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gtsam  4.0.0
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gtsam::SO3 Class Reference

Detailed Description

True SO(3), i.e., 3*3 matrix subgroup We guarantee (all but first) constructors only generate from sub-manifold.

However, round-off errors in repeated composition could move off it...

+ Inheritance diagram for gtsam::SO3:

Constructors

 SO3 ()
 Constructor from AngleAxisd.
 
template<typename Derived >
 SO3 (const MatrixBase< Derived > &R)
 Constructor from Eigen Matrix.
 
 SO3 (const Eigen::AngleAxisd &angleAxis)
 Constructor from AngleAxisd.
 
static SO3 AxisAngle (const Vector3 &axis, double theta)
 Static, named constructor TODO think about relation with above.
 

Group

SO3 inverse () const
 inverse of a rotation = transpose
 
static SO3 identity ()
 identity rotation for group operation
 

Lie Group

Matrix3 AdjointMap () const
 
static SO3 Expmap (const Vector3 &omega, ChartJacobian H=boost::none)
 Exponential map at identity - create a rotation from canonical coordinates \( [R_x,R_y,R_z] \) using Rodrigues' formula.
 
static Matrix3 ExpmapDerivative (const Vector3 &omega)
 Derivative of Expmap.
 
static Vector3 Logmap (const SO3 &R, ChartJacobian H=boost::none)
 Log map at identity - returns the canonical coordinates \( [R_x,R_y,R_z] \) of this rotation.
 
static Matrix3 LogmapDerivative (const Vector3 &omega)
 Derivative of Logmap. More...
 

Public Member Functions

Testable
void print (const std::string &s) const
 
bool equals (const SO3 &R, double tol) const
 
- Public Member Functions inherited from gtsam::LieGroup< SO3, 3 >
 BOOST_STATIC_ASSERT_MSG (N !=Eigen::Dynamic, "LieGroup not yet specialized for dynamically sized types.")
 
const SO3 & derived () const
 
SO3 compose (const SO3 &g) const
 
SO3 compose (const SO3 &g, ChartJacobian H1, ChartJacobian H2=boost::none) const
 
SO3 between (const SO3 &g) const
 
SO3 between (const SO3 &g, ChartJacobian H1, ChartJacobian H2=boost::none) const
 
SO3 inverse (ChartJacobian H) const
 
SO3 expmap (const TangentVector &v) const
 expmap as required by manifold concept Applies exponential map to v and composes with *this
 
SO3 expmap (const TangentVector &v, ChartJacobian H1, ChartJacobian H2=boost::none) const
 expmap with optional derivatives
 
TangentVector logmap (const SO3 &g) const
 logmap as required by manifold concept Applies logarithmic map to group element that takes *this to g
 
TangentVector logmap (const SO3 &g, ChartJacobian H1, ChartJacobian H2=boost::none) const
 logmap with optional derivatives
 
SO3 retract (const TangentVector &v) const
 retract as required by manifold concept: applies v at *this
 
SO3 retract (const TangentVector &v, ChartJacobian H1, ChartJacobian H2=boost::none) const
 retract with optional derivatives
 
TangentVector localCoordinates (const SO3 &g) const
 localCoordinates as required by manifold concept: finds tangent vector between *this and g
 
TangentVector localCoordinates (const SO3 &g, ChartJacobian H1, ChartJacobian H2=boost::none) const
 localCoordinates with optional derivatives
 

Public Types

enum  { dimension = 3 }
 
- Public Types inherited from gtsam::LieGroup< SO3, 3 >
enum  
 
typedef OptionalJacobian< N, N > ChartJacobian
 
typedef Eigen::Matrix< double, N, N > Jacobian
 
typedef Eigen::Matrix< double, N, 1 > TangentVector
 

Classes

struct  ChartAtOrigin
 

Additional Inherited Members

- Static Public Member Functions inherited from gtsam::LieGroup< SO3, 3 >
static SO3 Retract (const TangentVector &v)
 Retract at origin: possible in Lie group because it has an identity.
 
static SO3 Retract (const TangentVector &v, ChartJacobian H)
 Retract at origin with optional derivative.
 
static TangentVector LocalCoordinates (const SO3 &g)
 LocalCoordinates at origin: possible in Lie group because it has an identity.
 
static TangentVector LocalCoordinates (const SO3 &g, ChartJacobian H)
 LocalCoordinates at origin with optional derivative.
 

Member Function Documentation

◆ LogmapDerivative()

Matrix3 gtsam::SO3::LogmapDerivative ( const Vector3 &  omega)
static

Derivative of Logmap.

Right Jacobian for Log map in SO(3) - equation (10.86) and following equations in G.S. Chirikjian, "Stochastic Models, Information Theory, and Lie Groups", Volume 2, 2008. logmap( Rhat * expmap(omega) ) \approx logmap( Rhat ) + Jrinv * omega where Jrinv = LogmapDerivative(omega); This maps a perturbation on the manifold (expmap(omega)) to a perturbation in the tangent space (Jrinv * omega)

The documentation for this class was generated from the following files: