Struct cgmath::Quaternion

#[repr(C)]
pub struct Quaternion<S> {
    pub s: S,
    pub v: Vector3<S>,
}

A quaternion in scalar/vector form.

This type is marked as #[repr(C)].

Fields

s: S

The scalar part of the quaternion.

v: Vector3<S>

The vector part of the quaternion.

Methods

impl<S> Quaternion<S>

pub const fn new(w: S, xi: S, yj: S, zk: S) -> Quaternion<S>

Construct a new quaternion from one scalar component and three imaginary components.

pub const fn from_sv(s: S, v: Vector3<S>) -> Quaternion<S>

Construct a new quaternion from a scalar and a vector.

impl<S: BaseFloat> Quaternion<S>

pub fn from_arc(
    src: Vector3<S>,
    dst: Vector3<S>,
    fallback: Option<Vector3<S>>
) -> Quaternion<S>

Construct a new quaternion as a closest arc between two vectors

Return the closest rotation that turns src vector into dst.

• [Related StackOverflow question] (http://stackoverflow.com/questions/1171849/finding-quaternion-representing-the-rotation-from-one-vector-to-another)
• [Ogre implementation for normalized vectors] (https://bitbucket.org/sinbad/ogre/src/9db75e3ba05c/OgreMain/include/OgreVector3.h?fileviewer=file-view-default#cl-651)

pub fn conjugate(self) -> Quaternion<S>

The conjugate of the quaternion.

pub fn nlerp(self, other: Quaternion<S>, amount: S) -> Quaternion<S>

Do a normalized linear interpolation with other, by amount.

pub fn slerp(self, other: Quaternion<S>, amount: S) -> Quaternion<S>

Spherical Linear Interpolation

Return the spherical linear interpolation between the quaternion and other. Both quaternions should be normalized first.

Performance notes

The acos operation used in slerp is an expensive operation, so unless your quaternions are far away from each other it's generally more advisable to use nlerp when you know your rotations are going to be small.

• [Understanding Slerp, Then Not Using It] (http://number-none.com/product/Understanding%20Slerp,%20Then%20Not%20Using%20It/)
• [Arcsynthesis OpenGL tutorial] (http://www.arcsynthesis.org/gltut/Positioning/Tut08%20Interpolation.html)

pub fn is_finite(&self) -> bool

impl<S: NumCast + Copy> Quaternion<S>

pub fn cast<T: BaseFloat>(&self) -> Option<Quaternion<T>>

Component-wise casting to another type.

Trait Implementations

impl<S: BaseFloat> VectorSpace for Quaternion<S>

type Scalar = S

The associated scalar.

fn lerp(self, other: Self, amount: Self::Scalar) -> Self

Returns the result of linearly interpolating the vector towards other by the specified amount.

impl<S: BaseFloat> MetricSpace for Quaternion<S>

type Metric = S

The metric to be returned by the distance function.

fn distance2(self, other: Self) -> S

Returns the squared distance.

fn distance(self, other: Self) -> Self::Metric

The distance between two values.

impl<S: BaseFloat> InnerSpace for Quaternion<S>

fn dot(self, other: Quaternion<S>) -> S

Vector dot (or inner) product.

fn is_perpendicular(self, other: Self) -> bool

Returns true if the vector is perpendicular (at right angles) to the other vector.

fn magnitude2(self) -> Self::Scalar

Returns the squared magnitude.

fn magnitude(self) -> Self::Scalar

The distance from the tail to the tip of the vector.

fn angle(self, other: Self) -> Rad<Self::Scalar>

Returns the angle between two vectors in radians.

fn normalize(self) -> Self

Returns a vector with the same direction, but with a magnitude of 1.

fn normalize_to(self, magnitude: Self::Scalar) -> Self

Returns a vector with the same direction and a given magnitude.

fn project_on(self, other: Self) -> Self

Returns the vector projection of the current inner space projected onto the supplied argument.

impl<S: BaseFloat> Rotation<Point3<S>> for Quaternion<S>

fn look_at(dir: Vector3<S>, up: Vector3<S>) -> Quaternion<S>

Create a rotation to a given direction with an 'up' vector.

fn between_vectors(a: Vector3<S>, b: Vector3<S>) -> Quaternion<S>

Create a shortest rotation to transform vector 'a' into 'b'. Both given vectors are assumed to have unit length.

fn rotate_vector(&self, vec: Vector3<S>) -> Vector3<S>

Rotate a vector using this rotation.

fn invert(&self) -> Quaternion<S>

Create a new rotation which "un-does" this rotation. That is, r * r.invert() is the identity.

