Rot3 is a 3D rotation represented as a rotation matrix if the preprocessor symbol GTSAM_USE_QUATERNIONS is not defined, or as a quaternion if it is defined. More...

#include <Rot3.h>

Inheritance diagram for gtsam::Rot3:

[legend]

Classes
struct	CayleyChart

struct	ChartAtOrigin

Public Member Functions
Testable
void	print (const std::string &s="") const

bool	equals (const Rot3 &p, double tol=1e-9) const

Group Action on Point3
Point3	rotate (const Point3 &p, OptionalJacobian< 3, 3 > H1={}, OptionalJacobian< 3, 3 > H2={}) const

Point3	operator* (const Point3 &p) const
	rotate point from rotated coordinate frame to world = R*p More...

Point3	unrotate (const Point3 &p, OptionalJacobian< 3, 3 > H1={}, OptionalJacobian< 3, 3 > H2={}) const
	rotate point from world to rotated frame More...

Group Action on Unit3
Unit3	rotate (const Unit3 &p, OptionalJacobian< 2, 3 > HR={}, OptionalJacobian< 2, 2 > Hp={}) const
	rotate 3D direction from rotated coordinate frame to world frame More...

Unit3	unrotate (const Unit3 &p, OptionalJacobian< 2, 3 > HR={}, OptionalJacobian< 2, 2 > Hp={}) const
	unrotate 3D direction from world frame to rotated coordinate frame More...

Unit3	operator* (const Unit3 &p) const
	rotate 3D direction from rotated coordinate frame to world frame More...

Standard Interface
Matrix3	matrix () const

Matrix3	transpose () const

Point3	r1 () const
	first column More...

Point3	r2 () const
	second column More...

Point3	r3 () const
	third column More...

Vector3	xyz (OptionalJacobian< 3, 3 > H={}) const

Vector3	ypr (OptionalJacobian< 3, 3 > H={}) const

Vector3	rpy (OptionalJacobian< 3, 3 > H={}) const

double	roll (OptionalJacobian< 1, 3 > H={}) const

double	pitch (OptionalJacobian< 1, 3 > H={}) const

double	yaw (OptionalJacobian< 1, 3 > H={}) const

Public Member Functions inherited from gtsam::LieGroup< Rot3, 3 >
Rot3	between (const Rot3 &g) const

Rot3	between (const Rot3 &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

Rot3	compose (const Rot3 &g) const

Rot3	compose (const Rot3 &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 Rot3 &	derived () const

Rot3	expmap (const TangentVector &v) const

Rot3	expmap (const TangentVector &v, ChartJacobian H1, ChartJacobian H2={}) const
	expmap with optional derivatives More...

Rot3	inverse (ChartJacobian H) const

TangentVector	localCoordinates (const Rot3 &g) const
	localCoordinates as required by manifold concept: finds tangent vector between *this and g More...

TangentVector	localCoordinates (const Rot3 &g, ChartJacobian H1, ChartJacobian H2={}) const
	localCoordinates with optional derivatives More...

TangentVector	logmap (const Rot3 &g) const

TangentVector	logmap (const Rot3 &g, ChartJacobian H1, ChartJacobian H2={}) const
	logmap with optional derivatives More...

Rot3	retract (const TangentVector &v) const
	retract as required by manifold concept: applies v at *this More...

Rot3	retract (const TangentVector &v, ChartJacobian H1, ChartJacobian H2={}) const
	retract with optional derivatives More...

