Struct nalgebra::Quaternion

pub struct Quaternion<N> {
    pub w: N,
    pub i: N,
    pub j: N,
    pub k: N,
}

A quaternion. See the UnitQuaternion type alias for a quaternion that can be used as a rotation.

Fields

w: N

The scalar component of the quaternion.

i: N

The first vector component of the quaternion.

j: N

The second vector component of the quaternion.

k: N

The third vector component of the quaternion.

Methods

impl<N: Copy> Quaternion<N>

fn vector(&self) -> &Vector3<N>

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

fn scalar(&self) -> N

The scalar part w of this quaternion.

impl<N: BaseNum + Neg<Output=N>> Quaternion<N>

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

Compute the conjugate of this quaternion.

fn conjugate_mut(&mut self)

Replaces this quaternion by its conjugate.

impl<N: BaseFloat> Quaternion<N>

fn from_parts(scalar: N, vector: Vector3<N>) -> Quaternion<N>

Creates a new quaternion from its scalar and vector parts.

fn from_polar_decomposition(scale: N, theta: N, axis: Unit<Vector3<N>>) -> Quaternion<N>

Creates a new quaternion from its polar decomposition.

Note that axis is assumed to be a unit vector.

fn polar_decomposition(&self) -> (N, N, 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 the y axis.

impl<N: BaseFloat> Quaternion<N>

fn exp(&self) -> Self

Compute the exponential of a quaternion.

fn ln(&self) -> Self

Compute the natural logarithm of a quaternion.

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

Raise the quaternion to a given floating power.

impl<N: Zero + One> Quaternion<N>

fn w() -> Quaternion<N>

Create the element of the canonical basis having this component set to one and all the others set to zero.

fn i() -> Quaternion<N>

Create the element of the canonical basis having this component set to one and all the others set to zero.

fn j() -> Quaternion<N>

Create the element of the canonical basis having this component set to one and all the others set to zero.

fn k() -> Quaternion<N>

Create the element of the canonical basis having this component set to one and all the others set to zero.

impl<N> Quaternion<N>

fn new(w: N, i: N, j: N, k: N) -> Quaternion<N>

Creation from component values.

impl<N: Copy> Quaternion<N>

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

Unsafe read access to a vector element by index.

unsafe fn set_fast(&mut self, i: usize, val: N)

Unsafe write access to a vector element by index.

impl<N> Quaternion<N>

fn len(&self) -> usize

The dimension of this entity.

Trait Implementations

impl<N: Copy> Copy for Quaternion<N>

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

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

Formats the value using the given formatter.

impl<N: Hash> Hash for Quaternion<N>

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

Feeds this value into the state given, updating the hasher as necessary.

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

Feeds a slice of this type into the state provided.

impl<N: Clone> Clone for Quaternion<N>

fn clone(&self) -> Quaternion<N>

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<N: Decodable> Decodable for Quaternion<N>

fn decode<__DN: Decoder>(__arg_0: &mut __DN) -> Result<Quaternion<N>, __DN::Error>

impl<N: Encodable> Encodable for Quaternion<N>

fn encode<__SN: Encoder>(&self, __arg_0: &mut __SN) -> Result<(), __SN::Error>

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

fn eq(&self, __arg_0: &Quaternion<N>) -> bool

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

fn ne(&self, __arg_0: &Quaternion<N>) -> bool

This method tests for !=.

impl<N: Eq> Eq for Quaternion<N>

impl<N: BaseFloat> Inverse for Quaternion<N>

fn inverse(&self) -> Option<Quaternion<N>>

Returns the inverse of m.

fn inverse_mut(&mut self) -> bool

In-place version of inverse.

impl<N: BaseFloat> Norm for Quaternion<N>

type NormType = N

The scalar type for the norm (i.e. the undelying field).

fn norm_squared(&self) -> N

Computes the squared norm of self.

fn normalize(&self) -> Quaternion<N>

Gets the normalized version of a copy of v.

fn normalize_mut(&mut self) -> N

Normalizes self.

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

Gets the normalized version of a copy of v or None if the vector has a norm smaller or equal to min_norm. In particular, .try_normalize(0.0) returns None if the norm is exactly zero.

