gtsam::Unit3 Class Reference

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

#include <Unit3.h>

Public Types
enum	{ dimension = 2 }

Constructors
	Unit3 ()
	Default constructor.
	Unit3 (const Vector3 &p)
	Construct from point.
	Unit3 (double x, double y, double z)
	Construct from x,y,z.
	Unit3 (const Point2 &p, double f)
	Unit3 (const Unit3 &u)
	Copy constructor.
Unit3 &	operator= (const Unit3 &u)
	Copy assignment.
static Unit3	FromPoint3 (const Point3 &point, OptionalJacobian< 2, 3 > H={})
	Named constructor from Point3 with optional Jacobian.
static Unit3	Random (std::mt19937 &rng)

Testable
void	print (const std::string &s=std::string()) const
	The print fuction.
bool	equals (const Unit3 &s, double tol=1e-9) const
	The equals function with tolerance.
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.
Point3	point3 (OptionalJacobian< 3, 2 > H={}) const
	Return unit-norm Point3.
Vector3	unitVector (OptionalJacobian< 3, 2 > H={}) const
	Return unit-norm Vector.
double	dot (const Unit3 &q, OptionalJacobian< 1, 2 > H1={}, OptionalJacobian< 1, 2 > H2={}) const
	Return dot product with q.
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.
Unit3	cross (const Unit3 &q) const
	Cross-product between two Unit3s.
Point3	cross (const Point3 &q) const
	Cross-product w Point3.
Point3	operator* (double s, const Unit3 &d)
	Return scaled direction as Point3.

Manifold
enum	CoordinatesMode { EXPMAP, RENORM }
size_t	dim () const
	Dimensionality of tangent space = 2 DOF.
Unit3	retract (const Vector2 &v, OptionalJacobian< 2, 2 > H={}) const
	The retract function.
Vector2	localCoordinates (const Unit3 &s) const
	The local coordinates function.
static size_t	Dim ()
	Dimensionality of tangent space = 2 DOF.

Detailed Description

Represents a 3D point on a unit sphere.

Member Enumeration Documentation

CoordinatesMode

enum gtsam::Unit3::CoordinatesMode

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

Constructor & Destructor Documentation

Unit3()

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

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.

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.

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.

Random()

static 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);

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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/Unit3.h