Struct nalgebra::geometry::Quaternion

#[repr(C)]
pub struct Quaternion<N: Real> {
    pub coords: Vector4<N>,
}

A quaternion. See the type alias UnitQuaternion = Unit<Quaternion> for a quaternion that may be used as a rotation.

Fields

coords: Vector4<N>

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

Methods

impl<N: Real> Quaternion<N>

pub fn into_owned(self) -> Quaternion<N>

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>

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>

Normalizes this quaternion.

pub fn conjugate(&self) -> Quaternion<N>

Compute the conjugate of this quaternion.

pub fn try_inverse(&self) -> Option<Quaternion<N>>

Inverts this quaternion if it is not zero.

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

Linear interpolation between two quaternion.

pub fn vector(
    &self
) -> MatrixSlice<N, U3, U1, RStride<N, U4, U1>, CStride<N, U4, U1>>

The vector part (i, j, k) of this quaternion.

pub fn scalar(&self) -> N

The scalar part w of this quaternion.

pub fn as_vector(&self) -> &Vector4<N>

Reinterprets this quaternion as a 4D vector.

pub fn norm(&self) -> N

The norm of this quaternion.

pub fn norm_squared(&self) -> N

The squared norm of this quaternion.

pub fn polar_decomposition(&self) -> (N, N, Option<Unit<Vector3<N>>>)

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.

pub fn exp(&self) -> Quaternion<N>

Compute the exponential of a quaternion.

pub fn exp_eps(&self, eps: N) -> Quaternion<N>

Compute the exponential of a quaternion.

pub fn ln(&self) -> Quaternion<N>

Compute the natural logarithm of a quaternion.

pub fn powf(&self, n: N) -> Quaternion<N>

Raise the quaternion to a given floating power.

pub fn as_vector_mut(&mut self) -> &mut Vector4<N>

Transforms this quaternion into its 4D vector form (Vector part, Scalar part).

pub fn vector_mut(
    &mut self
) -> MatrixSliceMut<N, U3, U1, RStride<N, U4, U1>, CStride<N, U4, U1>>

The mutable vector part (i, j, k) of this quaternion.

pub fn conjugate_mut(&mut self)

Replaces this quaternion by its conjugate.

pub fn try_inverse_mut(&mut self) -> bool

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

pub fn normalize_mut(&mut self) -> N

Normalizes this quaternion.

impl<N: Real> Quaternion<N>

pub fn from_vector(vector: Vector4<N>) -> Self

Creates a quaternion from a 4D vector. The quaternion scalar part corresponds to the w vector component.

pub fn new(w: N, x: N, y: N, z: N) -> Self

Creates a new quaternion from its individual components. Note that the arguments order does not follow the storage order.

The storage order is [ x, y, z, w ].

pub fn from_parts<SB>(scalar: N, vector: Vector<N, U3, SB>) -> Self where
    SB: Storage<N, U3>, 

Creates a new quaternion from its scalar and vector parts. Note that the arguments order does not follow the storage order.

The storage order is [ vector, scalar ].

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

Creates a new quaternion from its polar decomposition.

Note that axis is assumed to be a unit vector.

pub fn identity() -> Self

The quaternion multiplicative identity.

Trait Implementations

impl<N: Debug + Real> Debug for Quaternion<N>

fn fmt(&self, __arg_0: &mut Formatter) -> Result

Formats the value using the given formatter.

impl<N: Real + Eq> Eq for Quaternion<N>

impl<N: Real> PartialEq for Quaternion<N>

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

This method tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

This method tests for !=.

impl<N: Real + Hash> Hash for Quaternion<N>

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

Feeds this value into the given [Hasher].

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

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

impl<N: Real> Copy for Quaternion<N>

impl<N: Real> Clone for Quaternion<N>

fn clone(&self) -> Self

Returns a copy of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl<N: Real + ApproxEq<Epsilon = N>> ApproxEq for Quaternion<N>

type Epsilon = N

Used for specifying relative comparisons.

fn default_epsilon() -> Self::Epsilon

The default tolerance to use when testing values that are close together.

fn default_max_relative() -> Self::Epsilon

The default relative tolerance for testing values that are far-apart.

fn default_max_ulps() -> u32

The default ULPs to tolerate when testing values that are far-apart.

