Struct nalgebra::geometry::QuaternionBase

#[repr(C)]
pub struct QuaternionBase<N: Real, S: Storage<N, U4, U1>> {
    pub coords: ColumnVector<N, U4, S>,
}

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

Fields

coords: ColumnVector<N, U4, S>

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

Methods

impl<N, S> QuaternionBase<N, S> where
    N: Real,
    S: Storage<N, U4, U1>, 

fn into_owned(self) -> OwnedQuaternionBase<N, S::Alloc>

Moves this quaternion into one that owns its data.

fn clone_owned(&self) -> OwnedQuaternionBase<N, S::Alloc>

Clones this quaternion into one that owns its data.

fn vector(&self) -> MatrixSlice<N, U3, U1, S::RStride, S::CStride, S::Alloc>

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

fn scalar(&self) -> N

The scalar part w of this quaternion.

fn as_vector(&self) -> &ColumnVector<N, U4, S>

Reinterprets this quaternion as a 4D vector.

fn norm(&self) -> N

The norm of this quaternion.

fn norm_squared(&self) -> N

The squared norm of this quaternion.

fn normalize(&self) -> OwnedQuaternionBase<N, S::Alloc>

Normalizes this quaternion.

fn conjugate(&self) -> OwnedQuaternionBase<N, S::Alloc>

Compute the conjugate of this quaternion.

fn try_inverse(&self) -> Option<OwnedQuaternionBase<N, S::Alloc>>

Inverts this quaternion if it is not zero.

fn lerp<S2>(
    &self,
    other: &QuaternionBase<N, S2>,
    t: N
) -> OwnedQuaternionBase<N, S::Alloc> where
    S2: Storage<N, U4, U1>, 

Linear interpolation between two quaternion.

impl<N, S> QuaternionBase<N, S> where
    N: Real,
    S: Storage<N, U4, U1>,
    S::Alloc: Allocator<N, U3, U1>, 

fn polar_decomposition(
    &self
) -> (N, N, Option<Unit<OwnedColumnVector<N, U3, S::Alloc>>>)

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.

fn exp(&self) -> OwnedQuaternionBase<N, S::Alloc>

Compute the exponential of a quaternion.

fn ln(&self) -> OwnedQuaternionBase<N, S::Alloc>

Compute the natural logarithm of a quaternion.

fn powf(&self, n: N) -> OwnedQuaternionBase<N, S::Alloc>

Raise the quaternion to a given floating power.

impl<N, S> QuaternionBase<N, S> where
    N: Real,
    S: StorageMut<N, U4, U1>, 

fn as_vector_mut(&mut self) -> &mut ColumnVector<N, U4, S>

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

fn vector_mut(
    &mut self
) -> MatrixSliceMut<N, U3, U1, S::RStride, S::CStride, S::Alloc>

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

fn conjugate_mut(&mut self)

Replaces this quaternion by its conjugate.

fn try_inverse_mut(&mut self) -> bool

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

fn normalize_mut(&mut self) -> N

Normalizes this quaternion.

impl<N, S> QuaternionBase<N, S> where
    N: Real,
    S: Storage<N, U4, U1>, 

fn from_vector(vector: ColumnVector<N, U4, S>) -> Self

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

impl<N, S> QuaternionBase<N, S> where
    N: Real,
    S: OwnedStorage<N, U4, U1>,
    S::Alloc: OwnedAllocator<N, U4, U1, S>, 

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 ].

fn from_parts<SB>(scalar: N, vector: ColumnVector<N, U3, SB>) -> Self where
    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 ].

fn from_polar_decomposition<SB>(
    scale: N,
    theta: N,
    axis: Unit<ColumnVector<N, U3, SB>>
) -> Self where
    SB: Storage<N, U3, U1>, 

Creates a new quaternion from its polar decomposition.

Note that axis is assumed to be a unit vector.

fn identity() -> Self

The quaternion multiplicative identity.