fn rotate_point(&self, point: P) -> P

Rotate a point using this rotation, by converting it to its representation as a vector.

impl<S: BaseFloat> Rotation3<S> for Quaternion<S>

fn from_axis_angle<A: Into<Rad<S>>>(axis: Vector3<S>, angle: A) -> Quaternion<S>

Create a rotation using an angle around a given axis.

fn from_angle_x<A: Into<Rad<S>>>(theta: A) -> Self

Create a rotation from an angle around the x axis (pitch).

fn from_angle_y<A: Into<Rad<S>>>(theta: A) -> Self

Create a rotation from an angle around the y axis (yaw).

fn from_angle_z<A: Into<Rad<S>>>(theta: A) -> Self

Create a rotation from an angle around the z axis (roll).

impl<S: BaseFloat> Into<[S; 4]> for Quaternion<S>

fn into(self) -> [S; 4]

Performs the conversion.

impl<S: BaseFloat> Into<(S, S, S, S)> for Quaternion<S>

fn into(self) -> (S, S, S, S)

Performs the conversion.

impl<S: BaseFloat> AsMut<[S; 4]> for Quaternion<S>

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

Performs the conversion.

impl<S: BaseFloat> AsMut<(S, S, S, S)> for Quaternion<S>

fn as_mut(&mut self) -> &mut (S, S, S, S)

Performs the conversion.

impl<S: Clone> Clone for Quaternion<S>

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

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<S: BaseFloat> AsRef<[S; 4]> for Quaternion<S>

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

Performs the conversion.

impl<S: BaseFloat> AsRef<(S, S, S, S)> for Quaternion<S>

fn as_ref(&self) -> &(S, S, S, S)

Performs the conversion.

impl<S: PartialEq> PartialEq<Quaternion<S>> for Quaternion<S>

fn eq(&self, other: &Quaternion<S>) -> bool

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

fn ne(&self, other: &Quaternion<S>) -> bool

This method tests for !=.

impl<S: BaseFloat> From<Matrix3<S>> for Quaternion<S>

fn from(mat: Matrix3<S>) -> Quaternion<S>

Convert the matrix to a quaternion

impl<A> From<Euler<A>> for Quaternion<A::Unitless> where
    A: Angle + Into<Rad<<A as Angle>::Unitless>>, 

fn from(src: Euler<A>) -> Quaternion<A::Unitless>

Performs the conversion.

impl<S: BaseFloat> From<Quaternion<S>> for Matrix3<S>

fn from(quat: Quaternion<S>) -> Matrix3<S>

Convert the quaternion to a 3 x 3 rotation matrix.

impl<S: BaseFloat> From<Quaternion<S>> for Matrix4<S>

fn from(quat: Quaternion<S>) -> Matrix4<S>

Convert the quaternion to a 4 x 4 rotation matrix.

impl<S: BaseFloat> From<Quaternion<S>> for Basis3<S>

fn from(quat: Quaternion<S>) -> Basis3<S>

Performs the conversion.

impl<S: BaseFloat> From<[S; 4]> for Quaternion<S>

fn from(v: [S; 4]) -> Quaternion<S>

Performs the conversion.

impl<'a, S: BaseFloat> From<&'a [S; 4]> for &'a Quaternion<S>

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

Performs the conversion.

impl<'a, S: BaseFloat> From<&'a mut [S; 4]> for &'a mut Quaternion<S>

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

Performs the conversion.

impl<S: BaseFloat> From<(S, S, S, S)> for Quaternion<S>

fn from(v: (S, S, S, S)) -> Quaternion<S>

Performs the conversion.

impl<'a, S: BaseFloat> From<&'a (S, S, S, S)> for &'a Quaternion<S>

fn from(v: &'a (S, S, S, S)) -> &'a Quaternion<S>

Performs the conversion.

impl<'a, S: BaseFloat> From<&'a mut (S, S, S, S)> for &'a mut Quaternion<S>

fn from(v: &'a mut (S, S, S, S)) -> &'a mut Quaternion<S>

Performs the conversion.

impl<S: BaseFloat> From<Quaternion<S>> for Euler<Rad<S>>

fn from(src: Quaternion<S>) -> Euler<Rad<S>>

Performs the conversion.

impl<S: BaseFloat> From<Basis3<S>> for Quaternion<S>

fn from(b: Basis3<S>) -> Quaternion<S>

Performs the conversion.

impl<S: Copy> Copy for Quaternion<S>

impl<S: BaseFloat> Add<Quaternion<S>> for Quaternion<S>

type Output = Quaternion<S>

The resulting type after applying the + operator.

