#include <Rot2.h>

Inheritance diagram for gtsam::Rot2:

Classes
struct	ChartAtOrigin

Private Member Functions
Rot2 &	normalize ()

	Rot2 (double c, double s)

Private Attributes
double	c_

double	s_

Constructors and named constructors
	Rot2 ()

	Rot2 (const Rot2 &r)

	Rot2 (double theta)
	Constructor from angle in radians == exponential map at identity. More...

static Rot2	fromAngle (double theta)
	Named constructor from angle in radians. More...

static Rot2	fromDegrees (double theta)
	Named constructor from angle in degrees. More...

static Rot2	fromCosSin (double c, double s)
	Named constructor from cos(theta),sin(theta) pair. More...

static Rot2	relativeBearing (const Point2 &d, OptionalJacobian< 1, 2 > H={})

static Rot2	atan2 (double y, double x)

static Rot2	Random (std::mt19937 &rng)

Testable
void	print (const std::string &s="theta") const

bool	equals (const Rot2 &R, double tol=1e-9) const

Group
Rot2	inverse () const

Rot2	operator* (const Rot2 &R) const

static Rot2	Identity ()

Lie Group
Matrix1	AdjointMap () const

static Rot2	Expmap (const Vector1 &v, ChartJacobian H={})
	Exponential map at identity - create a rotation from canonical coordinates. More...

static Vector1	Logmap (const Rot2 &r, ChartJacobian H={})
	Log map at identity - return the canonical coordinates of this rotation. More...

static Matrix	ExpmapDerivative (const Vector &)
	Left-trivialized derivative of the exponential map. More...

static Matrix	LogmapDerivative (const Vector &)
	Left-trivialized derivative inverse of the exponential map. More...

Group Action on Point2
Point2	rotate (const Point2 &p, OptionalJacobian< 2, 1 > H1={}, OptionalJacobian< 2, 2 > H2={}) const

Point2	operator* (const Point2 &p) const

Point2	unrotate (const Point2 &p, OptionalJacobian< 2, 1 > H1={}, OptionalJacobian< 2, 2 > H2={}) const

Standard Interface
Point2	unit () const
	Creates a unit vector as a Point2. More...

double	theta () const

double	degrees () const

double	c () const

double	s () const

Matrix2	matrix () const

Matrix2	transpose () const

static Rot2	ClosestTo (const Matrix2 &M)

Additional Inherited Members
Public Types inherited from gtsam::LieGroup< Rot2, 1 >
enum

typedef OptionalJacobian< N, N >	ChartJacobian

typedef Eigen::Matrix< double, N, N >	Jacobian

typedef Eigen::Matrix< double, N, 1 >	TangentVector

Public Member Functions inherited from gtsam::LieGroup< Rot2, 1 >
Rot2	between (const Rot2 &g) const

Rot2	between (const Rot2 &g, ChartJacobian H1, ChartJacobian H2={}) const

SOn	between (const SOn &g, DynamicJacobian H1, DynamicJacobian H2) const

GTSAM_EXPORT SOn	between (const SOn &g, DynamicJacobian H1, DynamicJacobian H2) const

Rot2	compose (const Rot2 &g) const

Rot2	compose (const Rot2 &g, ChartJacobian H1, ChartJacobian H2={}) const

SOn	compose (const SOn &g, DynamicJacobian H1, DynamicJacobian H2) const

GTSAM_EXPORT SOn	compose (const SOn &g, DynamicJacobian H1, DynamicJacobian H2) const

const Rot2 &	derived () const

Rot2	expmap (const TangentVector &v) const

Rot2	expmap (const TangentVector &v, ChartJacobian H1, ChartJacobian H2={}) const
	expmap with optional derivatives More...

Rot2	inverse (ChartJacobian H) const

TangentVector	localCoordinates (const Rot2 &g) const
	localCoordinates as required by manifold concept: finds tangent vector between *this and g More...

TangentVector	localCoordinates (const Rot2 &g, ChartJacobian H1, ChartJacobian H2={}) const
	localCoordinates with optional derivatives More...

TangentVector	logmap (const Rot2 &g) const

TangentVector	logmap (const Rot2 &g, ChartJacobian H1, ChartJacobian H2={}) const
	logmap with optional derivatives More...

Rot2	retract (const TangentVector &v) const
	retract as required by manifold concept: applies v at *this More...

Rot2	retract (const TangentVector &v, ChartJacobian H1, ChartJacobian H2={}) const
	retract with optional derivatives More...