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

Normalized v or does nothing if the vector has a norm smaller or equal to min_norm.

fn norm(&self) -> Self::NormType

Computes the norm of self.

impl<N> Mul<Quaternion<N>> for Quaternion<N> where N: Copy + Mul<N, Output=N> + Sub<N, Output=N> + Add<N, Output=N>

type Output = Quaternion<N>

The resulting type after applying the * operator

fn mul(self, right: Quaternion<N>) -> Quaternion<N>

The method for the * operator

impl<N> MulAssign<Quaternion<N>> for Quaternion<N> where N: Copy + Mul<N, Output=N> + Sub<N, Output=N> + Add<N, Output=N>

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

The method for the *= operator

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

type Output = Quaternion<N>

The resulting type after applying the / operator

fn div(self, right: Quaternion<N>) -> Quaternion<N>

The method for the / operator

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

fn div_assign(&mut self, right: Quaternion<N>)

The method for the /= operator

impl<T> One for Quaternion<T> where T: Copy + One + Zero + Sub<T, Output=T> + Add<T, Output=T>

fn one() -> Self

Returns the multiplicative identity element of Self, 1.

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

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

Formats the value using the given formatter.

impl<N: Zero> Zero for Quaternion<N>

fn zero() -> Quaternion<N>

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: Add<N, Output=N>> Add<Quaternion<N>> for Quaternion<N>

type Output = Quaternion<N>

The resulting type after applying the + operator

fn add(self, right: Quaternion<N>) -> Quaternion<N>

The method for the + operator

impl<N: AddAssign<N>> AddAssign<Quaternion<N>> for Quaternion<N>

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

The method for the += operator

impl<'a, 'b, N> Add<&'a Quaternion<N>> for &'b Quaternion<N> where &'b N: Add<&'a N, Output=N>

type Output = Quaternion<N>

The resulting type after applying the + operator

fn add(self, right: &'a Quaternion<N>) -> Quaternion<N>

The method for the + operator

impl<'a, N> Add<&'a Quaternion<N>> for Quaternion<N> where N: Add<&'a N, Output=N>

type Output = Quaternion<N>

The resulting type after applying the + operator

fn add(self, right: &'a Quaternion<N>) -> Quaternion<N>

The method for the + operator

impl<'a, N> Add<Quaternion<N>> for &'a Quaternion<N> where &'a N: Add<N, Output=N>

type Output = Quaternion<N>

The resulting type after applying the + operator

fn add(self, right: Quaternion<N>) -> Quaternion<N>

The method for the + operator

impl<N: Sub<N, Output=N>> Sub<Quaternion<N>> for Quaternion<N>

type Output = Quaternion<N>

The resulting type after applying the - operator

fn sub(self, right: Quaternion<N>) -> Quaternion<N>

The method for the - operator

impl<N: SubAssign<N>> SubAssign<Quaternion<N>> for Quaternion<N>

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

The method for the -= operator

impl<'a, 'b, N> Sub<&'a Quaternion<N>> for &'b Quaternion<N> where &'b N: Sub<&'a N, Output=N>

type Output = Quaternion<N>

The resulting type after applying the - operator

fn sub(self, right: &'a Quaternion<N>) -> Quaternion<N>

The method for the - operator

impl<'a, N> Sub<&'a Quaternion<N>> for Quaternion<N> where N: Sub<&'a N, Output=N>

type Output = Quaternion<N>

The resulting type after applying the - operator

fn sub(self, right: &'a Quaternion<N>) -> Quaternion<N>

The method for the - operator

impl<'a, N> Sub<Quaternion<N>> for &'a Quaternion<N> where &'a N: Sub<N, Output=N>

type Output = Quaternion<N>

The resulting type after applying the - operator

fn sub(self, right: Quaternion<N>) -> Quaternion<N>

The method for the - operator

impl<N> FromIterator<N> for Quaternion<N>

fn from_iter<I: IntoIterator<Item=N>>(iterator: I) -> Quaternion<N>

Creates a value from an iterator.

impl<N: Neg<Output=N> + Copy> Neg for Quaternion<N>

type Output = Quaternion<N>

The resulting type after applying the - operator

fn neg(self) -> Quaternion<N>

The method for the unary - operator

impl<'a, N> Neg for &'a Quaternion<N> where &'a N: Neg<Output=N>

type Output = Quaternion<N>

The resulting type after applying the - operator

fn neg(self) -> Quaternion<N>

The method for the unary - operator

impl<N: Copy> Repeat<N> for Quaternion<N>

fn repeat(val: N) -> Quaternion<N>

Returns a value with filled by val.

impl<N: Rand> Rand for Quaternion<N>

fn rand<R: Rng>(rng: &mut R) -> Quaternion<N>

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

impl<N: Copy + AddAssign<N>> AddAssign<N> for Quaternion<N>

fn add_assign(&mut self, right: N)

