Unigine::Ellipsoid Class

Warning

The functionality described in this article is not available in the Community SDK edition.
You should upgrade to Engineering / Sim SDK edition to use it.

Header:

#include <UnigineEllipsoid.h>

The Ellipsoid class handles the geodetic transformations:

Specifies the Ellipsoid settings: semimajor axis, flattening coefficient
Performs systems coordinates (ECF, ENU, NED, Geodetic) conversion
Solves direct and inverse geodetic problems with different calculation mode (Great Circle and Vincenty algorithms)

This class is used to create an Ellipsoid instance to the GeodeticPivot class.

Here is a code snippet of the Ellipsoid class usage:

Source code (C++)

#include "UnigineMathLib.h"
#include "UnigineGeodetics.h"
#include "UnigineEllipsoid.h"

using namespace Unigine;
using namespace Unigine::Math;

/* ... */

// define the geodetic origin
dvec3 tomsk_origin = dvec3(58.49771, 84.97437, 117.0);

// create a new GeodeticPivot object
GeodeticPivotPtr pivot = GeodeticPivot::create();

// create a new ellipsoid and specify its settings
EllipsoidPtr ellipsoid = pivot->getEllipsoid();
ellipsoid->setSemimajorAxis(80000.0f);
ellipsoid->setMode(Ellipsoid::MODE_FAST);

// set the ellipsoid to the pivot
pivot->setOrigin(tomsk_origin);
pivot->setEllipsoid(ellipsoid);

Methods:

Name	Description View: Sort by:
*create*	Constructor.
setFlattening	Sets new flattening for the ellipsoid.
getFlattening	Returns flattening coefficient of the ellipsoid.
getMeanRadius	Returns the mean radius of the ellipsoid.
setMode	Sets the calculation mode.
getMode	Returns the calculation mode int value: 1 if the mode is MODE_ACCURATE, 0 if the mode is MODE_FAST.
setSemimajorAxis	Sets new semimajor axis of the ellipsoid.
getSemimajorAxis	Returns semimajor axis length of the ellipsoid in units.
getSemimajorEccentricitySqr	Returns the squared eccentricity calculated along the semimajor axis.
getSemiminorAxis	Returns semiminor axis of the ellipsoid in units.
getSemiminorEccentricitySqr	Returns the squared eccentricity calculated along the semiminor axis.
getENUSurfacePoint	Returns surface point by using tangent point coordinates.
getENUTangentPoint	Returns tangent point ENU coordinates based on the geographical coordinates.
getENUWorldRotation	Returns the world rotation quaternion in ENU coordinates.
getENUWorldTransform	Returns the world transformation matrix in ENU coordinates.
isSupported	Returns a value indicating if the geodetics feature is enabled.
getNEDSurfacePoint	Returns surface point by using tangent point coordinates.
getNEDTangentPoint	Returns tangent point NED coordinates based on the geographical coordinates.
getNEDWorldRotation	Returns the world rotation quaternion in NED coordinates.
getNEDWorldTransform	Returns the world transformation matrix in NED coordinates.
solveGeodeticDirect	Solves the direct geodetic problem: calculates end point coordinates on the ellipsoid by using given start point, distance between points, and bearing value.
solveGeodeticInverse	Solves the inverse geodetic problem: calculates distance and bearing values by using given start and end points on the ellipsoid.
toECF	Converts geodetic coordinates to Cartesian (ECF).
toENU	Converts geodetic coordinates to ENU (East, North, Up).
toGeodetic	Converts Cartesian (ECF) coordinates to Ellipsoid.
toNED	Converts geodetics coordinates to NED (North, East, Down).

Variables:

Name	Description
MODE_ACCURATE = 1	A calculation mode uses Vincenty's formula to calculate distances on the surface of the ellipsoid with a millimeter precision. It takes more time for calculation, but the accuracy of positioning is awesome.
MODE_FAST = 0	A calculation mode is computed by using Great-circle distance formula. It works pretty fast, but you'll get positioning errors on big (~80000x80000 units) distances.