Private Attributes
SO3	rot_

Constructors and named constructors
	Rot3 ()

	Rot3 (const Point3 &col1, const Point3 &col2, const Point3 &col3)

	Rot3 (double R11, double R12, double R13, double R21, double R22, double R23, double R31, double R32, double R33)
	Construct from a rotation matrix, as doubles in row-major order !!! More...

template<typename Derived >
	Rot3 (const Eigen::MatrixBase< Derived > &R)

	Rot3 (const Matrix3 &R)

	Rot3 (const SO3 &R)

	Rot3 (const Quaternion &q)

	Rot3 (double w, double x, double y, double z)

virtual	~Rot3 ()

Rot3	normalized () const

static Rot3	Random (std::mt19937 &rng)

static Rot3	Rx (double t)
	Rotation around X axis as in http://en.wikipedia.org/wiki/Rotation_matrix, counterclockwise when looking from unchanging axis. More...

static Rot3	Ry (double t)
	Rotation around Y axis as in http://en.wikipedia.org/wiki/Rotation_matrix, counterclockwise when looking from unchanging axis. More...

static Rot3	Rz (double t)
	Rotation around Z axis as in http://en.wikipedia.org/wiki/Rotation_matrix, counterclockwise when looking from unchanging axis. More...

static Rot3	RzRyRx (double x, double y, double z, OptionalJacobian< 3, 1 > Hx={}, OptionalJacobian< 3, 1 > Hy={}, OptionalJacobian< 3, 1 > Hz={})
	Rotations around Z, Y, then X axes as in http://en.wikipedia.org/wiki/Rotation_matrix, counterclockwise when looking from unchanging axis. More...

static Rot3	RzRyRx (const Vector &xyz, OptionalJacobian< 3, 3 > H={})
	Rotations around Z, Y, then X axes as in http://en.wikipedia.org/wiki/Rotation_matrix, counterclockwise when looking from unchanging axis. More...

static Rot3	Yaw (double t)
	Positive yaw is to right (as in aircraft heading). See ypr. More...

static Rot3	Pitch (double t)
	Positive pitch is up (increasing aircraft altitude).See ypr. More...

static Rot3	Roll (double t)

static Rot3	Ypr (double y, double p, double r, OptionalJacobian< 3, 1 > Hy={}, OptionalJacobian< 3, 1 > Hp={}, OptionalJacobian< 3, 1 > Hr={})

static Rot3	Quaternion (double w, double x, double y, double z)

static Rot3	AxisAngle (const Point3 &axis, double angle)

static Rot3	AxisAngle (const Unit3 &axis, double angle)

static Rot3	Rodrigues (const Vector3 &w)

static Rot3	Rodrigues (double wx, double wy, double wz)

static Rot3	AlignPair (const Unit3 &axis, const Unit3 &a_p, const Unit3 &b_p)
	Determine a rotation to bring two vectors into alignment, using the rotation axis provided. More...

static Rot3	AlignTwoPairs (const Unit3 &a_p, const Unit3 &b_p, const Unit3 &a_q, const Unit3 &b_q)
	Calculate rotation from two pairs of homogeneous points using two successive rotations. More...

static Rot3	ClosestTo (const Matrix3 &M)

Group
Rot3	operator* (const Rot3 &R2) const
	Syntatic sugar for composing two rotations. More...

Rot3	inverse () const
	inverse of a rotation More...

Rot3	conjugate (const Rot3 &cRb) const

static Rot3	Identity ()
	identity rotation for group operation More...

Manifold
enum	CoordinatesMode { EXPMAP, CAYLEY }

Rot3	retractCayley (const Vector &omega) const
	Retraction from R^3 to Rot3 manifold using the Cayley transform. More...

Vector3	localCayley (const Rot3 &other) const
	Inverse of retractCayley. More...

Lie Group
using	LieAlgebra = Matrix3

Matrix3	AdjointMap () const

static Rot3	Expmap (const Vector3 &v, OptionalJacobian< 3, 3 > H={})

static Vector3	Logmap (const Rot3 &R, OptionalJacobian< 3, 3 > H={})

static Matrix3	ExpmapDerivative (const Vector3 &x)
	Derivative of Expmap. More...

static Matrix3	LogmapDerivative (const Vector3 &x)
	Derivative of Logmap. More...

static Matrix3	Hat (const Vector3 &xi)
	Hat maps from tangent vector to Lie algebra. More...

static Vector3	Vee (const Matrix3 &X)
	Vee maps from Lie algebra to tangent vector. More...