The method for the += operator

impl<N: Copy + Add<N, Output=N>> Add<N> for Quaternion<N>

type Output = Quaternion<N>

The resulting type after applying the + operator

fn add(self, right: N) -> Quaternion<N>

The method for the + operator

impl<'a, 'b, N> Add<&'a N> for &'b Quaternion<N> where &'b N: Add<&'a N, Output=N>

type Output = Quaternion<N>

The resulting type after applying the + operator

fn add(self, right: &'a N) -> Quaternion<N>

The method for the + operator

impl<'a, N> Add<N> for &'a Quaternion<N> where &'a N: Add<&'b N, Output=N>

type Output = Quaternion<N>

The resulting type after applying the + operator

fn add(self, right: N) -> Quaternion<N>

The method for the + operator

impl<'a, N> Add<&'a N> for Quaternion<N> where N: Add<&'a N, Output=N>

type Output = Quaternion<N>

The resulting type after applying the + operator

fn add(self, right: &'a N) -> Quaternion<N>

The method for the + operator

impl<N: Copy + SubAssign<N>> SubAssign<N> for Quaternion<N>

fn sub_assign(&mut self, right: N)

The method for the -= operator

impl<N: Copy + Sub<N, Output=N>> Sub<N> for Quaternion<N>

type Output = Quaternion<N>

The resulting type after applying the - operator

fn sub(self, right: N) -> Quaternion<N>

The method for the - operator

impl<'a, 'b, N> Sub<&'a N> for &'b Quaternion<N> where &'b N: Sub<&'a N, Output=N>

type Output = Quaternion<N>

The resulting type after applying the - operator

fn sub(self, right: &'a N) -> Quaternion<N>

The method for the - operator

impl<'a, N> Sub<N> for &'a Quaternion<N> where &'a N: Sub<&'b N, Output=N>

type Output = Quaternion<N>

The resulting type after applying the - operator

fn sub(self, right: N) -> Quaternion<N>

The method for the - operator

impl<'a, N> Sub<&'a N> for Quaternion<N> where N: Sub<&'a N, Output=N>

type Output = Quaternion<N>

The resulting type after applying the - operator

fn sub(self, right: &'a N) -> Quaternion<N>

The method for the - operator

impl<N: Copy + MulAssign<N>> MulAssign<N> for Quaternion<N>

fn mul_assign(&mut self, right: N)

The method for the *= operator

impl<N: Copy + Mul<N, Output=N>> Mul<N> for Quaternion<N>

type Output = Quaternion<N>

The resulting type after applying the * operator

fn mul(self, right: N) -> Quaternion<N>

The method for the * operator

impl<'a, 'b, N> Mul<&'a N> for &'b Quaternion<N> where &'b N: Mul<&'a N, Output=N>

type Output = Quaternion<N>

The resulting type after applying the * operator

fn mul(self, right: &'a N) -> Quaternion<N>

The method for the * operator

impl<'a, N> Mul<N> for &'a Quaternion<N> where &'a N: Mul<&'b N, Output=N>

type Output = Quaternion<N>

The resulting type after applying the * operator

fn mul(self, right: N) -> Quaternion<N>

The method for the * operator

impl<'a, N> Mul<&'a N> for Quaternion<N> where N: Mul<&'a N, Output=N>

type Output = Quaternion<N>

The resulting type after applying the * operator

fn mul(self, right: &'a N) -> Quaternion<N>

The method for the * operator

impl<N: Copy + DivAssign<N>> DivAssign<N> for Quaternion<N>

fn div_assign(&mut self, right: N)

The method for the /= operator

impl<N: Copy + Div<N, Output=N>> Div<N> for Quaternion<N>

type Output = Quaternion<N>

The resulting type after applying the / operator

fn div(self, right: N) -> Quaternion<N>

The method for the / operator

impl<'a, 'b, N> Div<&'a N> for &'b Quaternion<N> where &'b N: Div<&'a N, Output=N>

type Output = Quaternion<N>

The resulting type after applying the / operator

fn div(self, right: &'a N) -> Quaternion<N>

The method for the / operator

impl<'a, N> Div<N> for &'a Quaternion<N> where &'a N: Div<&'b N, Output=N>

type Output = Quaternion<N>

The resulting type after applying the / operator

fn div(self, right: N) -> Quaternion<N>

The method for the / operator

impl<'a, N> Div<&'a N> for Quaternion<N> where N: Div<&'a N, Output=N>

type Output = Quaternion<N>

The resulting type after applying the / operator

fn div(self, right: &'a N) -> Quaternion<N>

The method for the / operator

impl<N: BaseFloat> PartialOrder for Quaternion<N>

fn inf(&self, other: &Quaternion<N>) -> Quaternion<N>

Returns the infimum of this value and another

fn sup(&self, other: &Quaternion<N>) -> Quaternion<N>

Returns the supremum of this value and another

fn partial_cmp(&self, other: &Quaternion<N>) -> PartialOrdering

Compare self and other using a partial ordering relation.

