Struct Sim3 

pub struct Sim3 { /* private fields */ }

Sim(3) group element representing similarity transformations in 3D.

Stored as a flat SVector<f64, 8> = [tx, ty, tz, qw, qx, qy, qz, scale].

Implementations

impl Sim3

pub const DIM: usize = 3

Space dimension - dimension of the ambient space

pub const DOF: usize = 7

Degrees of freedom - dimension of the tangent space

pub const REP_SIZE: usize = 8

Representation size - size of the underlying data representation

pub fn identity() -> Sim3

Get the identity element of the group.

pub fn jacobian_identity() -> Matrix<f64, Const<7>, Const<7>, ArrayStorage<f64, 7, 7>>

Get the identity matrix for Jacobians.

pub fn new( translation: Matrix<f64, Const<3>, Const<1>, ArrayStorage<f64, 3, 1>>, rotation: Unit<Quaternion<f64>>, scale: f64, ) -> Sim3

Create a new Sim(3) element from translation, rotation, and scale.

Arguments

• translation - Translation vector [x, y, z]
• rotation - Unit quaternion representing rotation
• scale - Scale factor (must be positive)

pub fn from_components( translation: Matrix<f64, Const<3>, Const<1>, ArrayStorage<f64, 3, 1>>, rotation: SO3, scale: f64, ) -> Sim3

Create Sim(3) from components.

pub fn translation( &self, ) -> Matrix<f64, Const<3>, Const<1>, ArrayStorage<f64, 3, 1>>

Get the translation part as a Vector3.

pub fn scale(&self) -> f64

Get the scale factor.

pub fn rotation_so3(&self) -> SO3

Get the rotation part as SO3.

pub fn rotation_quaternion(&self) -> Unit<Quaternion<f64>>

Get the rotation part as a UnitQuaternion.

pub fn rotation_matrix( &self, ) -> Matrix<f64, Const<3>, Const<3>, ArrayStorage<f64, 3, 3>>

Get the rotation matrix (3x3).

pub fn matrix(&self) -> Matrix<f64, Const<4>, Const<4>, ArrayStorage<f64, 4, 4>>

Get the 4x4 homogeneous transformation matrix.

pub fn x(&self) -> f64

Get the x component of translation.

pub fn y(&self) -> f64

Get the y component of translation.

pub fn z(&self) -> f64

Get the z component of translation.

pub fn coeffs(&self) -> [f64; 8]

Get the parameter vector [tx, ty, tz, qw, qx, qy, qz, s].

Trait Implementations

impl Clone for Sim3

fn clone(&self) -> Sim3

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Display for Sim3

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

Formats the value using the given formatter.

impl LieGroup for Sim3

fn inverse( &self, jacobian: Option<&mut <Sim3 as LieGroup>::JacobianMatrix>, ) -> Sim3

Get the inverse.

For Sim(3): g^{-1} = (R^T, -R^T * t / s, 1/s)

fn compose( &self, other: &Sim3, jacobian_self: Option<&mut <Sim3 as LieGroup>::JacobianMatrix>, jacobian_other: Option<&mut <Sim3 as LieGroup>::JacobianMatrix>, ) -> Sim3

Composition of this and another Sim(3) element.

g1 ∘ g2 = (R1R2, s1R1t2 + t1, s1s2)

fn log( &self, jacobian: Option<&mut <Sim3 as LieGroup>::JacobianMatrix>, ) -> <Sim3 as LieGroup>::TangentVector

Logarithmic map from Sim(3) to its tangent space.

const NAME: &'static str = "Sim3"

Human-readable name for serialization and logging.

type TangentVector = Sim3Tangent

The tangent space vector type

type JacobianMatrix = Matrix<f64, Const<7>, Const<7>, ArrayStorage<f64, 7, 7>>

The Jacobian matrix type

type LieAlgebra = Matrix<f64, Const<4>, Const<4>, ArrayStorage<f64, 4, 4>>

Associated Lie algebra type

fn act( &self, vector: &Matrix<f64, Const<3>, Const<1>, ArrayStorage<f64, 3, 1>>, jacobian_self: Option<&mut <Sim3 as LieGroup>::JacobianMatrix>, jacobian_vector: Option<&mut Matrix<f64, Const<3>, Const<3>, ArrayStorage<f64, 3, 3>>>, ) -> Matrix<f64, Const<3>, Const<1>, ArrayStorage<f64, 3, 1>>

Act on a vector v: g ⊙ v.

fn adjoint(&self) -> <Sim3 as LieGroup>::JacobianMatrix

Adjoint matrix Ad(g).

fn random() -> Sim3

Generate a random element (useful for testing and initialization).

fn normalize(&mut self)

Normalize/project the element to the manifold.

fn is_valid(&self, tolerance: f64) -> bool

Check if the element is approximately on the manifold.

fn as_param_slice(&self) -> &[f64]

Returns the manifold parameters as a contiguous flat slice.

fn as_param_slice_mut(&mut self) -> &mut [f64]

Mutably borrows the raw parameter storage for in-place retraction updates.

fn from_param_slice(s: &[f64]) -> Sim3

Constructs from a raw parameter slice (same layout as as_param_slice).

