bool[src]

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

Example

let mut q = Quaternion::new(1.0, 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(0.0, 0.0, 0.0, 0.0);
assert!(!q.try_inverse_mut());

pub fn normalize_mut(&mut self) -> N[src]

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);

impl<N> Quaternion<N> where
    N: Real, 
[src]

pub fn from_vector(
    vector: Matrix<N, U4, U1, <DefaultAllocator as Allocator<N, U4, U1>>::Buffer>
) -> Quaternion<N>
[src]

Deprecated:

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>[src]

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));

pub fn from_parts<SB>(scalar: N, vector: Matrix<N, U3, U1, SB>) -> Quaternion<N> where
    SB: Storage<N, U3, U1>, 
[src]

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_polar_decomposition<SB>(
    scale: N,
    theta: N,
    axis: Unit<Matrix<N, U3, U1, SB>>
) -> Quaternion<N> where
    SB: Storage<N, U3, U1>, 
[src]

Creates a new quaternion from its polar decomposition.

Note that axis is assumed to be a unit vector.

pub fn identity() -> Quaternion<N>[src]

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);

Trait Implementations

impl<N> PartialEq<Quaternion<N>> for Quaternion<N> where
    N: Real, 
[src]

#[must_use]
fn ne(&self, other: &Rhs) -> bool
1.0.0
[src]

This method tests for !=.

impl<N> NormedSpace for Quaternion<N> where
    N: Real, 
[src]

impl<'a, 'b, N> Mul<&'b Quaternion<N>> for &'a Quaternion<N> where
    N: Real,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U4, U1>, 
[src]

type Output = Quaternion<N>

The resulting type after applying the * operator.

impl<N> Mul<N> for Quaternion<N> where
    N: Real, 
[src]

type Output = Quaternion<N>

The resulting type after applying the * operator.

impl<'a, N> Mul<N> for &'a Quaternion<N> where
    N: Real, 
[src]

type Output = Quaternion<N>

The resulting type after applying the * operator.

impl<'b, N> Mul<&'b Quaternion<N>> for Quaternion<N> where
    N: Real,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U4, U1>, 
[src]

type Output = Quaternion<N>

The resulting type after applying the * operator.

impl<'a, N> Mul<Quaternion<N>> for &'a Quaternion<N> where
    N: Real,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U4, U1>, 
[src]

type Output = Quaternion<N>

The resulting type after applying the * operator.

impl<N> Mul<Quaternion<N>> for Quaternion<N> where
    N: Real,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U4, U1>, 
[src]

type Output = Quaternion<N>

The resulting type after applying the * operator.

impl<N> From<Matrix<N, U4, U1, <DefaultAllocator as Allocator<N, U4, U1>>::Buffer>> for Quaternion<N> where
    N: Real, 
[src]

impl<N> AbstractGroupAbelian<Additive> for Quaternion<N> where
    N: Real, 
[src]

fn prop_is_commutative_approx(args: (Self, Self)) -> bool where
    Self: RelativeEq, 

Returns true if the operator is commutative for the given argument tuple. Approximate equality is used for verifications. Read more

fn prop_is_commutative(args: (Self, Self)) -> bool where
    Self: Eq

Returns true if the operator is commutative for the given argument tuple.

impl<N> AbstractGroup<Additive> for Quaternion<N> where
    N: Real, 
[src]

impl<N> One for Quaternion<N> where
    N: Real, 
[src]

fn is_one(&self) -> bool where
    Self: PartialEq<Self>, 
[src]

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

impl<N> Neg for Quaternion<N> where
    N: Real, 
[src]

type Output = Quaternion<N>

The resulting type after applying the - operator.

impl<'a, N> Neg for &'a Quaternion<N> where
    N: Real, 
[src]

type Output = Quaternion<N>

The resulting type after applying the - operator.

impl<N> Index<usize> for Quaternion<N> where
    N: Real, 
[src]

type Output = N

The returned type after indexing.

impl<N> Copy for Quaternion<N> where
    N: Real, 
[src]

impl<N> MulAssign<Quaternion<N>> for Quaternion<N> where
    N: Real,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U4, U1>, 
[src]

impl<'b, N> MulAssign<&'b Quaternion<N>> for Quaternion<N> where
    N: Real,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U4, U1>, 
[src]

impl<N> MulAssign<N> for Quaternion<N> where
    N: Real, 
[src]

impl<N> AbstractMagma<Additive> for Quaternion<N> where
    N: Real, 
[src]

fn op(&self, O, lhs: &Self) -> Self

Performs specific operation.

impl<N> AbstractMagma<Multiplicative> for Quaternion<N> where
    N: Real, 
[src]

fn op(&self, O, lhs: &Self) -> Self

Performs specific operation.

impl<N> DivAssign<N> for Quaternion<N> where
    N: Real, 
[src]

impl<N> AbstractLoop<Additive> for Quaternion<N> where
    N: Real, 
[src]

impl<'b, N> AddAssign<&'b Quaternion<N>> for Quaternion<N> where
    N: Real,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U4, U1>, 
[src]

impl<N> AddAssign<Quaternion<N>> for Quaternion<N> where
    N: Real,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U4, U1>, 
[src]

impl<N> Clone for Quaternion<N> where
    N: Real, 
[src]

fn clone_from(&mut self, source: &Self)
1.0.0
[src]