Advanced Interface
std::pair< Unit3, double >	axisAngle () const

gtsam::Quaternion	toQuaternion () const

Rot3	slerp (double t, const Rot3 &other) const
	Spherical Linear intERPolation between *this and other. More...

Vector9	vec (OptionalJacobian< 9, 3 > H={}) const
	Vee maps from Lie algebra to tangent vector. More...

GTSAM_EXPORT friend std::ostream &	operator<< (std::ostream &os, const Rot3 &p)
	Output stream operator. More...

Additional Inherited Members
Public Types inherited from gtsam::LieGroup< Rot3, 3 >
typedef OptionalJacobian< N, N >	ChartJacobian

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

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

Static Public Member Functions inherited from gtsam::LieGroup< Rot3, 3 >
static TangentVector	LocalCoordinates (const Rot3 &g)
	LocalCoordinates at origin: possible in Lie group because it has an identity. More...

static TangentVector	LocalCoordinates (const Rot3 &g, ChartJacobian H)
	LocalCoordinates at origin with optional derivative. More...

static Rot3	Retract (const TangentVector &v)
	Retract at origin: possible in Lie group because it has an identity. More...

static Rot3	Retract (const TangentVector &v, ChartJacobian H)
	Retract at origin with optional derivative. More...

Static Public Attributes inherited from gtsam::LieGroup< Rot3, 3 >
constexpr static auto	dimension

Detailed Description

Rot3 is a 3D rotation represented as a rotation matrix if the preprocessor symbol GTSAM_USE_QUATERNIONS is not defined, or as a quaternion if it is defined.

Definition at line 58 of file Rot3.h.

Member Typedef Documentation

◆ LieAlgebra

using gtsam::Rot3::LieAlgebra = Matrix3

Definition at line 374 of file Rot3.h.

Member Enumeration Documentation

◆ CoordinatesMode

enum gtsam::Rot3::CoordinatesMode

The method retract() is used to map from the tangent space back to the manifold. Its inverse, is localCoordinates(). For Lie groups, an obvious retraction is the exponential map, but this can be expensive to compute. The following Enum is used to indicate which method should be used. The default is determined by ROT3_DEFAULT_COORDINATES_MODE, which may be set at compile time, and itself defaults to Rot3::CAYLEY, or if GTSAM_USE_QUATERNIONS is defined, to Rot3::EXPMAP.

Enumerator
EXPMAP	Use the Lie group exponential map to retract.
CAYLEY	Retract and localCoordinates using the Cayley transform.

Definition at line 343 of file Rot3.h.

Constructor & Destructor Documentation

◆ Rot3() [1/8]

gtsam::Rot3::Rot3 ( )

default constructor, unit rotation

Definition at line 34 of file Rot3M.cpp.

◆ Rot3() [2/8]

gtsam::Rot3::Rot3	(	const Point3 &	col1,
		const Point3 &	col2,
		const Point3 &	col3
	)

Constructor from columns

Parameters

r1	X-axis of rotated frame
r2	Y-axis of rotated frame
r3	Z-axis of rotated frame

Definition at line 37 of file Rot3M.cpp.

◆ Rot3() [3/8]

gtsam::Rot3::Rot3	(	double	R11,
		double	R12,
		double	R13,
		double	R21,
		double	R22,
		double	R23,
		double	R31,
		double	R32,
		double	R33
	)

Construct from a rotation matrix, as doubles in row-major order !!!

Definition at line 44 of file Rot3M.cpp.

◆ Rot3() [4/8]

template<typename Derived >

gtsam::Rot3::Rot3 ( const Eigen::MatrixBase< Derived > & R )

inlineexplicit

Constructor from a rotation matrix Version for generic matrices. Need casting to Matrix3 in quaternion mode, since Eigen's quaternion doesn't allow assignment/construction from a generic matrix. See: http://stackoverflow.com/questions/27094132/cannot-understand-if-this-is-circular-dependency-or-clang#tab-top

Definition at line 101 of file Rot3.h.