fn vee(&self) -> <Sim3 as LieGroup>::TangentVector

Vee operator: log(g)^∨.

fn is_approx(&self, other: &Sim3, tolerance: f64) -> bool

Check if the element is approximately equal to another element.

fn jacobian_identity() -> <Sim3 as LieGroup>::JacobianMatrix

Get the identity matrix for Jacobians.

fn zero_jacobian() -> <Sim3 as LieGroup>::JacobianMatrix

Get a zero Jacobian matrix.

fn right_plus( &self, tangent: &Self::TangentVector, jacobian_self: Option<&mut Self::JacobianMatrix>, jacobian_tangent: Option<&mut Self::JacobianMatrix>, ) -> Self

Right plus operation: g ⊞ φ = g ∘ exp(φ^∧).

fn right_minus( &self, other: &Self, jacobian_self: Option<&mut Self::JacobianMatrix>, jacobian_other: Option<&mut Self::JacobianMatrix>, ) -> Self::TangentVector

Right minus operation: g₁ ⊟ g₂ = log(g₂⁻¹ ∘ g₁)^∨.

fn left_plus( &self, tangent: &Self::TangentVector, jacobian_tangent: Option<&mut Self::JacobianMatrix>, jacobian_self: Option<&mut Self::JacobianMatrix>, ) -> Self

Left plus operation: φ ⊞ g = exp(φ^∧) ∘ g.

fn left_minus( &self, other: &Self, jacobian_self: Option<&mut Self::JacobianMatrix>, jacobian_other: Option<&mut Self::JacobianMatrix>, ) -> Self::TangentVector

Left minus operation: g₁ ⊟ g₂ = log(g₁ ∘ g₂⁻¹)^∨.

fn plus( &self, tangent: &Self::TangentVector, jacobian_self: Option<&mut Self::JacobianMatrix>, jacobian_tangent: Option<&mut Self::JacobianMatrix>, ) -> Self

Convenience method for right_plus. Equivalent to g ⊞ φ.

fn minus( &self, other: &Self, jacobian_self: Option<&mut Self::JacobianMatrix>, jacobian_other: Option<&mut Self::JacobianMatrix>, ) -> Self::TangentVector

Convenience method for right_minus. Equivalent to g₁ ⊟ g₂.

fn between( &self, other: &Self, jacobian_self: Option<&mut Self::JacobianMatrix>, jacobian_other: Option<&mut Self::JacobianMatrix>, ) -> Self

Compute g₁⁻¹ ∘ g₂ (relative transformation).

fn tangent_dim(&self) -> usize

Get the dimension of the tangent space for this manifold element.

impl PartialEq for Sim3

fn eq(&self, other: &Sim3) -> bool

Equality operator ==.

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

Inequality operator !=.

impl StructuralPartialEq for Sim3

impl Tangent<Sim3> for Sim3Tangent

fn exp(&self, jacobian: Option<&mut <Sim3 as LieGroup>::JacobianMatrix>) -> Sim3

Exponential map to Sim(3).

fn right_jacobian(&self) -> <Sim3 as LieGroup>::JacobianMatrix

Right Jacobian for Sim(3).

fn left_jacobian(&self) -> <Sim3 as LieGroup>::JacobianMatrix

Left Jacobian for Sim(3).

fn right_jacobian_inv(&self) -> <Sim3 as LieGroup>::JacobianMatrix

Inverse of right Jacobian.

fn left_jacobian_inv(&self) -> <Sim3 as LieGroup>::JacobianMatrix

Inverse of left Jacobian.

fn hat(&self) -> <Sim3 as LieGroup>::LieAlgebra

Hat operator: maps tangent vector to Lie algebra matrix (4x4).

const DIM: usize = 7

Dimension of the tangent space.

fn zero() -> <Sim3 as LieGroup>::TangentVector

Zero tangent vector.

fn random() -> <Sim3 as LieGroup>::TangentVector

Random tangent vector (useful for testing).

fn is_zero(&self, tolerance: f64) -> bool

Check if the tangent vector is approximately zero.

fn normalize(&mut self)

Normalize the tangent vector to unit norm.

fn normalized(&self) -> <Sim3 as LieGroup>::TangentVector

Return a unit tangent vector in the same direction.

fn as_slice(&self) -> &[f64]

Borrows the raw tangent data as a flat slice. Zero allocation.

fn from_slice(s: &[f64]) -> Sim3Tangent

Constructs from a raw slice (same layout as as_slice).

fn small_adj(&self) -> <Sim3 as LieGroup>::JacobianMatrix

Small adjugate operator: adj(φ) = φ^∧.

fn lie_bracket(&self, other: &Sim3Tangent) -> <Sim3 as LieGroup>::TangentVector

Lie bracket: [φ, ψ] = φ ∘ ψ - ψ ∘ φ.

fn is_approx(&self, other: &Sim3Tangent, tolerance: f64) -> bool

Check if the tangent vector is approximately equal to another tangent vector.

fn generator(&self, i: usize) -> <Sim3 as LieGroup>::LieAlgebra

Get the i-th generator of the Lie algebra.

fn is_dynamic() -> bool

Whether this tangent type has dynamic (runtime-determined) dimension.