Struct So3 

pub struct So3 { /* private fields */ }

A rotation of three-dimensional space.

Stored as a 3×3 matrix. Every constructor except from_matrix_unchecked guarantees orthogonality to within rounding error.

Implementations

impl So3

pub fn identity() -> Self

The identity rotation.

pub fn from_matrix_unchecked(matrix: Matrix3<f64>) -> Self

Wraps a matrix without checking orthogonality.

The caller is responsible for the matrix belonging to SO(3).

pub fn matrix(&self) -> &Matrix3<f64>

The rotation matrix.

pub fn exp(phi: &Vector3<f64>) -> Self

The exponential map so(3) → SO(3), i.e. the Rodrigues formula.

exp(φ) = I + (sin θ / θ) φ^ + ((1 − cos θ) / θ²) (φ^)² with θ = |φ|. For small θ the coefficients come from Taylor series, because the trigonometric form suffers catastrophic cancellation there.

pub fn log(&self) -> Vector3<f64>

The logarithm SO(3) → so(3); the result has norm in [0, π].

Three branches:

1. θ < THETA_SMALL — the series for θ / sin θ;
2. the middle range — the direct formula via the skew part;
3. θ near π — the axis is recovered from the symmetric part, since the skew part degenerates there: R − Rᵀ → 0.

At θ = π the result is defined only up to sign: exp(πa) and exp(−πa) are the same matrix.

pub fn inverse(&self) -> Self

The inverse rotation.

pub fn adjoint(&self) -> Matrix3<f64>

The adjoint representation. For SO(3) it is the matrix itself.

Trait Implementations

impl Clone for So3

fn clone(&self) -> So3

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Copy for So3

impl Debug for So3

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

Formats the value using the given formatter.

impl Default for So3

fn default() -> Self

Returns the “default value” for a type.

impl Mul for So3

type Output = So3

The resulting type after applying the * operator.

fn mul(self, rhs: So3) -> So3

Performs the * operation.

impl Mul<Matrix<f64, Const<3>, Const<1>, ArrayStorage<f64, 3, 1>>> for So3

type Output = Matrix<f64, Const<3>, Const<1>, ArrayStorage<f64, 3, 1>>

The resulting type after applying the * operator.

fn mul(self, rhs: Vector3<f64>) -> Vector3<f64>

Performs the * operation.

impl PartialEq for So3

fn eq(&self, other: &So3) -> bool

Equality operator ==.

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

Inequality operator !=.

impl StructuralPartialEq for So3