fn add(self, other: Quaternion<S>) -> Quaternion<S>

Performs the + operation.

impl<'a, S: BaseFloat> Add<&'a Quaternion<S>> for Quaternion<S>

type Output = Quaternion<S>

The resulting type after applying the + operator.

fn add(self, other: &'a Quaternion<S>) -> Quaternion<S>

Performs the + operation.

impl<'a, S: BaseFloat> Add<Quaternion<S>> for &'a Quaternion<S>

type Output = Quaternion<S>

The resulting type after applying the + operator.

fn add(self, other: Quaternion<S>) -> Quaternion<S>

Performs the + operation.

impl<'a, 'b, S: BaseFloat> Add<&'a Quaternion<S>> for &'b Quaternion<S>

type Output = Quaternion<S>

The resulting type after applying the + operator.

fn add(self, other: &'a Quaternion<S>) -> Quaternion<S>

Performs the + operation.

impl<S: BaseFloat> Sub<Quaternion<S>> for Quaternion<S>

type Output = Quaternion<S>

The resulting type after applying the - operator.

fn sub(self, other: Quaternion<S>) -> Quaternion<S>

Performs the - operation.

impl<'a, S: BaseFloat> Sub<&'a Quaternion<S>> for Quaternion<S>

type Output = Quaternion<S>

The resulting type after applying the - operator.

fn sub(self, other: &'a Quaternion<S>) -> Quaternion<S>

Performs the - operation.

impl<'a, S: BaseFloat> Sub<Quaternion<S>> for &'a Quaternion<S>

type Output = Quaternion<S>

The resulting type after applying the - operator.

fn sub(self, other: Quaternion<S>) -> Quaternion<S>

Performs the - operation.

impl<'a, 'b, S: BaseFloat> Sub<&'a Quaternion<S>> for &'b Quaternion<S>

type Output = Quaternion<S>

The resulting type after applying the - operator.

fn sub(self, other: &'a Quaternion<S>) -> Quaternion<S>

Performs the - operation.

impl<S: BaseFloat> Mul<S> for Quaternion<S>

type Output = Quaternion<S>

The resulting type after applying the * operator.

fn mul(self, other: S) -> Quaternion<S>

Performs the * operation.

impl<'a, S: BaseFloat> Mul<S> for &'a Quaternion<S>

type Output = Quaternion<S>

The resulting type after applying the * operator.

fn mul(self, other: S) -> Quaternion<S>

Performs the * operation.

impl<S: BaseFloat> Mul<Vector3<S>> for Quaternion<S>

type Output = Vector3<S>

The resulting type after applying the * operator.

fn mul(self, other: Vector3<S>) -> Vector3<S>

Performs the * operation.

impl<'a, S: BaseFloat> Mul<&'a Vector3<S>> for Quaternion<S>

type Output = Vector3<S>

The resulting type after applying the * operator.

fn mul(self, other: &'a Vector3<S>) -> Vector3<S>

Performs the * operation.

impl<'a, S: BaseFloat> Mul<Vector3<S>> for &'a Quaternion<S>

type Output = Vector3<S>

The resulting type after applying the * operator.

fn mul(self, other: Vector3<S>) -> Vector3<S>

Performs the * operation.

impl<'a, 'b, S: BaseFloat> Mul<&'a Vector3<S>> for &'b Quaternion<S>

type Output = Vector3<S>

The resulting type after applying the * operator.

fn mul(self, other: &'a Vector3<S>) -> Vector3<S>

Performs the * operation.

impl<S: BaseFloat> Mul<Quaternion<S>> for Quaternion<S>

type Output = Quaternion<S>

The resulting type after applying the * operator.

fn mul(self, other: Quaternion<S>) -> Quaternion<S>

Performs the * operation.

impl<'a, S: BaseFloat> Mul<&'a Quaternion<S>> for Quaternion<S>

type Output = Quaternion<S>

The resulting type after applying the * operator.

fn mul(self, other: &'a Quaternion<S>) -> Quaternion<S>

Performs the * operation.

impl<'a, S: BaseFloat> Mul<Quaternion<S>> for &'a Quaternion<S>

type Output = Quaternion<S>

The resulting type after applying the * operator.

fn mul(self, other: Quaternion<S>) -> Quaternion<S>

Performs the * operation.

impl<'a, 'b, S: BaseFloat> Mul<&'a Quaternion<S>> for &'b Quaternion<S>

type Output = Quaternion<S>

The resulting type after applying the * operator.

fn mul(self, other: &'a Quaternion<S>) -> Quaternion<S>

Performs the * operation.

impl Mul<Quaternion<f32>> for f32

type Output = Quaternion<f32>

The resulting type after applying the * operator.

fn mul(self, other: Quaternion<f32>) -> Quaternion<f32>

Performs the * operation.

