#include <Similarity2.h>
Classes | |
| struct | ChartAtOrigin |
| Chart at the origin. More... | |
Public Types | |
| enum | |
| typedef OptionalJacobian< N, N > | ChartJacobian |
| typedef Eigen::Matrix< double, N, N > | Jacobian |
| typedef Eigen::Matrix< double, N, 1 > | TangentVector |
Public Member Functions | |
| const Similarity2 & | derived () const |
| Similarity2 | compose (const Similarity2 &g) const |
| Similarity2 | compose (const Similarity2 &g, ChartJacobian H1, ChartJacobian H2={}) const |
| GTSAM_EXPORT SOn | compose (const SOn &g, DynamicJacobian H1, DynamicJacobian H2) const |
| Similarity2 | between (const Similarity2 &g) const |
| Similarity2 | between (const Similarity2 &g, ChartJacobian H1, ChartJacobian H2={}) const |
| GTSAM_EXPORT SOn | between (const SOn &g, DynamicJacobian H1, DynamicJacobian H2) const |
| Similarity2 | inverse (ChartJacobian H) const |
| Similarity2 | expmap (const TangentVector &v) const |
| Similarity2 | expmap (const TangentVector &v, ChartJacobian H1, ChartJacobian H2={}) const |
| expmap with optional derivatives | |
| TangentVector | logmap (const Similarity2 &g) const |
| TangentVector | logmap (const Similarity2 &g, ChartJacobian H1, ChartJacobian H2={}) const |
| logmap with optional derivatives | |
| Similarity2 | retract (const TangentVector &v) const |
| retract as required by manifold concept: applies v at *this | |
| Similarity2 | retract (const TangentVector &v, ChartJacobian H1, ChartJacobian H2={}) const |
| retract with optional derivatives | |
| TangentVector | localCoordinates (const Similarity2 &g) const |
| localCoordinates as required by manifold concept: finds tangent vector between *this and g | |
| TangentVector | localCoordinates (const Similarity2 &g, ChartJacobian H1, ChartJacobian H2={}) const |
| localCoordinates with optional derivatives | |
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]. | |
Static Public Member Functions | |
| static Similarity2 | Retract (const TangentVector &v) |
| Retract at origin: possible in Lie group because it has an identity. | |
| static Similarity2 | Retract (const TangentVector &v, ChartJacobian H) |
| Retract at origin with optional derivative. | |
| static TangentVector | LocalCoordinates (const Similarity2 &g) |
| LocalCoordinates at origin: possible in Lie group because it has an identity. | |
| static TangentVector | LocalCoordinates (const Similarity2 &g, ChartJacobian H) |
| LocalCoordinates at origin with optional derivative. | |
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. | |
| 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 |
| Point2 | operator* (const Point2 &p) const |
| static Similarity2 | Align (const Point2Pairs &abPointPairs) |
| static Similarity2 | Align (const Pose2Pairs &abPosePairs) |
Lie Group | |
| Matrix4 | AdjointMap () const |
| Project from one tangent space to another. | |
| static Vector4 | Logmap (const Similarity2 &S, OptionalJacobian< 4, 4 > Hm={}) |
| static Similarity2 | Expmap (const Vector4 &v, OptionalJacobian< 4, 4 > Hm={}) |
| Exponential map at the identity. | |
Standard interface | |
| Matrix3 | matrix () const |
| Calculate 4*4 matrix group equivalent. | |
| Rot2 | rotation () const |
| Return a GTSAM rotation. | |
| Point2 | translation () const |
| Return a GTSAM translation. | |
| double | scale () const |
| Return the scale. | |
| size_t | dim () const |
| Dimensionality of tangent space = 4 DOF. | |
| static size_t | Dim () |
| Dimensionality of tangent space = 4 DOF - used to autodetect sizes. | |
Detailed Description
2D similarity transform
Member Function Documentation
◆ Align() [1/2]
|
static |
Create Similarity2 by aligning at least two point pairs
◆ Align() [2/2]
|
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
◆ expmap()
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inlineinherited |
expmap as required by manifold concept Applies exponential map to v and composes with *this
◆ logmap()
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inlineinherited |
logmap as required by manifold concept Applies logarithmic map to group element that takes *this to g
◆ Logmap()
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static |
Log map at the identity \( [t_x, t_y, \delta, \lambda] \)
◆ transformFrom()
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 file:
- /home/docs/checkouts/readthedocs.org/user_builds/gtsam-jlblanco-docs/checkouts/latest/gtsam/geometry/Similarity2.h
