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gtsam::Similarity2 Class Reference

Detailed Description

2D similarity transform

Inheritance diagram for gtsam::Similarity2:

Lie Group

using LieAlgebra = Matrix3
Matrix4 AdjointMap () const
 Project from one tangent space to another.
static Matrix2 GetV (double theta, double lambda)
 Calculate expmap and logmap coefficients.
static Vector4 Logmap (const Similarity2 &S)
 Log map at the identity \( [t_x, t_y, \delta, \lambda] \).
static Similarity2 Expmap (const Vector4 &v)
 Exponential map at the identity.
static Matrix3 Hat (const Vector4 &xi)
 Hat maps from tangent vector to Lie algebra.
static Vector4 Vee (const Matrix3 &X)
 Vee maps from Lie algebra to tangent vector.

Testable

bool equals (const Similarity2 &sim, double tol) const
 Compare with tolerance.
bool operator== (const Similarity2 &other) const
 Exact equality.
void print (const std::string &s="") const
 Print with optional string.
GTSAM_EXPORT friend std::ostream & operator<< (std::ostream &os, const Similarity2 &p)

Group

Similarity2 operator* (const Similarity2 &S) const
 Composition.
Similarity2 inverse () const
 Return the inverse.
static Similarity2 Identity ()
 Return an identity transform.

Group action on Point2

Point2 transformFrom (const Point2 &p) const
 Action on a point p is s*(R*p+t).
Pose2 transformFrom (const Pose2 &T) const
 Action on a pose T.
Point2 operator* (const Point2 &p) const
static Similarity2 Align (const Point2Pairs &abPointPairs)
 Create Similarity2 by aligning at least two point pairs.
static Similarity2 Align (const Pose2Pairs &abPosePairs)
 Create the Similarity2 object that aligns at least two pose pairs.

Public Member Functions

Constructors
 Similarity2 ()
 Default constructor.
 Similarity2 (double s)
 Construct pure scaling.
 Similarity2 (const Rot2 &R, const Point2 &t, double s)
 Construct from GTSAM types.
 Similarity2 (const Matrix2 &R, const Vector2 &t, double s)
 Construct from Eigen types.
 Similarity2 (const Matrix3 &T)
 Construct from matrix [R t; 0 s^-1].
Standard interface
Matrix3 matrix () const
 Calculate 3*3 matrix group equivalent.
Rot2 rotation () const
 Return a GTSAM rotation.
Point2 translation () const
 Return a GTSAM translation.
double scale () const
 Return the scale.
Public Member Functions inherited from gtsam::MatrixLieGroup< Similarity2, 4, 3 >
std::enable_if_t< M !=Eigen::Dynamic, int > dim () const
 Provided fixed dimension in dim() if needed.
Eigen::Matrix< double, internal::product(N, N), 1 > vec (OptionalJacobian< internal::product(N, N), D > H={}) const
 Vectorize the matrix representation of a Lie group element.
Jacobian AdjointMap () const
 A generic implementation of AdjointMap for matrix Lie groups.
TangentVector Adjoint (const TangentVector &xi, ChartJacobian H_this={}, ChartJacobian H_xi={}) const
 Adjoint action on a tangent vector.
TangentVector AdjointTranspose (const TangentVector &x, ChartJacobian H_this={}, ChartJacobian H_x={}) const
 Dual Adjoint action on a tangent covector.
Public Member Functions inherited from gtsam::LieGroup< Similarity2, D >
SOn compose (const SOn &g, DynamicJacobian H1, DynamicJacobian H2) const
SOn between (const SOn &g, DynamicJacobian H1, DynamicJacobian H2) const
GTSAM_EXPORT SOn compose (const SOn &g, DynamicJacobian H1, DynamicJacobian H2) const
GTSAM_EXPORT SOn between (const SOn &g, DynamicJacobian H1, DynamicJacobian H2) const
std::enable_if_t< M !=Eigen::Dynamic, int > dim () const
 Provided fixed dimension in dim() if needed.
const Similarity2 & derived () const
Similarity2 inverse (ChartJacobian H) const
Similarity2 expmap (const TangentVector &v) const
 expmap as required by manifold concept Applies exponential map to v and composes with *this
TangentVector logmap (const Similarity2 &g) const
 logmap as required by manifold concept Applies logarithmic map to group element that takes *this to g
Similarity2 retract (const TangentVector &v) const
 retract as required by manifold concept: applies v at *this
TangentVector localCoordinates (const Similarity2 &g) const
 localCoordinates as required by manifold concept: finds tangent vector between *this and g