Trait Implementations

impl<N: Hash + Real, S: Hash + Storage<N, U4, U1>> Hash for QuaternionBase<N, S>

fn hash<__HNS: Hasher>(&self, __arg_0: &mut __HNS)

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: Debug + Real, S: Debug + Storage<N, U4, U1>> Debug for QuaternionBase<N, S>

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

Formats the value using the given formatter.

impl<N: Copy + Real, S: Copy + Storage<N, U4, U1>> Copy for QuaternionBase<N, S>

impl<N: Clone + Real, S: Clone + Storage<N, U4, U1>> Clone for QuaternionBase<N, S>

fn clone(&self) -> QuaternionBase<N, S>

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<N, S> Eq for QuaternionBase<N, S> where
    N: Real + Eq,
    S: Storage<N, U4, U1>, 

impl<N, S> PartialEq for QuaternionBase<N, S> where
    N: Real,
    S: Storage<N, U4, U1>, 

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, S> ApproxEq for QuaternionBase<N, S> where
    N: Real + ApproxEq<Epsilon = N>,
    S: Storage<N, U4, U1>, 

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, S> Display for QuaternionBase<N, S> where
    N: Real + Display,
    S: Storage<N, U4, U1>, 

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

Formats the value using the given formatter.

impl<N, S> One for QuaternionBase<N, S> where
    N: Real,
    S: OwnedStorage<N, U4, U1>,
    S::Alloc: OwnedAllocator<N, U4, U1, S>, 

fn one() -> Self

Returns the multiplicative identity element of Self, 1.

impl<N, S> Zero for QuaternionBase<N, S> where
    N: Real,
    S: OwnedStorage<N, U4, U1>,
    S::Alloc: OwnedAllocator<N, U4, U1, S>, 

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, S> Rand for QuaternionBase<N, S> where
    N: Real + Rand,
    S: OwnedStorage<N, U4, U1>,
    S::Alloc: OwnedAllocator<N, U4, U1, S>, 

fn rand<R: Rng>(rng: &mut R) -> Self

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

impl<N, S> Index<usize> for QuaternionBase<N, S> where
    N: Real,
    S: Storage<N, U4, U1>, 

type Output = N

The returned type after indexing

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

The method for the indexing (container[index]) operation

impl<N, S> IndexMut<usize> for QuaternionBase<N, S> where
    N: Real,
    S: StorageMut<N, U4, U1>, 

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

The method for the mutable indexing (container[index]) operation

impl<'a, 'b, N, SA, SB> Add<&'b QuaternionBase<N, SB>> for &'a QuaternionBase<N, SA> where
    N: Real,
    SA: Storage<N, U4, U1>,
    SB: Storage<N, U4, U1>, 

type Output = OwnedQuaternionBase<N, SA::Alloc>

The resulting type after applying the + operator

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

The method for the + operator

impl<'a, N, SA, SB> Add<QuaternionBase<N, SB>> for &'a QuaternionBase<N, SA> where
    N: Real,
    SA: Storage<N, U4, U1>,
    SB: Storage<N, U4, U1>, 

type Output = OwnedQuaternionBase<N, SB::Alloc>

The resulting type after applying the + operator

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

The method for the + operator

impl<'b, N, SA, SB> Add<&'b QuaternionBase<N, SB>> for QuaternionBase<N, SA> where
    N: Real,
    SA: Storage<N, U4, U1>,
    SB: Storage<N, U4, U1>, 

type Output = OwnedQuaternionBase<N, SA::Alloc>

The resulting type after applying the + operator

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

The method for the + operator

impl<N, SA, SB> Add<QuaternionBase<N, SB>> for QuaternionBase<N, SA> where
    N: Real,
    SA: Storage<N, U4, U1>,
    SB: Storage<N, U4, U1>, 

type Output = OwnedQuaternionBase<N, SA::Alloc>

The resulting type after applying the + operator

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

The method for the + operator

impl<'a, 'b, N, SA, SB> Sub<&'b QuaternionBase<N, SB>> for &'a QuaternionBase<N, SA> where
    N: Real,
    SA: Storage<N, U4, U1>,
    SB: Storage<N, U4, U1>, 