◆ Rot3() [5/8]

gtsam::Rot3::Rot3 ( const Matrix3 & R )

inlineexplicit

Constructor from a rotation matrix Overload version for Matrix3 to avoid casting in quaternion mode.

Definition at line 112 of file Rot3.h.

◆ Rot3() [6/8]

gtsam::Rot3::Rot3 ( const SO3 & R )

inlineexplicit

Constructor from an SO3 instance

Definition at line 121 of file Rot3.h.

◆ Rot3() [7/8]

gtsam::Rot3::Rot3 ( const Quaternion & q )

Constructor from a quaternion. This can also be called using a plain Vector, due to implicit conversion from Vector to Quaternion

Parameters

q	The quaternion

Definition at line 52 of file Rot3M.cpp.

◆ Rot3() [8/8]

gtsam::Rot3::Rot3	(	double	w,
		double	x,
		double	y,
		double	z
	)

inline

Definition at line 129 of file Rot3.h.

◆ ~Rot3()

virtual gtsam::Rot3::~Rot3 ( )

inlinevirtual

Virtual destructor

Definition at line 140 of file Rot3.h.

Member Function Documentation

◆ AdjointMap()

Matrix3 gtsam::Rot3::AdjointMap ( ) const

inline

Calculate Adjoint map

Definition at line 402 of file Rot3.h.

◆ AlignPair()

Rot3 gtsam::Rot3::AlignPair	(	const Unit3 &	axis,
		const Unit3 &	a_p,
		const Unit3 &	b_p
	)

static

Determine a rotation to bring two vectors into alignment, using the rotation axis provided.

Definition at line 50 of file Rot3.cpp.

◆ AlignTwoPairs()

Rot3 gtsam::Rot3::AlignTwoPairs	(	const Unit3 &	a_p,
		const Unit3 &	b_p,
		const Unit3 &	a_q,
		const Unit3 &	b_q
	)

static

Calculate rotation from two pairs of homogeneous points using two successive rotations.

Definition at line 74 of file Rot3.cpp.

◆ axisAngle()

pair< Unit3, double > gtsam::Rot3::axisAngle ( ) const

Compute the Euler axis and angle (in radians) representation of this rotation. The angle is in the range [0, π]. If the angle is not in the range, the axis is flipped around accordingly so that the returned angle is within the specified range.

Returns: pair consisting of Unit3 axis and angle in radians

Definition at line 233 of file Rot3.cpp.

◆ AxisAngle() [1/2]

static Rot3 gtsam::Rot3::AxisAngle	(	const Point3 &	axis,
		double	angle
	)

inlinestatic

Convert from axis/angle representation

Parameters

axis	is the rotation axis, unit length
angle	rotation angle

Returns: incremental rotation

Definition at line 219 of file Rot3.h.

◆ AxisAngle() [2/2]

static Rot3 gtsam::Rot3::AxisAngle	(	const Unit3 &	axis,
		double	angle
	)

inlinestatic

Convert from axis/angle representation

Parameters

axis	is the rotation axis
angle	rotation angle

Returns: incremental rotation

Definition at line 235 of file Rot3.h.

◆ ClosestTo()

static Rot3 gtsam::Rot3::ClosestTo ( const Matrix3 & M )

inlinestatic

Static, named constructor that finds Rot3 element closest to M in Frobenius norm.

Uses Full SVD to compute the orthogonal matrix, thus is highly accurate and robust.

N. J. Higham. Matrix nearness problems and applications. In M. J. C. Gover and S. Barnett, editors, Applications of Matrix Theory, pages 1–27. Oxford University Press, 1989.

Definition at line 275 of file Rot3.h.

◆ conjugate()

Rot3 gtsam::Rot3::conjugate ( const Rot3 & cRb ) const

inline

Conjugation: given a rotation acting in frame B, compute rotation c1Rc2 acting in a frame C

Parameters

cRb	rotation from B frame to C frame

Returns: c1Rc2 = cRb * b1Rb2 * cRb'

Definition at line 325 of file Rot3.h.

◆ equals()

bool gtsam::Rot3::equals	(	const Rot3 &	p,
		double	tol = `1e-9`
	)		const

equals with an tolerance

Definition at line 100 of file Rot3.cpp.

◆ Expmap()

static Rot3 gtsam::Rot3::Expmap	(	const Vector3 &	v,
		OptionalJacobian< 3, 3 >	H = `{}`
	)

inlinestatic

Exponential map at identity - create a rotation from canonical coordinates $ [R_x,R_y,R_z] $ using Rodrigues' formula

Definition at line 380 of file Rot3.h.

◆ ExpmapDerivative()

Matrix3 gtsam::Rot3::ExpmapDerivative ( const Vector3 & x )

static

Derivative of Expmap.

Definition at line 239 of file Rot3.cpp.

◆ Hat()

static Matrix3 gtsam::Rot3::Hat ( const Vector3 & xi )

inlinestatic

Hat maps from tangent vector to Lie algebra.

Definition at line 413 of file Rot3.h.

◆ Identity()

static Rot3 gtsam::Rot3::Identity ( )

inlinestatic

identity rotation for group operation

Definition at line 304 of file Rot3.h.

◆ inverse()

Rot3 gtsam::Rot3::inverse ( ) const

inline

inverse of a rotation

Definition at line 312 of file Rot3.h.

◆ localCayley()

Vector3 gtsam::Rot3::localCayley ( const Rot3 & other ) const

inline

Inverse of retractCayley.

Definition at line 364 of file Rot3.h.

◆ Logmap()

Vector3 gtsam::Rot3::Logmap	(	const Rot3 &	R,
		OptionalJacobian< 3, 3 >	H = `{}`
	)

static

Log map at identity - returns the canonical coordinates $ [R_x,R_y,R_z] $ of this rotation

Definition at line 157 of file Rot3M.cpp.

◆ LogmapDerivative()

Matrix3 gtsam::Rot3::LogmapDerivative ( const Vector3 & x )

static

Derivative of Logmap.

Definition at line 244 of file Rot3.cpp.

◆ matrix()

Matrix3 gtsam::Rot3::matrix ( ) const

return 3*3 rotation matrix

Definition at line 218 of file Rot3M.cpp.

◆ normalized()

Rot3 gtsam::Rot3::normalized ( ) const

Normalize rotation so that its determinant is 1. This means either re-orthogonalizing the Matrix representation or normalizing the quaternion representation.

This method is akin to ClosestTo but uses a computationally cheaper algorithm.

Ref: https://drive.google.com/file/d/0B9rLLz1XQKmaZTlQdV81QjNoZTA/view

Implementation from here: https://stackoverflow.com/a/23082112/1236990

Essentially, this computes the orthogonalization error, distributes the error to the x and y rows, and then performs a Taylor expansion to orthogonalize.

Definition at line 111 of file Rot3M.cpp.

◆ operator*() [1/3]

Point3 gtsam::Rot3::operator* ( const Point3 & p ) const

rotate point from rotated coordinate frame to world = R*p

Definition at line 105 of file Rot3.cpp.

◆ operator*() [2/3]

Rot3 gtsam::Rot3::operator* ( const Rot3 & R2 ) const

Syntatic sugar for composing two rotations.

Definition at line 138 of file Rot3M.cpp.

◆ operator*() [3/3]

Unit3 gtsam::Rot3::operator* ( const Unit3 & p ) const

rotate 3D direction from rotated coordinate frame to world frame

Definition at line 130 of file Rot3.cpp.

◆ Pitch()

static Rot3 gtsam::Rot3::Pitch ( double t )

inlinestatic

Positive pitch is up (increasing aircraft altitude).See ypr.

Definition at line 181 of file Rot3.h.

◆ pitch()

double gtsam::Rot3::pitch ( OptionalJacobian< 1, 3 > H = {} ) const

Accessor to get to component of angle representations NOTE: these are not efficient to get to multiple separate parts, you should instead use xyz() or ypr() TODO: make this more efficient

Definition at line 209 of file Rot3.cpp.

◆ print()

void gtsam::Rot3::print ( const std::string & s = "" ) const

print

Definition at line 34 of file Rot3.cpp.

◆ Quaternion()

static Rot3 gtsam::Rot3::Quaternion	(	double	w,
		double	x,
		double	y,
		double	z
	)

inlinestatic

Create from Quaternion coefficients

Definition at line 208 of file Rot3.h.

◆ r1()

Point3 gtsam::Rot3::r1 ( ) const

first column

Definition at line 223 of file Rot3M.cpp.

◆ r2()

Point3 gtsam::Rot3::r2 ( ) const

second column

Definition at line 226 of file Rot3M.cpp.

◆ r3()

Point3 gtsam::Rot3::r3 ( ) const

third column

Definition at line 229 of file Rot3M.cpp.

◆ Random()

Rot3 gtsam::Rot3::Random ( std::mt19937 & rng )

static

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

Definition at line 40 of file Rot3.cpp.

◆ retractCayley()

Rot3 gtsam::Rot3::retractCayley ( const Vector & omega ) const

inline

Retraction from R^3 to Rot3 manifold using the Cayley transform.

Definition at line 359 of file Rot3.h.

◆ Rodrigues() [1/2]

static Rot3 gtsam::Rot3::Rodrigues ( const Vector3 & w )

inlinestatic

Rodrigues' formula to compute an incremental rotation

Parameters

w	a vector of incremental roll,pitch,yaw

Returns: incremental rotation

Definition at line 244 of file Rot3.h.

◆ Rodrigues() [2/2]

static Rot3 gtsam::Rot3::Rodrigues	(	double	wx,
		double	wy,
		double	wz
	)

inlinestatic

Rodrigues' formula to compute an incremental rotation

Parameters

wx	Incremental roll (about X)
wy	Incremental pitch (about Y)
wz	Incremental yaw (about Z)

Returns: incremental rotation

Definition at line 255 of file Rot3.h.

◆ Roll()

static Rot3 gtsam::Rot3::Roll ( double t )

inlinestatic

Definition at line 184 of file Rot3.h.

◆ roll()

double gtsam::Rot3::roll ( OptionalJacobian< 1, 3 > H = {} ) const

Accessor to get to component of angle representations NOTE: these are not efficient to get to multiple separate parts, you should instead use xyz() or ypr() TODO: make this more efficient

Definition at line 197 of file Rot3.cpp.

◆ rotate() [1/2]

Point3 gtsam::Rot3::rotate	(	const Point3 &	p,
		OptionalJacobian< 3, 3 >	H1 = `{}`,
		OptionalJacobian< 3, 3 >	H2 = `{}`
	)		const

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

Definition at line 148 of file Rot3M.cpp.

◆ rotate() [2/2]

Unit3 gtsam::Rot3::rotate	(	const Unit3 &	p,
		OptionalJacobian< 2, 3 >	HR = `{}`,
		OptionalJacobian< 2, 2 >	Hp = `{}`
	)		const

rotate 3D direction from rotated coordinate frame to world frame

Definition at line 110 of file Rot3.cpp.

◆ rpy()

Vector3 gtsam::Rot3::rpy ( OptionalJacobian< 3, 3 > H = {} ) const

Use RQ to calculate roll-pitch-yaw angle representation

Returns: a vector containing rpy s.t. R = Rot3::Ypr(y,p,r)

Definition at line 194 of file Rot3.cpp.

◆ Rx()

Rot3 gtsam::Rot3::Rx ( double t )

static

Rotation around X axis as in http://en.wikipedia.org/wiki/Rotation_matrix, counterclockwise when looking from unchanging axis.

Definition at line 56 of file Rot3M.cpp.

◆ Ry()

Rot3 gtsam::Rot3::Ry ( double t )

static

Rotation around Y axis as in http://en.wikipedia.org/wiki/Rotation_matrix, counterclockwise when looking from unchanging axis.