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

A test for equality that uses a relative comparison if the values are far apart.

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

A test for equality that uses units in the last place (ULP) if the values are far apart.

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

The inverse of ApproxEq::relative_eq.

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

The inverse of ApproxEq::ulps_eq.

impl<N: Real + Display> Display for Quaternion<N>

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

Formats the value using the given formatter.

impl<N: Real> One for Quaternion<N>

fn one() -> Self

Returns the multiplicative identity element of Self, 1.

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

Returns true if self is equal to the multiplicative identity.

impl<N: Real> Zero for Quaternion<N>

fn zero() -> Self

Returns the additive identity element of Self, 0.

fn is_zero(&self) -> bool

Returns true if self is equal to the additive identity.

impl<N: Real + Rand> Rand for Quaternion<N>

fn rand<R: Rng>(rng: &mut R) -> Self

Generates a random instance of this type using the specified source of randomness.

impl<N: Real> Index<usize> for Quaternion<N>

type Output = N

The returned type after indexing.

Important traits for &'a mut W

impl<'a, W> Write for &'a mut W where
    W: Write + ?Sized, impl<'a, R> Read for &'a mut R where
    R: Read + ?Sized, impl<'a, I> Iterator for &'a mut I where
    I: Iterator + ?Sized,  type Item = <I as Iterator>::Item;

fn index(&self, i: usize) -> &N

Performs the indexing (container[index]) operation.

impl<N: Real> IndexMut<usize> for Quaternion<N>

Important traits for &'a mut W

impl<'a, W> Write for &'a mut W where
    W: Write + ?Sized, impl<'a, R> Read for &'a mut R where
    R: Read + ?Sized, impl<'a, I> Iterator for &'a mut I where
    I: Iterator + ?Sized,  type Item = <I as Iterator>::Item;

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

Performs the mutable indexing (container[index]) operation.

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

type Output = Quaternion<N>

The resulting type after applying the + operator.

fn add(self, rhs: &'b Quaternion<N>) -> Self::Output

Performs the + operation.

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

type Output = Quaternion<N>

The resulting type after applying the + operator.

fn add(self, rhs: Quaternion<N>) -> Self::Output

Performs the + operation.

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

type Output = Quaternion<N>

The resulting type after applying the + operator.

fn add(self, rhs: &'b Quaternion<N>) -> Self::Output

Performs the + operation.

impl<N: Real> Add<Quaternion<N>> for Quaternion<N> where
    DefaultAllocator: Allocator<N, U4, U1> + Allocator<N, U4, U1>, 

type Output = Quaternion<N>

The resulting type after applying the + operator.

fn add(self, rhs: Quaternion<N>) -> Self::Output

Performs the + operation.

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

type Output = Quaternion<N>

The resulting type after applying the - operator.

fn sub(self, rhs: &'b Quaternion<N>) -> Self::Output

Performs the - operation.

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

type Output = Quaternion<N>

The resulting type after applying the - operator.

fn sub(self, rhs: Quaternion<N>) -> Self::Output

Performs the - operation.

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

type Output = Quaternion<N>

The resulting type after applying the - operator.

fn sub(self, rhs: &'b Quaternion<N>) -> Self::Output

Performs the - operation.

impl<N: Real> Sub<Quaternion<N>> for Quaternion<N> where
    DefaultAllocator: Allocator<N, U4, U1> + Allocator<N, U4, U1>, 

type Output = Quaternion<N>

The resulting type after applying the - operator.

fn sub(self, rhs: Quaternion<N>) -> Self::Output

Performs the - operation.

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

type Output = Quaternion<N>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Quaternion<N>) -> Self::Output

Performs the * operation.

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

type Output = Quaternion<N>

The resulting type after applying the * operator.

fn mul(self, rhs: Quaternion<N>) -> Self::Output

Performs the * operation.