type Output = OwnedQuaternionBase<N, SA::Alloc>

The resulting type after applying the - operator

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

The method for the - operator

impl<'a, N, SA, SB> Sub<QuaternionBase<N, SB>> for &'a QuaternionBase<N, SA> where
    N: Real,
    SA: Storage<N, U4, U1>,
    SB: Storage<N, U4, U1>, 

type Output = OwnedQuaternionBase<N, SB::Alloc>

The resulting type after applying the - operator

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

The method for the - operator

impl<'b, N, SA, SB> Sub<&'b QuaternionBase<N, SB>> for QuaternionBase<N, SA> where
    N: Real,
    SA: Storage<N, U4, U1>,
    SB: Storage<N, U4, U1>, 

type Output = OwnedQuaternionBase<N, SA::Alloc>

The resulting type after applying the - operator

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

The method for the - operator

impl<N, SA, SB> Sub<QuaternionBase<N, SB>> for QuaternionBase<N, SA> where
    N: Real,
    SA: Storage<N, U4, U1>,
    SB: Storage<N, U4, U1>, 

type Output = OwnedQuaternionBase<N, SA::Alloc>

The resulting type after applying the - operator

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

The method for the - operator

impl<'a, 'b, N, SA, SB> Mul<&'b QuaternionBase<N, SB>> for &'a QuaternionBase<N, SA> where
    N: Real,
    SA: Storage<N, U4, U1>,
    SB: Storage<N, U4, U1>, 

type Output = OwnedQuaternionBase<N, SA::Alloc>

The resulting type after applying the * operator

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

The method for the * operator

impl<'a, N, SA, SB> Mul<QuaternionBase<N, SB>> for &'a QuaternionBase<N, SA> where
    N: Real,
    SA: Storage<N, U4, U1>,
    SB: Storage<N, U4, U1>, 

type Output = OwnedQuaternionBase<N, SA::Alloc>

The resulting type after applying the * operator

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

The method for the * operator

impl<'b, N, SA, SB> Mul<&'b QuaternionBase<N, SB>> for QuaternionBase<N, SA> where
    N: Real,
    SA: Storage<N, U4, U1>,
    SB: Storage<N, U4, U1>, 

type Output = OwnedQuaternionBase<N, SA::Alloc>

The resulting type after applying the * operator

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

The method for the * operator

impl<N, SA, SB> Mul<QuaternionBase<N, SB>> for QuaternionBase<N, SA> where
    N: Real,
    SA: Storage<N, U4, U1>,
    SB: Storage<N, U4, U1>, 

type Output = OwnedQuaternionBase<N, SA::Alloc>

The resulting type after applying the * operator

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

The method for the * operator

impl<N, S> Mul<N> for QuaternionBase<N, S> where
    N: Real,
    S: Storage<N, U4, U1>, 

type Output = OwnedQuaternionBase<N, S::Alloc>

The resulting type after applying the * operator

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

The method for the * operator

impl<'a, N, S> Mul<N> for &'a QuaternionBase<N, S> where
    N: Real,
    S: Storage<N, U4, U1>, 

type Output = OwnedQuaternionBase<N, S::Alloc>

The resulting type after applying the * operator

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

The method for the * operator

impl<N, S> MulAssign<N> for QuaternionBase<N, S> where
    N: Real,
    S: StorageMut<N, U4, U1>, 

fn mul_assign(&mut self, n: N)

The method for the *= operator

impl<N, S> Div<N> for QuaternionBase<N, S> where
    N: Real,
    S: Storage<N, U4, U1>, 

type Output = OwnedQuaternionBase<N, S::Alloc>

The resulting type after applying the / operator

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

The method for the / operator

impl<'a, N, S> Div<N> for &'a QuaternionBase<N, S> where
    N: Real,
    S: Storage<N, U4, U1>, 

type Output = OwnedQuaternionBase<N, S::Alloc>

The resulting type after applying the / operator

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

The method for the / operator

impl<N, S> DivAssign<N> for QuaternionBase<N, S> where
    N: Real,
    S: StorageMut<N, U4, U1>, 

fn div_assign(&mut self, n: N)