Performs copy-assignment from source. Read more

impl<N> SubAssign<Quaternion<N>> for Quaternion<N> where
    N: Real,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U4, U1>, 
[src]

impl<'b, N> SubAssign<&'b Quaternion<N>> for Quaternion<N> where
    N: Real,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U4, U1>, 
[src]

impl<N> Eq for Quaternion<N> where
    N: Eq + Real, 
[src]

impl<'a, N> Sub<Quaternion<N>> for &'a Quaternion<N> where
    N: Real,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U4, U1>, 
[src]

type Output = Quaternion<N>

The resulting type after applying the - operator.

impl<'b, N> Sub<&'b Quaternion<N>> for Quaternion<N> where
    N: Real,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U4, U1>, 
[src]

type Output = Quaternion<N>

The resulting type after applying the - operator.

impl<N> Sub<Quaternion<N>> for Quaternion<N> where
    N: Real,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U4, U1>, 
[src]

type Output = Quaternion<N>

The resulting type after applying the - operator.

impl<'a, 'b, N> Sub<&'b Quaternion<N>> for &'a Quaternion<N> where
    N: Real,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U4, U1>, 
[src]

type Output = Quaternion<N>

The resulting type after applying the - operator.

impl<N> Display for Quaternion<N> where
    N: Display + Real, 
[src]

impl<'b, N> Add<&'b Quaternion<N>> for Quaternion<N> where
    N: Real,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U4, U1>, 
[src]

type Output = Quaternion<N>

The resulting type after applying the + operator.

impl<N> Add<Quaternion<N>> for Quaternion<N> where
    N: Real,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U4, U1>, 
[src]

type Output = Quaternion<N>

The resulting type after applying the + operator.

impl<'a, 'b, N> Add<&'b Quaternion<N>> for &'a Quaternion<N> where
    N: Real,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U4, U1>, 
[src]

type Output = Quaternion<N>

The resulting type after applying the + operator.

impl<'a, N> Add<Quaternion<N>> for &'a Quaternion<N> where
    N: Real,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U4, U1>, 
[src]

type Output = Quaternion<N>

The resulting type after applying the + operator.

impl<N> FiniteDimVectorSpace for Quaternion<N> where
    N: Real, 
[src]

fn canonical_basis<F>(f: F) where
    F: FnMut(&Self) -> bool, 

Applies the given closule to each element of this vector space's canonical basis. Stops if f returns false. Read more

impl<N> IndexMut<usize> for Quaternion<N> where
    N: Real, 
[src]

impl<'a, N> Div<N> for &'a Quaternion<N> where
    N: Real, 
[src]

type Output = Quaternion<N>

The resulting type after applying the / operator.

impl<N> Div<N> for Quaternion<N> where
    N: Real, 
[src]

type Output = Quaternion<N>

The resulting type after applying the / operator.

impl<N> DerefMut for Quaternion<N> where
    N: Real, 
[src]

impl<N> AbstractMonoid<Multiplicative> for Quaternion<N> where
    N: Real, 
[src]

fn prop_operating_identity_element_is_noop_approx(args: (Self,)) -> bool where
    Self: RelativeEq, 

Checks whether operating with the identity element is a no-op for the given argument. Approximate equality is used for verifications. Read more

fn prop_operating_identity_element_is_noop(args: (Self,)) -> bool where
    Self: Eq

Checks whether operating with the identity element is a no-op for the given argument. Read more

impl<N> AbstractMonoid<Additive> for Quaternion<N> where
    N: Real, 
[src]

fn prop_operating_identity_element_is_noop_approx(args: (Self,)) -> bool where
    Self: RelativeEq, 

Checks whether operating with the identity element is a no-op for the given argument. Approximate equality is used for verifications. Read more

fn prop_operating_identity_element_is_noop(args: (Self,)) -> bool where
    Self: Eq

Checks whether operating with the identity element is a no-op for the given argument. Read more

impl<N> AbsDiffEq for Quaternion<N> where
    N: AbsDiffEq<Epsilon = N> + Real, 
[src]

type Epsilon = N

Used for specifying relative comparisons.

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

The inverse of ApproxEq::abs_diff_eq.

impl<N> AbstractModule<Additive, Additive, Multiplicative> for Quaternion<N> where
    N: Real, 
[src]

type AbstractRing = N

The underlying scalar field.

impl<N> TwoSidedInverse<Additive> for Quaternion<N> where
    N: Real, 
[src]

fn two_sided_inverse_mut(&mut self)

In-place inversion of self, relative to the operator O. Read more

impl<N> Identity<Additive> for Quaternion<N> where
    N: Real, 
[src]

fn id(O) -> Self

Specific identity.

impl<N> Identity<Multiplicative> for Quaternion<N> where
    N: Real, 
[src]

fn id(O) -> Self

Specific identity.

impl<N> Module for Quaternion<N> where
    N: Real, 
[src]

type Ring = N

The underlying scalar field.