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

type Output = Quaternion<N>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Quaternion<N>) -> Self::Output

Performs the * operation.

impl<N: Real> Mul<Quaternion<N>> for Quaternion<N> where
    DefaultAllocator: Allocator<N, U4, U1> + Allocator<N, U4, U1>, 

type Output = Quaternion<N>

The resulting type after applying the * operator.

fn mul(self, rhs: Quaternion<N>) -> Self::Output

Performs the * operation.

impl<N: Real> Mul<N> for Quaternion<N>

type Output = Quaternion<N>

The resulting type after applying the * operator.

fn mul(self, n: N) -> Self::Output

Performs the * operation.

impl<'a, N: Real> Mul<N> for &'a Quaternion<N>

type Output = Quaternion<N>

The resulting type after applying the * operator.

fn mul(self, n: N) -> Self::Output

Performs the * operation.

impl<N: Real> MulAssign<N> for Quaternion<N>

fn mul_assign(&mut self, n: N)

Performs the *= operation.

impl<N: Real> Div<N> for Quaternion<N>

type Output = Quaternion<N>

The resulting type after applying the / operator.

fn div(self, n: N) -> Self::Output

Performs the / operation.

impl<'a, N: Real> Div<N> for &'a Quaternion<N>

type Output = Quaternion<N>

The resulting type after applying the / operator.

fn div(self, n: N) -> Self::Output

Performs the / operation.

impl<N: Real> DivAssign<N> for Quaternion<N>

fn div_assign(&mut self, n: N)

Performs the /= operation.

impl Mul<Quaternion<f32>> for f32

type Output = Quaternion<f32>

The resulting type after applying the * operator.

fn mul(self, right: Quaternion<f32>) -> Self::Output

Performs the * operation.

impl<'b> Mul<&'b Quaternion<f32>> for f32

type Output = Quaternion<f32>

The resulting type after applying the * operator.

fn mul(self, right: &'b Quaternion<f32>) -> Self::Output

Performs the * operation.

impl Mul<Quaternion<f64>> for f64

type Output = Quaternion<f64>

The resulting type after applying the * operator.

fn mul(self, right: Quaternion<f64>) -> Self::Output

Performs the * operation.

impl<'b> Mul<&'b Quaternion<f64>> for f64

type Output = Quaternion<f64>

The resulting type after applying the * operator.

fn mul(self, right: &'b Quaternion<f64>) -> Self::Output

Performs the * operation.

impl<N: Real> Neg for Quaternion<N>

type Output = Quaternion<N>

The resulting type after applying the - operator.

fn neg(self) -> Self::Output

Performs the unary - operation.

impl<'a, N: Real> Neg for &'a Quaternion<N>

type Output = Quaternion<N>

The resulting type after applying the - operator.

fn neg(self) -> Self::Output

Performs the unary - operation.

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

fn add_assign(&mut self, rhs: &'b Quaternion<N>)

Performs the += operation.

impl<N: Real> AddAssign<Quaternion<N>> for Quaternion<N> where
    DefaultAllocator: Allocator<N, U4, U1> + Allocator<N, U4, U1>, 

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

Performs the += operation.

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

fn sub_assign(&mut self, rhs: &'b Quaternion<N>)

Performs the -= operation.

impl<N: Real> SubAssign<Quaternion<N>> for Quaternion<N> where
    DefaultAllocator: Allocator<N, U4, U1> + Allocator<N, U4, U1>, 

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

Performs the -= operation.

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

fn mul_assign(&mut self, rhs: &'b Quaternion<N>)

Performs the *= operation.

impl<N: Real> MulAssign<Quaternion<N>> for Quaternion<N> where
    DefaultAllocator: Allocator<N, U4, U1> + Allocator<N, U4, U1>, 

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

Performs the *= operation.

impl<N: Real> Identity<Multiplicative> for Quaternion<N>

fn identity() -> Self

The identity element.

fn id(O) -> Self

Specific identity.

impl<N: Real> Identity<Additive> for Quaternion<N>

fn identity() -> Self

The identity element.

fn id(O) -> Self

Specific identity.

impl<N: Real> AbstractMagma<Multiplicative> for Quaternion<N>

fn operate(&self, rhs: &Self) -> Self

Performs an operation.