The method for the /= operator

impl<N, S> Neg for QuaternionBase<N, S> where
    N: Real,
    S: Storage<N, U4, U1>, 

type Output = OwnedQuaternionBase<N, S::Alloc>

The resulting type after applying the - operator

fn neg(self) -> Self::Output

The method for the unary - operator

impl<'a, N, S> Neg for &'a QuaternionBase<N, S> where
    N: Real,
    S: Storage<N, U4, U1>, 

type Output = OwnedQuaternionBase<N, S::Alloc>

The resulting type after applying the - operator

fn neg(self) -> Self::Output

The method for the unary - operator

impl<'b, N, SA, SB> AddAssign<&'b QuaternionBase<N, SB>> for QuaternionBase<N, SA> where
    N: Real,
    SA: StorageMut<N, U4, U1>,
    SB: Storage<N, U4, U1>, 

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

The method for the += operator

impl<N, SA, SB> AddAssign<QuaternionBase<N, SB>> for QuaternionBase<N, SA> where
    N: Real,
    SA: StorageMut<N, U4, U1>,
    SB: Storage<N, U4, U1>, 

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

The method for the += operator

impl<'b, N, SA, SB> SubAssign<&'b QuaternionBase<N, SB>> for QuaternionBase<N, SA> where
    N: Real,
    SA: StorageMut<N, U4, U1>,
    SB: Storage<N, U4, U1>, 

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

The method for the -= operator

impl<N, SA, SB> SubAssign<QuaternionBase<N, SB>> for QuaternionBase<N, SA> where
    N: Real,
    SA: StorageMut<N, U4, U1>,
    SB: Storage<N, U4, U1>, 

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

The method for the -= operator

impl<'b, N, SA, SB> MulAssign<&'b QuaternionBase<N, SB>> for QuaternionBase<N, SA> where
    N: Real,
    SA: StorageMut<N, U4, U1>,
    SB: Storage<N, U4, U1>, 

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

The method for the *= operator

impl<N, SA, SB> MulAssign<QuaternionBase<N, SB>> for QuaternionBase<N, SA> where
    N: Real,
    SA: StorageMut<N, U4, U1>,
    SB: Storage<N, U4, U1>, 

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

The method for the *= operator

impl<N, S> Identity<Multiplicative> for QuaternionBase<N, S> where
    N: Real,
    S: OwnedStorage<N, U4, U1>,
    S::Alloc: OwnedAllocator<N, U4, U1, S>, 

fn identity() -> Self

The identity element.

impl<N, S> Identity<Additive> for QuaternionBase<N, S> where
    N: Real,
    S: OwnedStorage<N, U4, U1>,
    S::Alloc: OwnedAllocator<N, U4, U1, S>, 

fn identity() -> Self

The identity element.

impl<N, S> AbstractMagma<Multiplicative> for QuaternionBase<N, S> where
    N: Real,
    S: OwnedStorage<N, U4, U1>,
    S::Alloc: OwnedAllocator<N, U4, U1, S>, 

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

Performs an operation.

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

Performs specific operation.

impl<N, S> AbstractMagma<Additive> for QuaternionBase<N, S> where
    N: Real,
    S: OwnedStorage<N, U4, U1>,
    S::Alloc: OwnedAllocator<N, U4, U1, S>, 

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

Performs an operation.

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

Performs specific operation.

impl<N, S> Inverse<Additive> for QuaternionBase<N, S> where
    N: Real,
    S: OwnedStorage<N, U4, U1>,
    S::Alloc: OwnedAllocator<N, U4, U1, S>, 

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, S> AbstractSemigroup<Multiplicative> for QuaternionBase<N, S> where
    N: Real,
    S: OwnedStorage<N, U4, U1>,
    S::Alloc: OwnedAllocator<N, U4, U1, S>, 

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, S> AbstractMonoid<Multiplicative> for QuaternionBase<N, S> where
    N: Real,
    S: OwnedStorage<N, U4, U1>,
    S::Alloc: OwnedAllocator<N, U4, U1, S>, 

fn prop_operating_identity_element_is_noop_approx(a: 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(a: Self) -> bool where
    Self: Eq, 

