gtsam::Unit3 Class Reference

Detailed Description

Represents a 3D point on a unit sphere.

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.
Vector2	localCoordinates (const Unit3 &s, OptionalJacobian< 2, 2 > H1, OptionalJacobian< 2, 2 > H2={}) const
	Local coordinates with derivatives in the tangent bases of this and s.
static size_t	Dim ()
	Dimensionality of tangent space = 2 DOF.

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)
	Construct from 2D point in plane at focal length f Unit3(p,1) can be viewed as normalized homogeneous coordinates of 2D point.
	Unit3 (const Unit3 &u)
	Copy constructor: copies essential data and discards caches.
Unit3 &	operator= (const Unit3 &u)
	Copy assignment: copies essential data and invalidates local caches.
static Unit3	FromPoint3 (const Point3 &point, OptionalJacobian< 2, 3 > H={})
	Named constructor from Point3 with optional Jacobian.
static Unit3	Random (std::mt19937 &rng)
	Random direction, using boost::uniform_on_sphere Example: std::mt19937 engine(42); Unit3 unit = Unit3::Random(engine);.

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

Other functionality
const Matrix32 &	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.
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.
Vector3	scaled (double magnitude, OptionalJacobian< 3, 2 > H_this={}, OptionalJacobian< 3, 1 > H_magnitude={}) const
	Return this direction scaled by a magnitude, i.e.
double	dot (const Unit3 &q, OptionalJacobian< 1, 2 > H1={}, OptionalJacobian< 1, 2 > H2={}) const
	Return dot product with q.
Vector2	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.
double	distance (const Unit3 &q, OptionalJacobian< 1, 2 > H={}) const
	Distance between two directions.
Unit3	cross (const Unit3 &q, OptionalJacobian< 2, 2 > H_p={}, OptionalJacobian< 2, 2 > H_q={}) const
	Cross-product between two Unit3s.
Point3	cross (const Point3 &q, OptionalJacobian< 3, 2 > H_p={}, OptionalJacobian< 3, 3 > H_q={}) const
	Cross-product w Point3.
Point3	operator* (double s, const Unit3 &d)
	Return scaled direction as Point3 (no Jacobians; see scaled()).

Static Public Attributes
static constexpr auto	dimension = 2

Member Enumeration Documentation

CoordinatesMode

enum gtsam::Unit3::CoordinatesMode

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

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.

localCoordinates()

Vector2 gtsam::Unit3::localCoordinates	(	const Unit3 &	s,
		OptionalJacobian< 2, 2 >	H1,
		OptionalJacobian< 2, 2 >	H2 = {} ) const

Local coordinates with derivatives in the tangent bases of this and s.

Derivatives are undefined at the antipode; requesting them there throws std::domain_error. The value-only overload retains its antipodal convention.

scaled()

Vector3 gtsam::Unit3::scaled	(	double	magnitude,
		OptionalJacobian< 3, 2 >	H_this = {},
		OptionalJacobian< 3, 1 >	H_magnitude = {} ) const

Return this direction scaled by a magnitude, i.e.

magnitude * unitVector(). Useful to reconstruct a physical vector from a direction and a known (or separately estimated) magnitude, e.g. a gravity or magnetic field vector.

Parameters

magnitude	scale applied to the unit vector
H_this	optional 3x2 Jacobian wrt this direction
H_magnitude	optional 3x1 Jacobian wrt the magnitude

See also

operator*(double, const Unit3&), which returns the same value without Jacobians

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

• /tmp/gtsam-4.3.0-doxygen.rsXPUS/source/gtsam/geometry/Unit3.h
• /tmp/gtsam-4.3.0-doxygen.rsXPUS/source/gtsam/geometry/Unit3.cpp