#include <FramePrimitives.hpp>

Public Member Functions
	CoordinateFrame ()
	Default constructor - creates ECEF identity frame.
	CoordinateFrame (const Vec3< Scalar > &x, const Vec3< Scalar > &y, const Vec3< Scalar > &z, const Vec3< Scalar > &o)
	Construct from basis vectors and origin.
Vec3< Scalar >	from_ecef (const Vec3< Scalar > &v) const
Vec3< Scalar >	to_ecef (const Vec3< Scalar > &v) const
Vec3< Scalar >	position_from_ecef (const Vec3< Scalar > &pos_ecef) const
Vec3< Scalar >	position_to_ecef (const Vec3< Scalar > &pos_local) const
Mat3< Scalar >	dcm () const
Mat3< Scalar >	dcm_inverse () const
janus::Quaternion< Scalar >	quaternion () const
bool	is_valid (double tol=1e-9) const

Static Public Member Functions
static CoordinateFrame	from_quaternion (const janus::Quaternion< Scalar > &q, const Vec3< Scalar > &o=Vec3< Scalar >::Zero())
static CoordinateFrame	ecef ()
static CoordinateFrame	eci (Scalar gmst)
static CoordinateFrame	ned (Scalar lon, Scalar lat)
static CoordinateFrame	enu (Scalar lon, Scalar lat)

Public Attributes
Vec3< Scalar >	x_axis
	Unit X basis vector in ECEF.
Vec3< Scalar >	y_axis
	Unit Y basis vector in ECEF.
Vec3< Scalar >	z_axis
	Unit Z basis vector in ECEF.
Vec3< Scalar >	origin
	Frame origin in ECEF [m].

Detailed Description

template<typename Scalar>
struct vulcan::CoordinateFrame< Scalar >

Coordinate frame defined by orthonormal basis vectors expressed in ECEF

This is the central abstraction for coordinate transformations in Vulcan. All frames are represented by three unit basis vectors (X, Y, Z axes) expressed in the ECEF (Earth-Centered Earth-Fixed) frame, plus an origin point. Transformations between frames are performed via dot products (projections) through ECEF as the hub.

This representation follows the TAOS specification's "Unit Vector Projection Method" which provides O(2N) transformations instead of O(N²) direct matrix pairs.

Example:

// Create an ECI frame at some time
double gmst = rotation.gmst(t);
auto eci = CoordinateFrame<double>::eci(gmst);
 
// Transform a vector from ECEF to ECI
Vec3<double> v_ecef = {1000.0, 2000.0, 3000.0};
Vec3<double> v_eci = eci.from_ecef(v_ecef);

Template Parameters

Scalar Scalar type (double for numeric, janus::SymbolicScalar for symbolic)

Constructor & Destructor Documentation

◆ CoordinateFrame() [1/2]

template<typename Scalar>

vulcan::CoordinateFrame< Scalar >::CoordinateFrame ( )

inline

Default constructor - creates ECEF identity frame.

◆ CoordinateFrame() [2/2]

template<typename Scalar>

vulcan::CoordinateFrame< Scalar >::CoordinateFrame	(	const Vec3< Scalar > &	x,
		const Vec3< Scalar > &	y,
		const Vec3< Scalar > &	z,
		const Vec3< Scalar > &	o )

inline

Construct from basis vectors and origin.

Member Function Documentation

◆ dcm()

template<typename Scalar>

Mat3< Scalar > vulcan::CoordinateFrame< Scalar >::dcm ( ) const

inlinenodiscard

Compose DCM as column vectors [x_axis | y_axis | z_axis]

The DCM transforms vectors from this frame to ECEF: v_ecef = dcm() * v_local

Returns: 3x3 Direction Cosine Matrix

◆ dcm_inverse()

template<typename Scalar>

Mat3< Scalar > vulcan::CoordinateFrame< Scalar >::dcm_inverse ( ) const

inlinenodiscard

Compose inverse DCM (ECEF to local)

The inverse DCM transforms vectors from ECEF to this frame: v_local = dcm_inverse() * v_ecef

For orthonormal frames, this is simply the transpose.

Returns: 3x3 inverse (transpose) DCM

◆ ecef()

template<typename Scalar>

CoordinateFrame vulcan::CoordinateFrame< Scalar >::ecef ( )

inlinestatic

Create ECEF identity frame

X: Points to prime meridian at equator Y: Points to 90°E at equator Z: Points to North Pole

Returns: ECEF frame

◆ eci()

template<typename Scalar>

CoordinateFrame vulcan::CoordinateFrame< Scalar >::eci ( Scalar gmst )

inlinestatic

Create ECI (Earth-Centered Inertial) frame at given GMST

The ECI frame is rotated from ECEF about the Z-axis by the Greenwich Mean Sidereal Time (or Earth Rotation Angle).

At GMST=0, ECI aligns with ECEF (X points to vernal equinox, which coincides with Greenwich at epoch).

Parameters

gmst	Greenwich Mean Sidereal Time [rad]

Returns: ECI frame expressed in ECEF

◆ enu()

template<typename Scalar>

CoordinateFrame vulcan::CoordinateFrame< Scalar >::enu	(	Scalar	lon,
		Scalar	lat )

inlinestatic

Create ENU (East-North-Up) frame at given geodetic position

X: Points East (tangent to parallel) Y: Points North (tangent to meridian) Z: Points Up (ellipsoid normal)

Common in surveying and some navigation applications.

