Struct Quaternion 

pub struct Quaternion {
    pub w: f64,
    pub x: f64,
    pub y: f64,
    pub z: f64,
}

A quaternion w + xi + yj + zk.

Fields

w: f64

Scalar part.

x: f64

i coefficient.

y: f64

j coefficient.

z: f64

k coefficient.

Implementations

impl Quaternion

pub const IDENTITY: Self

The identity rotation.

pub const fn new(w: f64, x: f64, y: f64, z: f64) -> Self

From components.

pub fn from_axis_angle(axis: Direction, angle: f64) -> Self

The rotation of angle radians about axis, right-handed.

pub fn between( from: Direction, to: Direction, tol: Tolerances, ) -> OgeomResult<Self>

The shortest rotation taking from to to.

Errors

OgeomError::Construction if the two are antiparallel: infinitely many shortest rotations exist and picking one arbitrarily would make the result depend on unobservable rounding.

pub fn from_matrix(m: &Matrix3, tol: Tolerances) -> OgeomResult<Self>

From a rotation matrix.

Uses Shepperd’s method: pick the largest of the four possible divisors so the division is never by something near zero. The naive w-first formulation loses precision for rotations near π, where w → 0.

Errors

OgeomError::Construction if m is not orthonormal with determinant +1.

pub fn square_norm(self) -> f64

Squared norm.

pub fn norm(self) -> f64

Norm.

pub fn normalized(self, tol: Tolerances) -> OgeomResult<Self>

This quaternion scaled to unit norm.

Errors

OgeomError::Construction if the norm is below tol.confusion() or any component is non-finite.

pub fn is_finite(self) -> bool

Whether every component is finite.

pub const fn conjugate(self) -> Self

The conjugate. For a unit quaternion this is the inverse rotation.

pub fn inverse(self, tol: Tolerances) -> OgeomResult<Self>

The multiplicative inverse.

Errors

OgeomError::Numeric if the norm is degenerate.

pub fn rotate(self, v: Vector) -> Vector

Apply this rotation to a vector. Assumes unit norm.

Evaluated as v + 2w(u × v) + 2(u × (u × v)) with u the vector part, which costs fewer operations than building the matrix and avoids the intermediate rounding of a full quaternion sandwich product.

pub fn to_matrix(self) -> Matrix3

The equivalent rotation matrix. Assumes unit norm.

pub fn to_axis_angle(self, tol: Tolerances) -> OgeomResult<(Direction, f64)>

The rotation axis and angle. Assumes unit norm; angle is in [0, π].

Errors

OgeomError::Construction if the rotation is the identity, where the axis is undefined.

pub fn dot(self, o: Self) -> f64

Dot product, as 4-vectors.

pub fn slerp(self, other: Self, t: f64, tol: Tolerances) -> OgeomResult<Self>

Spherical linear interpolation, t = 0 giving self.

Takes the shorter of the two arcs, and falls back to normalized linear interpolation when the two are nearly coincident, where the sin in the denominator of the spherical form goes to zero.

Errors

OgeomError::Construction if either operand cannot be normalized.

pub fn angle_to(self, other: Self) -> f64

The rotation angle to other, in [0, π]. Assumes unit norms.

Trait Implementations

impl Add for Quaternion

type Output = Quaternion

The resulting type after applying the + operator.

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

Performs the + operation.

impl Clone for Quaternion

fn clone(&self) -> Quaternion

Returns a duplicate of the value.

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 Mul for Quaternion

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

Hamilton product. (a * b) rotates by b first, then by a.

type Output = Quaternion

The resulting type after applying the * operator.

impl Mul<f64> for Quaternion

type Output = Quaternion

The resulting type after applying the * operator.

fn mul(self, s: f64) -> Self

Performs the * operation.

impl Neg for Quaternion

type Output = Quaternion

The resulting type after applying the - operator.

fn neg(self) -> Self

Performs the unary - operation.

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 StructuralPartialEq for Quaternion

impl Sub for Quaternion

type Output = Quaternion

The resulting type after applying the - operator.

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

Performs the - operation.