fn partial_lt(&self, other: &Quaternion<N>) -> bool

Returns true iff self and other are comparable and self < other.

fn partial_le(&self, other: &Quaternion<N>) -> bool

Returns true iff self and other are comparable and self <= other.

fn partial_gt(&self, other: &Quaternion<N>) -> bool

Returns true iff self and other are comparable and self > other.

fn partial_ge(&self, other: &Quaternion<N>) -> bool

Returns true iff self and other are comparable and self >= other.

fn partial_min<'a>(&'a self, other: &'a Self) -> Option<&'a Self>

Return the minimum of self and other if they are comparable.

fn partial_max<'a>(&'a self, other: &'a Self) -> Option<&'a Self>

Return the maximum of self and other if they are comparable.

fn partial_clamp<'a>(&'a self, min: &'a Self, max: &'a Self) -> Option<&'a Self>

Clamp value between min and max. Returns None if value is not comparable to min or max.

impl<Nin: Copy, Nout: Copy + Cast<Nin>> Cast<Quaternion<Nin>> for Quaternion<Nout>

fn from(v: Quaternion<Nin>) -> Quaternion<Nout>

Converts an element of type T to an element of type Self.

impl<N: ApproxEq<N>> ApproxEq<N> for Quaternion<N>

fn approx_epsilon() -> N

Default epsilon for approximation.

fn approx_ulps() -> u32

Default ULPs for approximation.

fn approx_eq(&self, other: &Quaternion<N>) -> bool

Tests approximate equality.

fn approx_eq_eps(&self, other: &Quaternion<N>, eps: &N) -> bool

Tests approximate equality using a custom epsilon.

fn approx_eq_ulps(&self, other: &Quaternion<N>, ulps: u32) -> bool

Tests approximate equality using units in the last place (ULPs)

impl<N: Axpy<N>> Axpy<N> for Quaternion<N>

fn axpy(&mut self, a: &N, x: &Quaternion<N>)

Adds $$a * x$$ to self.

impl<N: Bounded> Bounded for Quaternion<N>

fn max_value() -> Quaternion<N>

The maximum value.

fn min_value() -> Quaternion<N>

The minimum value.

impl<N> AsRef<[N; 4]> for Quaternion<N>

fn as_ref(&self) -> &[N; 4]

Performs the conversion.

impl<N> AsMut<[N; 4]> for Quaternion<N>

fn as_mut(&mut self) -> &mut [N; 4]

Performs the conversion.

impl<'a, N> From<&'a [N; 4]> for &'a Quaternion<N>

fn from(arr: &'a [N; 4]) -> &'a Quaternion<N>

Performs the conversion.

impl<'a, N> From<&'a mut [N; 4]> for &'a mut Quaternion<N>

fn from(arr: &'a mut [N; 4]) -> &'a mut Quaternion<N>

Performs the conversion.

impl<'a, N: Clone> From<&'a [N; 4]> for Quaternion<N>

fn from(arr: &'a [N; 4]) -> Quaternion<N>

Performs the conversion.

impl<N> Dimension for Quaternion<N>

fn dimension(_: Option<Quaternion<N>>) -> usize

The dimension of the object.

impl<N> Shape<usize> for Quaternion<N>

fn shape(&self) -> usize

Returns the shape of an indexable object.

impl<N: Copy> Indexable<usize, N> for Quaternion<N>

fn swap(&mut self, i1: usize, i2: usize)

Swaps the i-th element of self with its j-th element.

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

Reads the i-th element of self.

unsafe fn unsafe_set(&mut self, i: usize, val: N)

Writes to the i-th element of self.

impl<N, T> Index<T> for Quaternion<N> where [N]: Index<T>

type Output = [N]::Output

The returned type after indexing

fn index(&self, i: T) -> &[N]::Output

The method for the indexing (Foo[Bar]) operation

impl<N, T> IndexMut<T> for Quaternion<N> where [N]: IndexMut<T>

fn index_mut(&mut self, i: T) -> &mut [N]::Output

The method for the indexing (Foo[Bar]) operation

impl<N> Iterable<N> for Quaternion<N>

fn iter(&self) -> Iter<N>

Gets a vector-like read-only iterator.

impl<N> IterableMut<N> for Quaternion<N>

fn iter_mut(&mut self) -> IterMut<N>

Gets a vector-like read-write iterator.