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

type Output = Quaternion<f32>

The resulting type after applying the * operator.

fn mul(self, other: &'a Quaternion<f32>) -> Quaternion<f32>

Performs the * operation.

impl Mul<Quaternion<f64>> for f64

type Output = Quaternion<f64>

The resulting type after applying the * operator.

fn mul(self, other: Quaternion<f64>) -> Quaternion<f64>

Performs the * operation.

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

type Output = Quaternion<f64>

The resulting type after applying the * operator.

fn mul(self, other: &'a Quaternion<f64>) -> Quaternion<f64>

Performs the * operation.

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

type Output = Quaternion<S>

The resulting type after applying the / operator.

fn div(self, other: S) -> Quaternion<S>

Performs the / operation.

impl<'a, S: BaseFloat> Div<S> for &'a Quaternion<S>

type Output = Quaternion<S>

The resulting type after applying the / operator.

fn div(self, other: S) -> Quaternion<S>

Performs the / operation.

impl Div<Quaternion<f32>> for f32

type Output = Quaternion<f32>

The resulting type after applying the / operator.

fn div(self, other: Quaternion<f32>) -> Quaternion<f32>

Performs the / operation.

impl<'a> Div<&'a Quaternion<f32>> for f32

type Output = Quaternion<f32>

The resulting type after applying the / operator.

fn div(self, other: &'a Quaternion<f32>) -> Quaternion<f32>

Performs the / operation.

impl Div<Quaternion<f64>> for f64

type Output = Quaternion<f64>

The resulting type after applying the / operator.

fn div(self, other: Quaternion<f64>) -> Quaternion<f64>

Performs the / operation.

impl<'a> Div<&'a Quaternion<f64>> for f64

type Output = Quaternion<f64>

The resulting type after applying the / operator.

fn div(self, other: &'a Quaternion<f64>) -> Quaternion<f64>

Performs the / operation.

impl<S: BaseFloat> Rem<S> for Quaternion<S>

type Output = Quaternion<S>

The resulting type after applying the % operator.

fn rem(self, other: S) -> Quaternion<S>

Performs the % operation.

impl<'a, S: BaseFloat> Rem<S> for &'a Quaternion<S>

type Output = Quaternion<S>

The resulting type after applying the % operator.

fn rem(self, other: S) -> Quaternion<S>

Performs the % operation.

impl<S: BaseFloat> Neg for Quaternion<S>

type Output = Quaternion<S>

The resulting type after applying the - operator.

fn neg(self) -> Quaternion<S>

Performs the unary - operation.

impl<'a, S: BaseFloat> Neg for &'a Quaternion<S>

type Output = Quaternion<S>

The resulting type after applying the - operator.

fn neg(self) -> Quaternion<S>

Performs the unary - operation.

impl<S: BaseFloat + AddAssign<S>> AddAssign<Quaternion<S>> for Quaternion<S>

fn add_assign(&mut self, other: Quaternion<S>)

Performs the += operation.

impl<S: BaseFloat + SubAssign<S>> SubAssign<Quaternion<S>> for Quaternion<S>

fn sub_assign(&mut self, other: Quaternion<S>)

Performs the -= operation.

impl<S: BaseFloat + MulAssign<S>> MulAssign<S> for Quaternion<S>

fn mul_assign(&mut self, scalar: S)

Performs the *= operation.

impl<S: BaseFloat + DivAssign<S>> DivAssign<S> for Quaternion<S>

fn div_assign(&mut self, scalar: S)

Performs the /= operation.

impl<S: BaseFloat + RemAssign<S>> RemAssign<S> for Quaternion<S>

fn rem_assign(&mut self, scalar: S)

Performs the %= operation.

impl<S: BaseFloat> Index<usize> for Quaternion<S>

type Output = S

The returned type after indexing.

fn index<'a>(&'a self, i: usize) -> &'a S

Performs the indexing (container[index]) operation.

impl<S: BaseFloat> Index<Range<usize>> for Quaternion<S>

type Output = [S]

The returned type after indexing.

fn index<'a>(&'a self, i: Range<usize>) -> &'a [S]

Performs the indexing (container[index]) operation.

impl<S: BaseFloat> Index<RangeTo<usize>> for Quaternion<S>

type Output = [S]