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

impl<N, S> AbstractSemigroup<Additive> for QuaternionBase<N, S> where
    N: Real,
    S: OwnedStorage<N, U4, U1>,
    S::Alloc: OwnedAllocator<N, U4, U1, S>, 

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, S> AbstractQuasigroup<Additive> for QuaternionBase<N, S> where
    N: Real,
    S: OwnedStorage<N, U4, U1>,
    S::Alloc: OwnedAllocator<N, U4, U1, S>, 

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, S> AbstractMonoid<Additive> for QuaternionBase<N, S> where
    N: Real,
    S: OwnedStorage<N, U4, U1>,
    S::Alloc: OwnedAllocator<N, U4, U1, S>, 

fn prop_operating_identity_element_is_noop_approx(a: 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(a: Self) -> bool where
    Self: Eq, 

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

impl<N, S> AbstractLoop<Additive> for QuaternionBase<N, S> where
    N: Real,
    S: OwnedStorage<N, U4, U1>,
    S::Alloc: OwnedAllocator<N, U4, U1, S>, 

impl<N, S> AbstractGroup<Additive> for QuaternionBase<N, S> where
    N: Real,
    S: OwnedStorage<N, U4, U1>,
    S::Alloc: OwnedAllocator<N, U4, U1, S>, 

impl<N, S> AbstractGroupAbelian<Additive> for QuaternionBase<N, S> where
    N: Real,
    S: OwnedStorage<N, U4, U1>,
    S::Alloc: OwnedAllocator<N, U4, U1, S>, 

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, S> AbstractModule for QuaternionBase<N, S> where
    N: Real,
    S: OwnedStorage<N, U4, U1>,
    S::Alloc: OwnedAllocator<N, U4, U1, S>, 

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, S> Module for QuaternionBase<N, S> where
    N: Real,
    S: OwnedStorage<N, U4, U1>,
    S::Alloc: OwnedAllocator<N, U4, U1, S>, 

type Ring = N

The underlying scalar field.

impl<N, S> VectorSpace for QuaternionBase<N, S> where
    N: Real,
    S: OwnedStorage<N, U4, U1>,
    S::Alloc: OwnedAllocator<N, U4, U1, S>, 

type Field = N

The underlying scalar field.

impl<N, S> FiniteDimVectorSpace for QuaternionBase<N, S> where
    N: Real,
    S: OwnedStorage<N, U4, U1>,
    S::Alloc: OwnedAllocator<N, U4, U1, S>, 

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.

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

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

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, S> NormedSpace for QuaternionBase<N, S> where
    N: Real,
    S: OwnedStorage<N, U4, U1>,
    S::Alloc: OwnedAllocator<N, U4, U1, S>, 

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<N, S> Deref for QuaternionBase<N, S> where
    N: Real,
    S: OwnedStorage<N, U4, U1>,
    S::Alloc: OwnedAllocator<N, U4, U1, S>, 

type Target = IJKW<N>

The resulting type after dereferencing

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

The method called to dereference a value

impl<N, S> DerefMut for QuaternionBase<N, S> where
    N: Real,
    S: OwnedStorage<N, U4, U1>,
    S::Alloc: OwnedAllocator<N, U4, U1, S>, 

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

The method called to mutably dereference a value

impl<N1, N2, SA, SB> SubsetOf<QuaternionBase<N2, SB>> for QuaternionBase<N1, SA> where
    N1: Real,
    N2: Real + SupersetOf<N1>,
    SA: OwnedStorage<N1, U4, U1>,
    SB: OwnedStorage<N2, U4, U1>,
    SA::Alloc: OwnedAllocator<N1, U4, U1, SA>,
    SB::Alloc: OwnedAllocator<N2, U4, U1, SB>, 

fn to_superset(&self) -> QuaternionBase<N2, SB>

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

fn is_in_subset(q: &QuaternionBase<N2, SB>) -> bool

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

unsafe fn from_superset_unchecked(q: &QuaternionBase<N2, SB>) -> 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.