Represents a 3D point on a unit sphere. More...

#include <Unit3.h>

Static Public Attributes
constexpr static auto	dimension = 2

Private Attributes
std::optional< Matrix32 >	B_
	Cached basis. More...

std::optional< Matrix62 >	H_B_
	Cached basis derivative. More...

Vector3	p_
	The location of the point on the unit sphere. More...

Constructors
	Unit3 ()
	Default constructor. More...

	Unit3 (const Vector3 &p)
	Construct from point. More...

	Unit3 (double x, double y, double z)
	Construct from x,y,z. More...

	Unit3 (const Point2 &p, double f)

	Unit3 (const Unit3 &u)
	Copy constructor. More...

Unit3 &	operator= (const Unit3 &u)
	Copy assignment. More...

static Unit3	FromPoint3 (const Point3 &point, OptionalJacobian< 2, 3 > H={})
	Named constructor from Point3 with optional Jacobian. More...

static Unit3	Random (std::mt19937 &rng)

Testable
void	print (const std::string &s=std::string()) const
	The print fuction. More...

bool	equals (const Unit3 &s, double tol=1e-9) const
	The equals function with tolerance. More...

GTSAM_EXPORT friend std::ostream &	operator<< (std::ostream &os, const Unit3 &pair)

Other functionality
const Matrix32 &	basis (OptionalJacobian< 6, 2 > H={}) const

Matrix3	skew () const
	Return skew-symmetric associated with 3D point on unit sphere. More...

Point3	point3 (OptionalJacobian< 3, 2 > H={}) const
	Return unit-norm Point3. More...

Vector3	unitVector (OptionalJacobian< 3, 2 > H={}) const
	Return unit-norm Vector. More...

double	dot (const Unit3 &q, OptionalJacobian< 1, 2 > H1={}, OptionalJacobian< 1, 2 > H2={}) const
	Return dot product with q. More...

Vector2	error (const Unit3 &q, OptionalJacobian< 2, 2 > H_q={}) const

Vector2	errorVector (const Unit3 &q, OptionalJacobian< 2, 2 > H_p={}, OptionalJacobian< 2, 2 > H_q={}) const

double	distance (const Unit3 &q, OptionalJacobian< 1, 2 > H={}) const
	Distance between two directions. More...

Unit3	cross (const Unit3 &q) const
	Cross-product between two Unit3s. More...

Point3	cross (const Point3 &q) const
	Cross-product w Point3. More...

Point3	operator* (double s, const Unit3 &d)
	Return scaled direction as Point3. More...

Manifold
enum	CoordinatesMode { EXPMAP, RENORM }

size_t	dim () const
	Dimensionality of tangent space = 2 DOF. More...

Unit3	retract (const Vector2 &v, OptionalJacobian< 2, 2 > H={}) const
	The retract function. More...

Vector2	localCoordinates (const Unit3 &s) const
	The local coordinates function. More...

static size_t	Dim ()
	Dimensionality of tangent space = 2 DOF. More...

Detailed Description

Represents a 3D point on a unit sphere.

Definition at line 42 of file Unit3.h.

Member Enumeration Documentation

◆ CoordinatesMode

enum gtsam::Unit3::CoordinatesMode

Enumerator
EXPMAP	Use the exponential map to retract.
RENORM	Retract with vector addition and renormalize.

Definition at line 184 of file Unit3.h.

Constructor & Destructor Documentation

◆ Unit3() [1/5]

gtsam::Unit3::Unit3 ( )

inline

Default constructor.

Definition at line 62 of file Unit3.h.

◆ Unit3() [2/5]

gtsam::Unit3::Unit3 ( const Vector3 & p )

explicit

Construct from point.

Definition at line 36 of file Unit3.cpp.

◆ Unit3() [3/5]

gtsam::Unit3::Unit3	(	double	x,
		double	y,
		double	z
	)

Construct from x,y,z.

Definition at line 38 of file Unit3.cpp.

◆ Unit3() [4/5]

gtsam::Unit3::Unit3	(	const Point2 &	p,
		double	f
	)

explicit

Construct from 2D point in plane at focal length f Unit3(p,1) can be viewed as normalized homogeneous coordinates of 2D point

Definition at line 40 of file Unit3.cpp.

◆ Unit3() [5/5]

gtsam::Unit3::Unit3 ( const Unit3 & u )

inline

Copy constructor.

Definition at line 77 of file Unit3.h.

Member Function Documentation

◆ basis()

const Matrix32 & gtsam::Unit3::basis ( OptionalJacobian< 6, 2 > H = {} ) const

Returns the local coordinate frame to tangent plane It is a 3*2 matrix [b1 b2] composed of two orthogonal directions tangent to the sphere at the current direction. Provides derivatives of the basis with the two basis vectors stacked up as a 6x1.

Definition at line 84 of file Unit3.cpp.

◆ cross() [1/2]

Point3 gtsam::Unit3::cross ( const Point3 & q ) const

inline

Cross-product w Point3.

Definition at line 165 of file Unit3.h.

◆ cross() [2/2]

Unit3 gtsam::Unit3::cross ( const Unit3 & q ) const

inline

Cross-product between two Unit3s.

Definition at line 160 of file Unit3.h.

◆ Dim()

static size_t gtsam::Unit3::Dim ( )

inlinestatic

Dimensionality of tangent space = 2 DOF.

Definition at line 175 of file Unit3.h.

◆ dim()

size_t gtsam::Unit3::dim ( ) const

inline

Dimensionality of tangent space = 2 DOF.