Parameters

lon	Longitude [rad]
lat	Geodetic latitude [rad]

Returns: ENU frame expressed in ECEF

◆ from_ecef()

template<typename Scalar>

Vec3< Scalar > vulcan::CoordinateFrame< Scalar >::from_ecef ( const Vec3< Scalar > & v ) const

inlinenodiscard

Project vector FROM ECEF TO this frame (rotation only)

Uses dot product projections onto basis vectors. This is equivalent to multiplying by the DCM transpose.

Parameters

v	Vector expressed in ECEF

Returns: Vector expressed in this frame

◆ from_quaternion()

template<typename Scalar>

CoordinateFrame vulcan::CoordinateFrame< Scalar >::from_quaternion	(	const janus::Quaternion< Scalar > &	q,
		const Vec3< Scalar > &	o = Vec3<Scalar>::Zero() )

inlinestatic

Create frame from quaternion and origin

The quaternion should represent the rotation from ECEF to the target frame (i.e., how to transform ECEF vectors to local coords).

Parameters

q	Quaternion (ECEF to local rotation)
o	Origin in ECEF [m]

Returns: CoordinateFrame

◆ is_valid()

template<typename Scalar>

bool vulcan::CoordinateFrame< Scalar >::is_valid ( double tol = 1e-9 ) const

inlinenodiscard

Check if frame is orthonormal within tolerance

Verifies:

All basis vectors are unit length
All basis vectors are mutually orthogonal

Parameters

tol	Tolerance for numerical checks

Returns: True if frame is valid

◆ ned()

template<typename Scalar>

CoordinateFrame vulcan::CoordinateFrame< Scalar >::ned	(	Scalar	lon,
		Scalar	lat )

inlinestatic

Create NED (North-East-Down) frame at given geodetic position

X: Points North (tangent to meridian) Y: Points East (tangent to parallel) Z: Points Down (opposite to ellipsoid normal)

This is the standard aerospace local horizon frame.

Parameters

lon	Longitude [rad]
lat	Geodetic latitude [rad]

Returns: NED frame expressed in ECEF

◆ position_from_ecef()

template<typename Scalar>

Vec3< Scalar > vulcan::CoordinateFrame< Scalar >::position_from_ecef ( const Vec3< Scalar > & pos_ecef ) const

inlinenodiscard

Transform position FROM ECEF TO this frame (includes origin offset)

Parameters

pos_ecef Position in ECEF [m]

Returns: Position in this frame [m]

◆ position_to_ecef()

template<typename Scalar>

Vec3< Scalar > vulcan::CoordinateFrame< Scalar >::position_to_ecef ( const Vec3< Scalar > & pos_local ) const

inlinenodiscard

Transform position FROM this frame TO ECEF (includes origin offset)

Parameters

pos_local Position in this frame [m]

Returns: Position in ECEF [m]

◆ quaternion()

template<typename Scalar>

janus::Quaternion< Scalar > vulcan::CoordinateFrame< Scalar >::quaternion ( ) const

inlinenodiscard

Get frame orientation as quaternion (rotation from ECEF to this frame)

The quaternion represents the rotation that transforms vectors from ECEF coordinates to this frame's coordinates.

Returns: Quaternion representing frame orientation

◆ to_ecef()

template<typename Scalar>

Vec3< Scalar > vulcan::CoordinateFrame< Scalar >::to_ecef ( const Vec3< Scalar > & v ) const

inlinenodiscard

Project vector FROM this frame TO ECEF (rotation only)

Reconstructs ECEF vector from local components. This is equivalent to multiplying by the DCM.

Parameters

v	Vector expressed in this frame

Returns: Vector expressed in ECEF

Member Data Documentation

◆ origin

template<typename Scalar>

Vec3<Scalar> vulcan::CoordinateFrame< Scalar >::origin

Frame origin in ECEF [m].

◆ x_axis

template<typename Scalar>

Vec3<Scalar> vulcan::CoordinateFrame< Scalar >::x_axis

Unit X basis vector in ECEF.

◆ y_axis

template<typename Scalar>

Vec3<Scalar> vulcan::CoordinateFrame< Scalar >::y_axis

Unit Y basis vector in ECEF.

◆ z_axis

template<typename Scalar>

Vec3<Scalar> vulcan::CoordinateFrame< Scalar >::z_axis

Unit Z basis vector in ECEF.

The documentation for this struct was generated from the following file:

include/vulcan/coordinates/FramePrimitives.hpp

Public Member Functions

Static Public Member Functions

Public Attributes

Detailed Description

Constructor & Destructor Documentation

◆ CoordinateFrame() [1/2]

◆ CoordinateFrame() [2/2]

Member Function Documentation

◆ dcm()

◆ dcm_inverse()

◆ ecef()

◆ eci()

◆ enu()

◆ from_ecef()

◆ from_quaternion()

◆ is_valid()

◆ ned()

◆ position_from_ecef()

◆ position_to_ecef()

◆ quaternion()

◆ to_ecef()

Member Data Documentation

◆ origin

◆ x_axis

◆ y_axis

◆ z_axis