The returned type after indexing.

fn index<'a>(&'a self, i: RangeTo<usize>) -> &'a [S]

Performs the indexing (container[index]) operation.

impl<S: BaseFloat> Index<RangeFrom<usize>> for Quaternion<S>

type Output = [S]

The returned type after indexing.

fn index<'a>(&'a self, i: RangeFrom<usize>) -> &'a [S]

Performs the indexing (container[index]) operation.

impl<S: BaseFloat> Index<RangeFull> for Quaternion<S>

type Output = [S]

The returned type after indexing.

fn index<'a>(&'a self, i: RangeFull) -> &'a [S]

Performs the indexing (container[index]) operation.

impl<S: BaseFloat> IndexMut<usize> for Quaternion<S>

fn index_mut<'a>(&'a mut self, i: usize) -> &'a mut S

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

impl<S: BaseFloat> IndexMut<Range<usize>> for Quaternion<S>

fn index_mut<'a>(&'a mut self, i: Range<usize>) -> &'a mut [S]

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

impl<S: BaseFloat> IndexMut<RangeTo<usize>> for Quaternion<S>

fn index_mut<'a>(&'a mut self, i: RangeTo<usize>) -> &'a mut [S]

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

impl<S: BaseFloat> IndexMut<RangeFrom<usize>> for Quaternion<S>

fn index_mut<'a>(&'a mut self, i: RangeFrom<usize>) -> &'a mut [S]

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

impl<S: BaseFloat> IndexMut<RangeFull> for Quaternion<S>

fn index_mut<'a>(&'a mut self, i: RangeFull) -> &'a mut [S]

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

impl<S: Debug> Debug for Quaternion<S>

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

Formats the value using the given formatter.

impl<S: BaseFloat> Product<Quaternion<S>> for Quaternion<S>

fn product<I: Iterator<Item = Quaternion<S>>>(iter: I) -> Quaternion<S>

Method which takes an iterator and generates Self from the elements by multiplying the items.

impl<'a, S: 'a + BaseFloat> Product<&'a Quaternion<S>> for Quaternion<S>

fn product<I: Iterator<Item = &'a Quaternion<S>>>(iter: I) -> Quaternion<S>

Method which takes an iterator and generates Self from the elements by multiplying the items.

impl<S: BaseFloat> Sum<Quaternion<S>> for Quaternion<S>

fn sum<I: Iterator<Item = Quaternion<S>>>(iter: I) -> Quaternion<S>

Method which takes an iterator and generates Self from the elements by "summing up" the items.

impl<'a, S: 'a + BaseFloat> Sum<&'a Quaternion<S>> for Quaternion<S>

fn sum<I: Iterator<Item = &'a Quaternion<S>>>(iter: I) -> Quaternion<S>

Method which takes an iterator and generates Self from the elements by "summing up" the items.

impl<S: BaseFloat> AbsDiffEq<Quaternion<S>> for Quaternion<S>

type Epsilon = S::Epsilon

Used for specifying relative comparisons.

fn default_epsilon() -> S::Epsilon

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

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

A test for equality that uses the absolute difference to compute the approximate equality of two numbers.

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

The inverse of ApproxEq::abs_diff_eq.

impl<S: BaseFloat> RelativeEq<Quaternion<S>> for Quaternion<S>

fn default_max_relative() -> S::Epsilon

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

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

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

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

The inverse of ApproxEq::relative_eq.

impl<S: BaseFloat> UlpsEq<Quaternion<S>> for Quaternion<S>

fn default_max_ulps() -> u32

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

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

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

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

The inverse of ApproxEq::ulps_eq.

impl<S: BaseFloat> Zero for Quaternion<S>

fn zero() -> Quaternion<S>

Returns the additive identity element of Self, 0. # Purity

fn is_zero(&self) -> bool

Returns true if self is equal to the additive identity.

fn set_zero(&mut self)

Sets self to the additive identity element of Self, 0.

impl<S: BaseFloat> One for Quaternion<S>

fn one() -> Quaternion<S>

Returns the multiplicative identity element of Self, 1.

fn set_one(&mut self)

Sets self to 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<S> Distribution<Quaternion<S>> for Standard where
    Standard: Distribution<S>,
    Standard: Distribution<Vector3<S>>,
    S: BaseFloat, 

fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> Quaternion<S>

Generate a random value of T, using rng as the source of randomness.

fn sample_iter<R>(&'a self, rng: &'a mut R) -> DistIter<'a, Self, R, T> where
    R: Rng, 

Create an iterator that generates random values of T, using rng as the source of randomness.