Static Public Member Functions inherited from gtsam::LieGroup< Rot2, 1 >
static TangentVector	LocalCoordinates (const Rot2 &g)
	LocalCoordinates at origin: possible in Lie group because it has an identity. More...

static TangentVector	LocalCoordinates (const Rot2 &g, ChartJacobian H)
	LocalCoordinates at origin with optional derivative. More...

static Rot2	Retract (const TangentVector &v)
	Retract at origin: possible in Lie group because it has an identity. More...

static Rot2	Retract (const TangentVector &v, ChartJacobian H)
	Retract at origin with optional derivative. More...

Detailed Description

Rotation matrix NOTE: the angle theta is in radians unless explicitly stated

Definition at line 35 of file Rot2.h.

Constructor & Destructor Documentation

◆ Rot2() [1/4]

gtsam::Rot2::Rot2	(	double	c,
		double	s
	)

inlineprivate

private constructor from cos/sin

Definition at line 44 of file Rot2.h.

◆ Rot2() [2/4]

gtsam::Rot2::Rot2 ( )

inline

default constructor, zero rotation

Definition at line 52 of file Rot2.h.

◆ Rot2() [3/4]

gtsam::Rot2::Rot2 ( const Rot2 & r )

inline

copy constructor

Definition at line 55 of file Rot2.h.

◆ Rot2() [4/4]

gtsam::Rot2::Rot2 ( double theta )

inline

Constructor from angle in radians == exponential map at identity.

Definition at line 58 of file Rot2.h.

Member Function Documentation

◆ AdjointMap()

Matrix1 gtsam::Rot2::AdjointMap ( ) const

inline

Calculate Adjoint map

Definition at line 131 of file Rot2.h.

◆ atan2()

Rot2 gtsam::Rot2::atan2	(	double	y,
		double	x
	)

static

Named constructor that behaves as atan2, i.e., y,x order (!) and normalizes

Definition at line 33 of file Rot2.cpp.

◆ c()

double gtsam::Rot2::c ( ) const

inline

return cos

Definition at line 197 of file Rot2.h.

◆ ClosestTo()

Rot2 gtsam::Rot2::ClosestTo ( const Matrix2 & M )

static

Find closest valid rotation matrix, given a 2x2 matrix

Definition at line 133 of file Rot2.cpp.

◆ degrees()

double gtsam::Rot2::degrees ( ) const

inline

return angle (DEGREES)

Definition at line 191 of file Rot2.h.

◆ equals()

bool gtsam::Rot2::equals	(	const Rot2 &	R,
		double	tol = `1e-9`
	)		const

equals with an tolerance

Definition at line 51 of file Rot2.cpp.

◆ Expmap()

Rot2 gtsam::Rot2::Expmap	(	const Vector1 &	v,
		ChartJacobian	H = `{}`
	)

static

Exponential map at identity - create a rotation from canonical coordinates.

Definition at line 67 of file Rot2.cpp.

◆ ExpmapDerivative()

static Matrix gtsam::Rot2::ExpmapDerivative ( const Vector & )

inlinestatic

Left-trivialized derivative of the exponential map.

Definition at line 134 of file Rot2.h.

◆ fromAngle()

static Rot2 gtsam::Rot2::fromAngle ( double theta )

inlinestatic

Named constructor from angle in radians.

Definition at line 61 of file Rot2.h.

◆ fromCosSin()

Rot2 gtsam::Rot2::fromCosSin	(	double	c,
		double	s
	)

static

Named constructor from cos(theta),sin(theta) pair.

Definition at line 27 of file Rot2.cpp.

◆ fromDegrees()

static Rot2 gtsam::Rot2::fromDegrees ( double theta )

inlinestatic

Named constructor from angle in degrees.

Definition at line 66 of file Rot2.h.

◆ Identity()

static Rot2 gtsam::Rot2::Identity ( )

inlinestatic

Identity

Definition at line 110 of file Rot2.h.

◆ inverse()

Rot2 gtsam::Rot2::inverse ( ) const

inline

The inverse rotation - negative angle

Definition at line 113 of file Rot2.h.

◆ Logmap()

Vector1 gtsam::Rot2::Logmap	(	const Rot2 &	r,
		ChartJacobian	H = `{}`
	)

static

Log map at identity - return the canonical coordinates of this rotation.

Definition at line 77 of file Rot2.cpp.