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

Performs specific operation.

impl<N: Real> AbstractMagma<Additive> for Quaternion<N>

fn operate(&self, rhs: &Self) -> Self

Performs an operation.

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

Performs specific operation.

impl<N: Real> Inverse<Additive> for Quaternion<N>

fn inverse(&self) -> Self

Returns the inverse of self, relative to the operator O.

fn inverse_mut(&mut self)

In-place inversin of self.

impl<N: Real> AbstractSemigroup<Multiplicative> for Quaternion<N>

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

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

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

Returns true if associativity holds for the given arguments.

impl<N: Real> AbstractMonoid<Multiplicative> for Quaternion<N>

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

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

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.

impl<N: Real> AbstractSemigroup<Additive> for Quaternion<N>

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

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

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

Returns true if associativity holds for the given arguments.

impl<N: Real> AbstractQuasigroup<Additive> for Quaternion<N>

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

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

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

Returns true if latin squareness holds for the given arguments.

impl<N: Real> AbstractMonoid<Additive> for Quaternion<N>

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

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

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.

impl<N: Real> AbstractLoop<Additive> for Quaternion<N>

impl<N: Real> AbstractGroup<Additive> for Quaternion<N>

impl<N: Real> AbstractGroupAbelian<Additive> for Quaternion<N>

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

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

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: Real> AbstractModule for Quaternion<N>

type AbstractRing = N

The underlying scalar field.

fn multiply_by(&self, n: N) -> Self

Multiplies an element of the ring with an element of the module.

impl<N: Real> Module for Quaternion<N>

type Ring = N

The underlying scalar field.

impl<N: Real> VectorSpace for Quaternion<N>

type Field = N

The underlying scalar field.

impl<N: Real> FiniteDimVectorSpace for Quaternion<N>

fn dimension() -> usize

The vector space dimension.

fn canonical_basis_element(i: usize) -> Self

The i-the canonical basis element.

fn dot(&self, other: &Self) -> N

The dot product between two vectors.

Important traits for &'a mut W

impl<'a, W> Write for &'a mut W where
    W: Write + ?Sized, impl<'a, R> Read for &'a mut R where
    R: Read + ?Sized, impl<'a, I> Iterator for &'a mut I where
    I: Iterator + ?Sized,  type Item = <I as Iterator>::Item;

unsafe fn component_unchecked(&self, i: usize) -> &N

Same as &self[i] but without bound-checking.

Important traits for &'a mut W

impl<'a, W> Write for &'a mut W where
    W: Write + ?Sized, impl<'a, R> Read for &'a mut R where
    R: Read + ?Sized, impl<'a, I> Iterator for &'a mut I where
    I: Iterator + ?Sized,  type Item = <I as Iterator>::Item;

unsafe fn component_unchecked_mut(&mut self, i: usize) -> &mut N

Same as &mut self[i] but without bound-checking.

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.

impl<N: Real> NormedSpace for Quaternion<N>

fn norm_squared(&self) -> N

The squared norm of this vector.

fn norm(&self) -> N

The norm of this vector.

fn normalize(&self) -> Self

Returns a normalized version of this vector.

fn normalize_mut(&mut self) -> N

Normalizes this vector in-place and returns its norm.

fn try_normalize(&self, min_norm: N) -> Option<Self>

Returns a normalized version of this vector unless its norm as smaller or equal to eps.

fn try_normalize_mut(&mut self, min_norm: N) -> Option<N>

Normalizes this vector in-place or does nothing if its norm is smaller or equal to eps.

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

fn to_superset(&self) -> Quaternion<N2>

The inclusion map: converts self to the equivalent element of its superset.

fn is_in_subset(q: &Quaternion<N2>) -> bool

Checks if element is actually part of the subset Self (and can be converted to it).

unsafe fn from_superset_unchecked(q: &Quaternion<N2>) -> Self

Use with care! Same as self.to_superset but without any property checks. Always succeeds.

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

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

impl<N: Real> Deref for Quaternion<N>

type Target = IJKW<N>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<N: Real> DerefMut for Quaternion<N>

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

Mutably dereferences the value.