Definition at line 65 of file Rot3M.cpp.

◆ Rz()

Rot3 gtsam::Rot3::Rz ( double t )

static

Rotation around Z axis as in http://en.wikipedia.org/wiki/Rotation_matrix, counterclockwise when looking from unchanging axis.

Definition at line 74 of file Rot3M.cpp.

◆ RzRyRx() [1/2]

static Rot3 gtsam::Rot3::RzRyRx	(	const Vector &	xyz,
		OptionalJacobian< 3, 3 >	H = `{}`
	)

inlinestatic

Rotations around Z, Y, then X axes as in http://en.wikipedia.org/wiki/Rotation_matrix, counterclockwise when looking from unchanging axis.

Definition at line 160 of file Rot3.h.

◆ RzRyRx() [2/2]

Rot3 gtsam::Rot3::RzRyRx	(	double	x,
		double	y,
		double	z,
		OptionalJacobian< 3, 1 >	Hx = `{}`,
		OptionalJacobian< 3, 1 >	Hy = `{}`,
		OptionalJacobian< 3, 1 >	Hz = `{}`
	)

static

Rotations around Z, Y, then X axes as in http://en.wikipedia.org/wiki/Rotation_matrix, counterclockwise when looking from unchanging axis.

Definition at line 84 of file Rot3M.cpp.

◆ slerp()

Rot3 gtsam::Rot3::slerp	(	double	t,
		const Rot3 &	other
	)		const

Spherical Linear intERPolation between *this and other.

Parameters

t	a value between 0 and 1
other	final point of interpolation geodesic on manifold

Definition at line 315 of file Rot3.cpp.

◆ toQuaternion()

gtsam::Quaternion gtsam::Rot3::toQuaternion ( ) const

Compute the quaternion representation of this rotation.

Returns: The quaternion

Definition at line 232 of file Rot3M.cpp.

◆ transpose()

Matrix3 gtsam::Rot3::transpose ( ) const

Return 3*3 transpose (inverse) rotation matrix

Definition at line 143 of file Rot3M.cpp.

◆ unrotate() [1/2]

Point3 gtsam::Rot3::unrotate	(	const Point3 &	p,
		OptionalJacobian< 3, 3 >	H1 = `{}`,
		OptionalJacobian< 3, 3 >	H2 = `{}`
	)		const

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

Definition at line 136 of file Rot3.cpp.

◆ unrotate() [2/2]

Unit3 gtsam::Rot3::unrotate	(	const Unit3 &	p,
		OptionalJacobian< 2, 3 >	HR = `{}`,
		OptionalJacobian< 2, 2 >	Hp = `{}`
	)		const

unrotate 3D direction from world frame to rotated coordinate frame

Definition at line 120 of file Rot3.cpp.

◆ vec()

Vector9 gtsam::Rot3::vec ( OptionalJacobian< 9, 3 > H = {} ) const

inline

Vee maps from Lie algebra to tangent vector.

Definition at line 535 of file Rot3.h.

◆ Vee()

static Vector3 gtsam::Rot3::Vee ( const Matrix3 & X )

inlinestatic

Vee maps from Lie algebra to tangent vector.

Definition at line 416 of file Rot3.h.

◆ xyz()

Vector3 gtsam::Rot3::xyz ( OptionalJacobian< 3, 3 > H = {} ) const

Use RQ to calculate xyz angle representation

Returns: a vector containing x,y,z s.t. R = Rot3::RzRyRx(x,y,z)

Definition at line 163 of file Rot3.cpp.

◆ Yaw()

static Rot3 gtsam::Rot3::Yaw ( double t )

inlinestatic

Positive yaw is to right (as in aircraft heading). See ypr.

Definition at line 178 of file Rot3.h.