◆ LogmapDerivative()

static Matrix gtsam::Rot2::LogmapDerivative ( const Vector & )

inlinestatic

Left-trivialized derivative inverse of the exponential map.

Definition at line 139 of file Rot2.h.

◆ matrix()

Matrix2 gtsam::Rot2::matrix ( ) const

return 2*2 rotation matrix

Definition at line 85 of file Rot2.cpp.

◆ normalize()

Rot2 & gtsam::Rot2::normalize ( )

private

normalize to make sure cos and sin form unit vector

Definition at line 56 of file Rot2.cpp.

◆ operator*() [1/2]

Point2 gtsam::Rot2::operator* ( const Point2 & p ) const

inline

syntactic sugar for rotate

Definition at line 166 of file Rot2.h.

◆ operator*() [2/2]

Rot2 gtsam::Rot2::operator* ( const Rot2 & R ) const

inline

Compose - make a new rotation by adding angles

Definition at line 116 of file Rot2.h.

◆ print()

void gtsam::Rot2::print ( const std::string & s = "theta" ) const

print

Definition at line 46 of file Rot2.cpp.

◆ Random()

Rot2 gtsam::Rot2::Random ( std::mt19937 & rng )

static

Random, generates random angle $\in$ [-pi,pi] Example: std::mt19937 engine(42); Unit3 unit = Unit3::Random(engine);

Definition at line 39 of file Rot2.cpp.

◆ relativeBearing()

Rot2 gtsam::Rot2::relativeBearing	(	const Point2 &	d,
		OptionalJacobian< 1, 2 >	H = `{}`
	)

static

Named constructor with derivative Calculate relative bearing to a landmark in local coordinate frame

Parameters

d	2D location of landmark
H	optional reference for Jacobian

Returns: 2D rotation $\in SO(2)$

Definition at line 119 of file Rot2.cpp.

◆ rotate()

Point2 gtsam::Rot2::rotate	(	const Point2 &	p,
		OptionalJacobian< 2, 1 >	H1 = `{}`,
		OptionalJacobian< 2, 2 >	H2 = `{}`
	)		const

rotate point from rotated coordinate frame to world $ p^w = R_c^w p^c $

Definition at line 100 of file Rot2.cpp.

◆ s()

double gtsam::Rot2::s ( ) const

inline

return sin

Definition at line 202 of file Rot2.h.

◆ theta()

double gtsam::Rot2::theta ( ) const

inline

return angle (RADIANS)

Definition at line 186 of file Rot2.h.

◆ transpose()

Matrix2 gtsam::Rot2::transpose ( ) const

return 2*2 transpose (inverse) rotation matrix

Definition at line 92 of file Rot2.cpp.

◆ unit()

Point2 gtsam::Rot2::unit ( ) const

inline

Creates a unit vector as a Point2.

Definition at line 181 of file Rot2.h.

◆ unrotate()

Point2 gtsam::Rot2::unrotate	(	const Point2 &	p,
		OptionalJacobian< 2, 1 >	H1 = `{}`,
		OptionalJacobian< 2, 2 >	H2 = `{}`
	)		const

rotate point from world to rotated frame $ p^c = (R_c^w)^T p^w $

Definition at line 110 of file Rot2.cpp.

Member Data Documentation

◆ c_

double gtsam::Rot2::c_

private

we store cos(theta) and sin(theta)

Definition at line 38 of file Rot2.h.

◆ s_

double gtsam::Rot2::s_

private

Definition at line 38 of file Rot2.h.

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

Classes

Private Member Functions

Private Attributes

Constructors and named constructors

Testable

Group

Lie Group

Group Action on Point2

Standard Interface

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ Rot2() [1/4]

◆ Rot2() [2/4]

◆ Rot2() [3/4]

◆ Rot2() [4/4]

Member Function Documentation

◆ AdjointMap()

◆ atan2()

◆ c()

◆ ClosestTo()

◆ degrees()

◆ equals()

◆ Expmap()

◆ ExpmapDerivative()

◆ fromAngle()

◆ fromCosSin()

◆ fromDegrees()

◆ Identity()

◆ inverse()

◆ Logmap()

◆ LogmapDerivative()

◆ matrix()

◆ normalize()

◆ operator*() [1/2]

◆ operator*() [2/2]

◆ print()

◆ Random()

◆ relativeBearing()

◆ rotate()

◆ s()

◆ theta()

◆ transpose()

◆ unit()

◆ unrotate()

Member Data Documentation

◆ c_

◆ s_