#include <Rot2.h>

Inheritance diagram for gtsam::Rot2:

Collaboration diagram for gtsam::Rot2:

Classes
struct	ChartAtOrigin

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 Rot2 &	derived () const

Rot2	compose (const Rot2 &g) const

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

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

Rot2	between (const Rot2 &g) const

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

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

Rot2	inverse (ChartJacobian H) const

Rot2	expmap (const TangentVector &v) const

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

TangentVector	logmap (const Rot2 &g) const

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

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

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

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

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

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

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

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

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

Constructors and named constructors
	Rot2 ()

	Rot2 (const Rot2 &r)

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

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

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

static Rot2	fromCosSin (double c, double s)
	Named constructor from cos(theta),sin(theta) pair, will not normalize!

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.

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

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

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

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.

double	theta () const

double	degrees () const

double	c () const

double	s () const

Matrix2	matrix () const

Matrix2	transpose () const

static Rot2	ClosestTo (const Matrix2 &M)

Detailed Description

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

Constructor & Destructor Documentation

◆ Rot2() [1/2]

gtsam::Rot2::Rot2 ( )

inline

default constructor, zero rotation

◆ Rot2() [2/2]

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

inline

copy constructor

Member Function Documentation

◆ AdjointMap()

Matrix1 gtsam::Rot2::AdjointMap ( ) const

inline

Calculate Adjoint map

◆ atan2()

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

static

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

◆ c()

double gtsam::Rot2::c ( ) const

inline

return cos

◆ ClosestTo()

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

static

Find closest valid rotation matrix, given a 2x2 matrix

◆ degrees()

double gtsam::Rot2::degrees ( ) const

inline

return angle (DEGREES)

◆ equals()

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

equals with an tolerance

◆ expmap()

Rot2 gtsam::LieGroup< Rot2 , N >::expmap ( const TangentVector & v ) const

inlineinherited

expmap as required by manifold concept Applies exponential map to v and composes with *this

◆ Identity()

static Rot2 gtsam::Rot2::Identity ( )

inlinestatic

Identity

◆ inverse()

Rot2 gtsam::Rot2::inverse ( ) const

inline

The inverse rotation - negative angle

◆ logmap()

TangentVector gtsam::LieGroup< Rot2 , N >::logmap ( const Rot2 & g ) const

inlineinherited

logmap as required by manifold concept Applies logarithmic map to group element that takes *this to g

◆ matrix()

Matrix2 gtsam::Rot2::matrix ( ) const

return 2*2 rotation matrix

◆ operator*() [1/2]

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

inline

Compose - make a new rotation by adding angles

◆ operator*() [2/2]

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

inline

syntactic sugar for rotate

◆ print()

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

print

◆ Random()

static 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);

◆ relativeBearing()

static 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 \( \in SO(2) \)

◆ 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 \( p^w = R_c^w p^c \)

◆ s()

double gtsam::Rot2::s ( ) const

inline

return sin

◆ theta()

double gtsam::Rot2::theta ( ) const

inline

return angle (RADIANS)

◆ transpose()

Matrix2 gtsam::Rot2::transpose ( ) const

return 2*2 transpose (inverse) rotation matrix

◆ unrotate()

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

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

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/Rot2.h

Classes

Public Types

Public Member Functions

Static Public Member Functions

Constructors and named constructors

Testable

Group

Lie Group

Group Action on Point2

Standard Interface

Detailed Description

Constructor & Destructor Documentation

◆ Rot2() [1/2]

◆ Rot2() [2/2]

Member Function Documentation

◆ AdjointMap()

◆ atan2()

◆ c()

◆ ClosestTo()

◆ degrees()

◆ equals()

◆ expmap()

◆ Identity()

◆ inverse()

◆ logmap()

◆ matrix()

◆ operator*() [1/2]

◆ operator*() [2/2]

◆ print()

◆ Random()

◆ relativeBearing()

◆ rotate()

◆ s()

◆ theta()

◆ transpose()

◆ unrotate()