Definition at line 180 of file Unit3.h.

◆ distance()

double gtsam::Unit3::distance	(	const Unit3 &	q,
		OptionalJacobian< 1, 2 >	H = `{}`
	)		const

Distance between two directions.

Definition at line 245 of file Unit3.cpp.

◆ dot()

double gtsam::Unit3::dot	(	const Unit3 &	q,
		OptionalJacobian< 1, 2 >	H1 = `{}`,
		OptionalJacobian< 1, 2 >	H2 = `{}`
	)		const

Return dot product with q.

Definition at line 174 of file Unit3.cpp.

◆ equals()

bool gtsam::Unit3::equals	(	const Unit3 &	s,
		double	tol = `1e-9`
	)		const

inline

The equals function with tolerance.

Definition at line 113 of file Unit3.h.

◆ error()

Vector2 gtsam::Unit3::error	(	const Unit3 &	q,
		OptionalJacobian< 2, 2 >	H_q = `{}`
	)		const

Signed, vector-valued error between two directions

Deprecated:: , errorVector has the proper derivatives, this confusingly has only the second.

Definition at line 199 of file Unit3.cpp.

◆ errorVector()

Vector2 gtsam::Unit3::errorVector	(	const Unit3 &	q,
		OptionalJacobian< 2, 2 >	H_p = `{}`,
		OptionalJacobian< 2, 2 >	H_q = `{}`
	)		const

Signed, vector-valued error between two directions NOTE(hayk): This method has zero derivatives if this (p) and q are orthogonal.

Definition at line 209 of file Unit3.cpp.

◆ FromPoint3()

Unit3 gtsam::Unit3::FromPoint3	(	const Point3 &	point,
		OptionalJacobian< 2, 3 >	H = `{}`
	)

static

Named constructor from Point3 with optional Jacobian.

Definition at line 44 of file Unit3.cpp.

◆ localCoordinates()

Vector2 gtsam::Unit3::localCoordinates ( const Unit3 & s ) const

The local coordinates function.

Definition at line 285 of file Unit3.cpp.

◆ operator=()

Unit3& gtsam::Unit3::operator= ( const Unit3 & u )

inline

Copy assignment.

Definition at line 82 of file Unit3.h.

◆ point3()

Point3 gtsam::Unit3::point3 ( OptionalJacobian< 3, 2 > H = {} ) const

Return unit-norm Point3.

Definition at line 144 of file Unit3.cpp.

◆ print()

void gtsam::Unit3::print ( const std::string & s = std::string() ) const

The print fuction.

Definition at line 164 of file Unit3.cpp.

◆ Random()

Unit3 gtsam::Unit3::Random ( std::mt19937 & rng )

static

Random direction, using boost::uniform_on_sphere Example: std::mt19937 engine(42); Unit3 unit = Unit3::Random(engine);

Definition at line 55 of file Unit3.cpp.

◆ retract()

Unit3 gtsam::Unit3::retract	(	const Vector2 &	v,
		OptionalJacobian< 2, 2 >	H = `{}`
	)		const

The retract function.

Definition at line 255 of file Unit3.cpp.

◆ skew()

Matrix3 gtsam::Unit3::skew ( ) const

Return skew-symmetric associated with 3D point on unit sphere.

Definition at line 169 of file Unit3.cpp.

◆ unitVector()

Vector3 gtsam::Unit3::unitVector ( OptionalJacobian< 3, 2 > H = {} ) const

Return unit-norm Vector.

Definition at line 151 of file Unit3.cpp.

Friends And Related Function Documentation

◆ operator*

Point3 operator*	(	double	s,
		const Unit3 &	d
	)

friend

Return scaled direction as Point3.

Definition at line 139 of file Unit3.h.

◆ operator<<

GTSAM_EXPORT friend std::ostream& operator<<	(	std::ostream &	os,
		const Unit3 &	pair
	)

friend

Definition at line 158 of file Unit3.cpp.

Member Data Documentation

◆ B_

std::optional<Matrix32> gtsam::Unit3::B_

mutableprivate

Cached basis.

Definition at line 47 of file Unit3.h.

◆ dimension

constexpr static auto gtsam::Unit3::dimension = 2

inlinestaticconstexpr

Definition at line 56 of file Unit3.h.

◆ H_B_

std::optional<Matrix62> gtsam::Unit3::H_B_

mutableprivate

Cached basis derivative.

Definition at line 48 of file Unit3.h.

◆ p_

Vector3 gtsam::Unit3::p_

private

The location of the point on the unit sphere.

Definition at line 46 of file Unit3.h.

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

Static Public Attributes

Private Attributes

Constructors

Testable

Other functionality

Manifold

Detailed Description

Member Enumeration Documentation

◆ CoordinatesMode

Constructor & Destructor Documentation

◆ Unit3() [1/5]

◆ Unit3() [2/5]

◆ Unit3() [3/5]

◆ Unit3() [4/5]

◆ Unit3() [5/5]

Member Function Documentation

◆ basis()

◆ cross() [1/2]

◆ cross() [2/2]

◆ Dim()

◆ dim()

◆ distance()

◆ dot()

◆ equals()

◆ error()

◆ errorVector()

◆ FromPoint3()

◆ localCoordinates()

◆ operator=()

◆ point3()

◆ print()

◆ Random()

◆ retract()

◆ skew()

◆ unitVector()

Friends And Related Function Documentation

◆ operator*

◆ operator<<

Member Data Documentation

◆ B_

◆ dimension

◆ H_B_

◆ p_