◆ yaw()

double gtsam::Rot3::yaw ( OptionalJacobian< 1, 3 > H = {} ) const

Accessor to get to component of angle representations NOTE: these are not efficient to get to multiple separate parts, you should instead use xyz() or ypr() TODO: make this more efficient

Definition at line 221 of file Rot3.cpp.

◆ Ypr()

static Rot3 gtsam::Rot3::Ypr	(	double	y,
		double	p,
		double	r,
		OptionalJacobian< 3, 1 >	Hy = `{}`,
		OptionalJacobian< 3, 1 >	Hp = `{}`,
		OptionalJacobian< 3, 1 >	Hr = `{}`
	)

inlinestatic

Returns rotation nRb from body to nav frame. For vehicle coordinate frame X forward, Y right, Z down: Positive yaw is to right (as in aircraft heading). Positive pitch is up (increasing aircraft altitude). Positive roll is to right (increasing yaw in aircraft). Tait-Bryan system from Spatial Reference Model (SRM) (x,y,z) = (roll,pitch,yaw) as described in http://www.sedris.org/wg8home/Documents/WG80462.pdf.

For vehicle coordinate frame X forward, Y left, Z up: Positive yaw is to left (as in aircraft heading). Positive pitch is down (decreasing aircraft altitude). Positive roll is to right (decreasing yaw in aircraft).

Definition at line 200 of file Rot3.h.

◆ ypr()

Vector3 gtsam::Rot3::ypr ( OptionalJacobian< 3, 3 > H = {} ) const

Use RQ to calculate yaw-pitch-roll angle representation

Returns: a vector containing ypr s.t. R = Rot3::Ypr(y,p,r)

Definition at line 186 of file Rot3.cpp.

Friends And Related Function Documentation

◆ operator<<

GTSAM_EXPORT friend std::ostream& operator<<	(	std::ostream &	os,
		const Rot3 &	p
	)

friend

Output stream operator.

Member Data Documentation

◆ rot_

SO3 gtsam::Rot3::rot_

private

Definition at line 65 of file Rot3.h.

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

Classes

Public Member Functions

Private Attributes

Constructors and named constructors

Group

Manifold

Lie Group

Advanced Interface

Additional Inherited Members

Detailed Description

Member Typedef Documentation

◆ LieAlgebra

Member Enumeration Documentation

◆ CoordinatesMode

Constructor & Destructor Documentation

◆ Rot3() [1/8]

◆ Rot3() [2/8]

◆ Rot3() [3/8]

◆ Rot3() [4/8]

◆ Rot3() [5/8]

◆ Rot3() [6/8]

◆ Rot3() [7/8]

◆ Rot3() [8/8]

◆ ~Rot3()

Member Function Documentation

◆ AdjointMap()

◆ AlignPair()

◆ AlignTwoPairs()

◆ axisAngle()

◆ AxisAngle() [1/2]

◆ AxisAngle() [2/2]

◆ ClosestTo()

◆ conjugate()

◆ equals()

◆ Expmap()

◆ ExpmapDerivative()

◆ Hat()

◆ Identity()

◆ inverse()

◆ localCayley()

◆ Logmap()

◆ LogmapDerivative()

◆ matrix()

◆ normalized()

◆ operator*() [1/3]

◆ operator*() [2/3]

◆ operator*() [3/3]

◆ Pitch()

◆ pitch()

◆ print()

◆ Quaternion()

◆ r1()

◆ r2()

◆ r3()

◆ Random()

◆ retractCayley()

◆ Rodrigues() [1/2]

◆ Rodrigues() [2/2]

◆ Roll()

◆ roll()

◆ rotate() [1/2]

◆ rotate() [2/2]

◆ rpy()

◆ Rx()

◆ Ry()

◆ Rz()

◆ RzRyRx() [1/2]

◆ RzRyRx() [2/2]

◆ slerp()

◆ toQuaternion()

◆ transpose()

◆ unrotate() [1/2]

◆ unrotate() [2/2]

◆ vec()

◆ Vee()

◆ xyz()

◆ Yaw()

◆ yaw()

◆ Ypr()

◆ ypr()