Struct SE3 

pub struct SE3(/* private fields */);

SE(3) transformation represented as an isometry matrix.

An SE(3) transformation combines a rotation and a translation in 3D space. It combines a rotation matrix $R\in \text{SO}(3)$ and a translation vector $t \in \mathbb{R}^3$

Implementations

impl SE3

pub fn new(translation: Vector3D, axis_angle: Vector3D) -> Self

Creates a new SE(3) transformation from a rotation (given as axis-angle) and a translation.

pub fn from_parts(translation: Vector3D, rotation: SpatialRotation) -> Self

Creates a new SE(3) transformation from a rotation and a translation.

pub fn identity() -> Self

Creates a new identity SE(3) transformation, with $R = I_3$ and $t = 0_3$.

pub fn inverse(&self) -> Self

Returns the inverse of the SE(3) transformation.

pub fn translation(&self) -> Vector3D

Returns the translation component of the SE(3) transformation.

pub fn rotation(&self) -> SpatialRotation

Returns the rotation component of the SE(3) transformation.

pub fn action_matrix(&self) -> Matrix6<f64>

Computes the action matrix of the SE(3) transformation.

Mathematically, the action matrix is: $$\begin{bmatrix}R & [t]_X R \\ 0 & R\end{bmatrix}$$ where $R$ is the rotation matrix and $[t]_X$ is the skew-symmetric matrix of the translation vector $t$.

pub fn dual_matrix(&self) -> Matrix6<f64>

Computes the dual action matrix of the SE(3) transformation.

Mathematically, the action matrix is: $$\begin{bmatrix}R & 0 \\ [t]_X R & R\end{bmatrix}$$ where $R$ is the rotation matrix and $[t]_X$ is the skew-symmetric matrix of the translation vector $t$.

pub fn inv_matrix(&self) -> Matrix6<f64>

Computes the inverse of the action matrix of the SE(3) transformation.

impl SE3

pub fn act<T: ActSE3>(&self, obj: &T) -> T

Applies the SE(3) transformation to an object implementing the ActSE3 trait.

pub fn act_inv<T: ActSE3>(&self, obj: &T) -> T

Applies the inverse SE(3) transformation to an object implementing the ActSE3 trait.

Trait Implementations

impl Clone for SE3

fn clone(&self) -> SE3

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for SE3

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

Formats the value using the given formatter.

impl Default for SE3

fn default() -> SE3

Returns the “default value” for a type.

impl Display for SE3

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

Formats the value using the given formatter.

impl Mul<&SE3> for &SE3

type Output = SE3

The resulting type after applying the * operator.

fn mul(self, rhs: &SE3) -> Self::Output

Performs the * operation.

impl Mul<&SE3> for SE3

type Output = SE3

The resulting type after applying the * operator.

fn mul(self, rhs: &SE3) -> Self::Output

Performs the * operation.

impl Mul<SE3> for &SE3

type Output = SE3

The resulting type after applying the * operator.

fn mul(self, rhs: SE3) -> Self::Output

Performs the * operation.

impl Mul for SE3

type Output = SE3

The resulting type after applying the * operator.

fn mul(self, rhs: Self) -> Self::Output

Performs the * operation.

impl PartialEq for SE3

fn eq(&self, other: &SE3) -> 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 Copy for SE3

impl StructuralPartialEq for SE3