impl<N> Zero for Quaternion<N> where
    N: Real, 
[src]

impl<N> Debug for Quaternion<N> where
    N: Debug + Real, 
[src]

impl<N> Deref for Quaternion<N> where
    N: Real, 
[src]

type Target = IJKW<N>

The resulting type after dereferencing.

impl<N> RelativeEq for Quaternion<N> where
    N: RelativeEq<Epsilon = N> + Real, 
[src]

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

The inverse of ApproxEq::relative_eq.

impl<N> VectorSpace for Quaternion<N> where
    N: Real, 
[src]

type Field = N

The underlying scalar field.

impl<N> AbstractQuasigroup<Additive> for Quaternion<N> where
    N: Real, 
[src]

fn prop_inv_is_latin_square_approx(args: (Self, Self)) -> bool where
    Self: RelativeEq, 

Returns true if latin squareness holds for the given arguments. Approximate equality is used for verifications. Read more

fn prop_inv_is_latin_square(args: (Self, Self)) -> bool where
    Self: Eq

Returns true if latin squareness holds for the given arguments. Read more

impl<N1, N2> SubsetOf<Quaternion<N2>> for Quaternion<N1> where
    N1: Real,
    N2: Real + SupersetOf<N1>, 
[src]

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

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

impl<N> AbstractSemigroup<Multiplicative> for Quaternion<N> where
    N: Real, 
[src]

fn prop_is_associative_approx(args: (Self, Self, Self)) -> bool where
    Self: RelativeEq, 

Returns true if associativity holds for the given arguments. Approximate equality is used for verifications. Read more

fn prop_is_associative(args: (Self, Self, Self)) -> bool where
    Self: Eq

Returns true if associativity holds for the given arguments.

impl<N> AbstractSemigroup<Additive> for Quaternion<N> where
    N: Real, 
[src]

fn prop_is_associative_approx(args: (Self, Self, Self)) -> bool where
    Self: RelativeEq, 

Returns true if associativity holds for the given arguments. Approximate equality is used for verifications. Read more

fn prop_is_associative(args: (Self, Self, Self)) -> bool where
    Self: Eq

Returns true if associativity holds for the given arguments.

impl<N> UlpsEq for Quaternion<N> where
    N: UlpsEq<Epsilon = N> + Real, 
[src]

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

The inverse of ApproxEq::ulps_eq.

impl<N> Hash for Quaternion<N> where
    N: Hash + Real, 
[src]

fn hash_slice<H>(data: &[Self], state: &mut H) where
    H: Hasher
1.3.0
[src]

Feeds a slice of this type into the given [Hasher]. Read more

Auto Trait Implementations

impl<N> Send for Quaternion<N> where
    N: Scalar

impl<N> Sync for Quaternion<N> where
    N: Scalar

Blanket Implementations

impl<T> From for T[src]

impl<T, U> TryFrom for T where
    U: Into<T>, 
[src]

type Error = !

🔬 This is a nightly-only experimental API. (try_from)

The type returned in the event of a conversion error.

impl<T, U> TryInto for T where
    U: TryFrom<T>, 
[src]

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

🔬 This is a nightly-only experimental API. (try_from)

The type returned in the event of a conversion error.

impl<T, U> Into for T where
    U: From<T>, 
[src]

impl<T> Borrow for T where
    T: ?Sized
[src]

impl<T> BorrowMut for T where
    T: ?Sized
[src]

impl<T> Any for T where
    T: 'static + ?Sized
[src]

impl<T> Scalar for T where
    T: Copy + PartialEq<T> + Any + Debug
[src]

fn is<T>() -> bool where
    T: Scalar
[src]

Tests if Self the same as the type T Read more

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

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

impl<T> Same for T

type Output = T

Should always be Self

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

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

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

impl<SS, SP> SupersetOf for SP where
    SS: SubsetOf<SP>, 

impl<T> MultiplicativeMonoid for T where
    T: AbstractMonoid<Multiplicative> + MultiplicativeSemigroup + One

impl<T> AdditiveMagma for T where
    T: AbstractMagma<Additive>, 

impl<T> AdditiveQuasigroup for T where
    T: AbstractQuasigroup<Additive> + ClosedSub<T> + AdditiveMagma, 

impl<T> AdditiveLoop for T where
    T: AbstractLoop<Additive> + ClosedNeg + AdditiveQuasigroup + Zero

impl<T> AdditiveSemigroup for T where
    T: AbstractSemigroup<Additive> + ClosedAdd<T> + AdditiveMagma, 

impl<T> AdditiveMonoid for T where
    T: AbstractMonoid<Additive> + AdditiveSemigroup + Zero

impl<T> AdditiveGroup for T where
    T: AbstractGroup<Additive> + AdditiveLoop + AdditiveMonoid, 

impl<T> AdditiveGroupAbelian for T where
    T: AbstractGroupAbelian<Additive> + AdditiveGroup, 

impl<T> MultiplicativeMagma for T where
    T: AbstractMagma<Multiplicative>, 

impl<T> MultiplicativeSemigroup for T where
    T: AbstractSemigroup<Multiplicative> + ClosedMul<T> + MultiplicativeMagma,