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.

Implementations

impl<S: BaseFloat> Quaternion<S>

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

Construct a new quaternion from a scalar and a vector

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 Intoperlation

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 quarternions 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)

Trait Implementations

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

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

Performs the += operation.

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

type Epsilon = <S as ApproxEq>::Epsilon

Used for specifying relative comparisons.

fn default_epsilon() -> S::Epsilon

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

fn default_max_relative() -> S::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: S::Epsilon, max_relative: S::Epsilon ) -> bool

A test for equality that uses a relative comparison if the values 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 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<S: BaseFloat> AsMut<[S; 4]> for Quaternion<S>

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

Converts this type into a mutable reference of the (usually inferred) input type.

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

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

Converts this type into a mutable reference of the (usually inferred) input type.

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

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

Converts this type into a shared reference of the (usually inferred) input type.

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

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

Converts this type into a shared reference of the (usually inferred) input type.

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: Debug> Debug for Quaternion<S>

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

Formats the value using the given formatter.

impl<S: Decodable> Decodable for Quaternion<S>

fn decode<__D: Decoder>(d: &mut __D) -> Result<Quaternion<S>, __D::Error>

Deserialize a value using a Decoder.

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<'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 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 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, 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<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<S: BaseFloat + DivAssign<S>> DivAssign<S> for Quaternion<S>

fn div_assign(&mut self, scalar: S)

Performs the /= operation.

impl<S: Encodable> Encodable for Quaternion<S>

fn encode<__S: Encoder>(&self, s: &mut __S) -> Result<(), __S::Error>

Serialize a value using an Encoder.

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

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

Converts to this type from the input type.

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>

Converts to this type from the input type.

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>

Converts to this type from the input type.

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>

Converts to this type from the input type.

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

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

Converts to this type from the input type.

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

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

Converts to this type from the input type.

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

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

Converts to this type from the input type.

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

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

Converts to this type from the input type.

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

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

Convert the matrix to a quaternion

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

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

Converts to this type from the input type.

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

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

Converts to this type from the input type.

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

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

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

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

Converts this type into the (usually inferred) input type.

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

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

Converts this type into the (usually inferred) input type.

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<'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<'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> 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<'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<'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<'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<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<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 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 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, 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<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<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<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<S: BaseFloat + MulAssign<S>> MulAssign<S> for Quaternion<S>

fn mul_assign(&mut self, scalar: S)

Performs the *= 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> 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<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) -> boolwhere Self: PartialEq<Self>,

Returns true if self is equal to the multiplicative identity.

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: &Rhs) -> bool

This method tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

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

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

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

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

fn rem_assign(&mut self, scalar: S)

Performs the %= operation.

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

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

Performs the -= operation.

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

type Scalar = S

The associated scalar.

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

fn zero() -> Quaternion<S>

Returns the additive identity element of Self, 0.

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: Copy> Copy for Quaternion<S>

impl<S> StructuralPartialEq for Quaternion<S>