Classes

struct  ChartAtOrigin
 Chart at the origin. More...

Additional Inherited Members

Static Public Member Functions inherited from gtsam::MatrixLieGroup< Similarity2, 4, 3 >
static constexpr int Dim ()
 Static method to get the dimension (compile-time or dynamic).
static Jacobian adjointMap (const TangentVector &xi)
 Lie algebra adjoint map ad_xi, with optional specialization in derived classes.
static TangentVector adjoint (const TangentVector &xi, const TangentVector &y, ChartJacobian Hxi={}, ChartJacobian H_y={})
 Lie algebra action ad_xi(y), with optional Jacobians.
static TangentVector adjointTranspose (const TangentVector &xi, const TangentVector &y, ChartJacobian Hxi={}, ChartJacobian H_y={})
 Dual Lie algebra action ad_xi^T(y), with optional Jacobians.
Static Public Member Functions inherited from gtsam::LieGroup< Similarity2, D >
static constexpr int Dim ()
 Static method to get the dimension (compile-time or dynamic).
static Similarity2 Retract (const TangentVector &v)
 Retract at origin: possible in Lie group because it has an identity.
static TangentVector LocalCoordinates (const Similarity2 &g)
 LocalCoordinates at origin: possible in Lie group because it has an identity.
Static Public Attributes inherited from gtsam::MatrixLieGroup< Similarity2, 4, 3 >
static constexpr auto dimension
Static Public Attributes inherited from gtsam::LieGroup< Similarity2, D >
static constexpr auto dimension
Public Types inherited from gtsam::MatrixLieGroup< Similarity2, 4, 3 >
using Base
using ChartJacobian
using Jacobian
using TangentVector
using Vectorized
using VectorizedJacobian
Public Types inherited from gtsam::LieGroup< Similarity2, D >
typedef OptionalJacobian< N, N > ChartJacobian
typedef Eigen::Matrix< double, N, N > Jacobian
typedef Eigen::Matrix< double, N, 1 > TangentVector

Member Function Documentation

◆ Align()

Similarity2 gtsam::Similarity2::Align ( const Pose2Pairs & abPosePairs)
static

Create the Similarity2 object that aligns at least two pose pairs.

Each pair is of the form (aTi, bTi). Given a list of pairs in frame a, and a list of pairs in frame b, Align() will compute the best-fit Similarity2 aSb transformation to align them. First, the rotation aRb will be computed as the average (Karcher mean) of many estimates aRb (from each pair). Afterwards, the scale factor will be computed using the algorithm described here: http://www5.informatik.uni-erlangen.de/Forschung/Publikationen/2005/Zinsser05-PSR.pdf

◆ transformFrom()

Pose2 gtsam::Similarity2::transformFrom ( const Pose2 & T) const

Action on a pose T.

|Rs ts| |R t| |Rs*R Rs*t+ts| |0 1/s| * |0 1| = | 0 1/s |, the result is still a Sim2 object. To retrieve a Pose2, we normalized the scale value into 1. |Rs*R Rs*t+ts| |Rs*R s(Rs*t+ts)| | 0 1/s | = | 0 1 |

This group action satisfies the compatibility condition. For more details, refer to: https://en.wikipedia.org/wiki/Group_action

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