Struct Quaternion 

pub struct Quaternion<T = Scalar> {
    pub w: T,
    pub x: T,
    pub y: T,
    pub z: T,
}

A quaternion w + x i + y j + z k.

Fields

w: T

x: T

y: T

z: T

Implementations

impl<T: Number> Quaternion<T>

pub fn new(w: T, x: T, y: T, z: T) -> Self

pub fn identity() -> Self

pub fn is_identity(&self) -> bool

Whether it is exactly the identity: every component sharp, 1 and three 0s — no rotation at all, rather than one too small to tell.

pub fn pure(v: &Vector3<T>) -> Self

0 + v: a vector as a pure quaternion.

pub fn vector(&self) -> Vector3<T>

Its vector part.

pub fn components(&self) -> [T; 4]

Its components [w, x, y, z].

pub fn map<U: Number>(&self, f: impl Fn(T) -> U) -> Quaternion<U>

Every component mapped by f.

pub fn mul(&self, o: &Self) -> Self

pub fn conj(&self) -> Self

pub fn scale(&self, s: T) -> Self

pub fn add(&self, o: &Self) -> Self

pub fn dot(&self, o: &Self) -> T

pub fn norm_sq(&self) -> T

pub fn normalized(&self) -> GeopResult<Self>

The unit quaternion of the same rotation; fails for one that could be zero, which stands for no rotation at all.

pub fn from_euler(degrees: [T; 3]) -> GeopResult<Self>

Turning by degrees about x, then y, then z — the world’s axes.

pub fn from_rotation_columns(columns: [Vector3<T>; 3]) -> GeopResult<Self>

The rotation whose matrix has the columns columns — where x, y and z turn to, orthonormal and right-handed: the inverse of Quaternion::rotation_columns, up to sign. Of the four ways to read it off the matrix (Shepperd’s), the one dividing by the largest of the trace and the diagonal: a free choice, and the well-conditioned one.

pub fn rotation_columns(&self) -> GeopResult<[Vector3<T>; 3]>

The rotation it stands for, as a matrix’s columns — where x, y and z turn to. It need not be unit: dividing by its norm squared makes the rotation of any non-zero quaternion, smoothly.

Trait Implementations

impl<T: Clone> Clone for Quaternion<T>

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

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<T: Copy> Copy for Quaternion<T>

impl<T: Debug> Debug for Quaternion<T>

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

Formats the value using the given formatter.

impl<T: PartialEq> PartialEq for Quaternion<T>

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

Equality operator ==.

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

Inequality operator !=.

impl<T: PartialEq> StructuralPartialEq for Quaternion<T>