Struct micromath::Quaternion

pub struct Quaternion(_, _, _, _);

This is supported on crate feature quaternion only.

Quaternions are a number system that extends the complex numbers which can be used for efficiently computing spatial rotations.

They’re computed as the quotient of two directed lines in a three-dimensional space, or equivalently as the quotient of two vectors.

For given real numbers a, b, c, and d, they take the form:

a + bi + cj + dk

where i, j, and k are the fundamental quaternion units:

i² = j² = k² = i*j*k = -1

Quaternion multiplication is non-commutative:

x	1	i	j	k
1	1	i	j	k
i	i	-1	k	-j
j	j	-k	-1	i
k	k	j	-i	-1

Implementations

impl Quaternion

pub const IDENTITY: Self

Identity quaternion.

pub const fn new(a: f32, b: f32, c: f32, d: f32) -> Self

Create a new quaternion.

pub fn conj(self) -> Self

Returns the conjugate of this quaternion.

pub fn dot(self, rhs: Self) -> f32

Returns the dot product of this quaternion.

pub fn inv(self) -> Self

Compute the inverse of this quaternion.

Panics if Quaternion::norm is zero.

pub fn magnitude(self) -> f32

Compute the magnitude (a.k.a length) of this quaternion.

pub fn norm(self) -> f32

Returns the norm of this quaternion, i.e. a²+b²+c²+d².

https://www.mathworks.com/help/aeroblks/quaternionnorm.html

pub fn axis_angle<C>(v: Vector3d<C>, theta: C) -> Self where
    C: Component + Into<f32>, 

This is supported on crate feature vector only.

Compute a quaternion for the given axis vector and angle.

pub fn rotate<C>(self, v: Vector3d<C>) -> F32x3 where
    C: Component + Into<f32>, 

This is supported on crate feature vector only.

Rotate a 3D vector using this quaternion.

pub fn scale<S>(self, scalar: S) -> Self where
    S: Into<f32>, 

Scale by a scalar.

pub fn to_array(&self) -> [f32; 4]

Convert this quaternion into an array.

Trait Implementations

impl Add<Quaternion> for Quaternion

type Output = Self

The resulting type after applying the + operator.

fn add(self, rhs: Self) -> Self

Performs the + operation.

impl AddAssign<Quaternion> for Quaternion

fn add_assign(&mut self, rhs: Self)

Performs the += operation.

impl Clone for Quaternion

fn clone(&self) -> Quaternion

Returns a copy of the value.

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

Performs copy-assignment from source.

impl Copy for Quaternion

impl Debug for Quaternion

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

Formats the value using the given formatter.

impl Default for Quaternion

fn default() -> Self

Returns the “default value” for a type.

impl From<(f32, f32, f32, f32)> for Quaternion

fn from(q: (f32, f32, f32, f32)) -> Quaternion

Performs the conversion.

impl<C> From<Vector3d<C>> for Quaternion where
    C: Component + Into<f32>, 

This is supported on crate feature vector only.

fn from(v: Vector3d<C>) -> Quaternion

Performs the conversion.

impl Mul<Quaternion> for Quaternion

type Output = Self

The resulting type after applying the * operator.

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

Performs the * operation.

impl<C> Mul<Vector3d<C>> for Quaternion where
    C: Component + Into<f32>, 

This is supported on crate feature vector only.

type Output = F32x3

The resulting type after applying the * operator.

fn mul(self, v: Vector3d<C>) -> F32x3

Performs the * operation.

impl Mul<f32> for Quaternion

type Output = Self

The resulting type after applying the * operator.

fn mul(self, k: f32) -> Self

Performs the * operation.

impl MulAssign<f32> for Quaternion

fn mul_assign(&mut self, k: f32)

Performs the *= operation.

impl PartialEq<Quaternion> for Quaternion

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

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

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

This method tests for !=.

impl StructuralPartialEq for Quaternion

impl Sub<Quaternion> for Quaternion

type Output = Self

The resulting type after applying the - operator.

fn sub(self, rhs: Self) -> Self

Performs the - operation.

impl SubAssign<Quaternion> for Quaternion

fn sub_assign(&mut self, rhs: Self)

Performs the -= operation.