Struct Quaternion

#[non_exhaustive]
pub struct Quaternion {
    pub x: f64,
    pub y: f64,
    pub z: f64,
    pub w: f64,
}

A quaternion is defined as the quotient of two directed lines in a three-dimensional space or equivalently as the quotient of two Euclidean vectors (https://en.wikipedia.org/wiki/Quaternion).

Quaternions are often used in calculations involving three-dimensional rotations (https://en.wikipedia.org/wiki/Quaternions_and_spatial_rotation), as they provide greater mathematical robustness by avoiding the gimbal lock problems that can be encountered when using Euler angles (https://en.wikipedia.org/wiki/Gimbal_lock).

Quaternions are generally represented in this form:

w + xi + yj + zk

where x, y, z, and w are real numbers, and i, j, and k are three imaginary numbers.

Our naming choice (x, y, z, w) comes from the desire to avoid confusion for those interested in the geometric properties of the quaternion in the 3D Cartesian space. Other texts often use alternative names or subscripts, such as (a, b, c, d), (1, i, j, k), or (0, 1, 2, 3), which are perhaps better suited for mathematical interpretations.

To avoid any confusion, as well as to maintain compatibility with a large number of software libraries, the quaternions represented using the protocol buffer below must follow the Hamilton convention, which defines ij = k (i.e. a right-handed algebra), and therefore:

i^2 = j^2 = k^2 = ijk = −1
ij = −ji = k
jk = −kj = i
ki = −ik = j

Please DO NOT use this to represent quaternions that follow the JPL convention, or any of the other quaternion flavors out there.

Definitions:

• Quaternion norm (or magnitude): sqrt(x^2 + y^2 + z^2 + w^2).
• Unit (or normalized) quaternion: a quaternion whose norm is 1.
• Pure quaternion: a quaternion whose scalar component (w) is 0.
• Rotation quaternion: a unit quaternion used to represent rotation.
• Orientation quaternion: a unit quaternion used to represent orientation.

A quaternion can be normalized by dividing it by its norm. The resulting quaternion maintains the same direction, but has a norm of 1, i.e. it moves on the unit sphere. This is generally necessary for rotation and orientation quaternions, to avoid rounding errors: https://en.wikipedia.org/wiki/Rotation_formalisms_in_three_dimensions

Note that (x, y, z, w) and (-x, -y, -z, -w) represent the same rotation, but normalization would be even more useful, e.g. for comparison purposes, if it would produce a unique representation. It is thus recommended that w be kept positive, which can be achieved by changing all the signs when w is negative.

Fields (Non-exhaustive)

Non-exhaustive structs could have additional fields added in future. Therefore, non-exhaustive structs cannot be constructed in external crates using the traditional Struct { .. } syntax; cannot be matched against without a wildcard ..; and struct update syntax will not work.

x: f64

The x component.

y: f64

The y component.

z: f64

The z component.

w: f64

The scalar component.

Implementations

impl Quaternion

pub fn set_x<T: Into<f64>>(self, v: T) -> Self

Sets the value of x.

pub fn set_y<T: Into<f64>>(self, v: T) -> Self

Sets the value of y.

pub fn set_z<T: Into<f64>>(self, v: T) -> Self

Sets the value of z.

pub fn set_w<T: Into<f64>>(self, v: T) -> Self

Sets the value of w.

Trait Implementations

impl Clone for Quaternion

fn clone(&self) -> Quaternion

Returns a copy of the value.

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

Performs copy-assignment from source.

impl Debug for Quaternion

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

Formats the value using the given formatter.

impl Default for Quaternion

fn default() -> Quaternion

Returns the “default value” for a type.

impl<'de> Deserialize<'de> for Quaternion

where Quaternion: Default,

fn deserialize<__D>(__deserializer: __D) -> Result<Self, __D::Error>

where __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl PartialEq for Quaternion

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

Tests for self and other values to be equal, and is used by ==.

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

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

impl Serialize for Quaternion

fn serialize<__S>(&self, __serializer: __S) -> Result<__S::Ok, __S::Error>

where __S: Serializer,

Serialize this value into the given Serde serializer.

impl StructuralPartialEq for Quaternion