Ellipsoid Class

Members

static EllipsoidPtr create ( double semimajor_axis, double flattening ) #

Constructor. Creates a new Ellipsoid class instance with given flattening and semimajor axis.

Arguments

double semimajor_axis - Semimajor axis.
double flattening - Flattening coefficient.

static EllipsoidPtr create ( ) #

Constructor. Creates a new Ellipsoid class instance (WGS84 Ellipsoid).

Math::dvec3 getENUSurfacePoint ( const Math::dvec3 & geodetic_origin, const Math::dvec3 & tangent_point ) #

Returns surface point by using tangent point coordinates.

NoticeThe Up-axis (Z+) direction in ENU points upward along the ellipsoid normal, while in UNIGINE implementation of ENU it goes from the Earth's center.

Arguments

const Math::dvec3 & geodetic_origin - The origin in ellipsoid coordinates (latitude (degrees), longitude (degrees) and altitude (meters).
const Math::dvec3 & tangent_point - Tangent point coordinates to converted (curved) to surface coordinates (offset related to point of junction).

Return value

Surface point coordinates.

Math::dvec3 getENUTangentPoint ( const Math::dvec3 & geodetic_origin, const Math::dvec3 & surface_point ) #

Returns tangent point ENU coordinates based on the geographical coordinates.

NoticeThe Up-axis (Z+) direction in ENU points upward along the ellipsoid normal, while in UNIGINE implementation of ENU it goes from the Earth's center.

Arguments

const Math::dvec3 & geodetic_origin - The origin in ellipsoid coordinates (latitude (degrees), longitude (degrees) and altitude (meters).
const Math::dvec3 & surface_point - Surface point coordinates to be converted (flatten) to tangent point (offset related to point of junction).

Return value

Tangent point coordinates.

Math::quat getENUWorldRotation ( const Math::dvec3 & geodetic_origin ) #

Returns the world rotation quaternion in ENU coordinates.

NoticeThe Up-axis (Z+) direction in ENU points upward along the ellipsoid normal, while in UNIGINE implementation of ENU it goes from the Earth's center.

Arguments

const Math::dvec3 & geodetic_origin - The origin in ellipsoid coordinates (latitude (degrees), longitude (degrees) and altitude (meters).

Return value

World rotation in ENU coordinates.

Math::dmat4 getENUWorldTransform ( const Math::dvec3 & geodetic_origin ) #

Returns the world transformation matrix in ENU coordinates.

NoticeThe Up-axis (Z+) direction in ENU points upward along the ellipsoid normal, while in UNIGINE implementation of ENU it goes from the Earth's center.

Arguments

const Math::dvec3 & geodetic_origin - The origin in ellipsoid coordinates (latitude (degrees), longitude (degrees) and altitude (meters).

Return value

World transformation matrix in ENU coordinates.

void setFlattening ( double flattening ) #

Sets new flattening for the ellipsoid.

Arguments

double flattening - Flattening coefficient of the ellipsoid. If the value is 0, the ellipsoid has a sphere shape, for 1 the ellipsoid has a circle (completely flat) shape.

double getFlattening ( ) #

Returns flattening coefficient of the ellipsoid.

Return value

Flattening coefficient of the ellipsoid.

double getMeanRadius ( ) #

Returns the mean radius of the ellipsoid.

Return value

The mean radius of the ellipsoid.

int isSupported ( ) #

Returns a value indicating if the geodetics feature is enabled.

Return value

1 if the geodetics feature is enabled; otherwise, 0.

void setMode ( int mode ) #

Sets the calculation mode.

Arguments

int mode - The variable of the calculation mode. It can be one of the following:
- MODE_FAST
- MODE_ACCURATE

int getMode ( ) #

Returns the calculation mode int value: 1 if the mode is MODE_ACCURATE, 0 if the mode is MODE_FAST.

Return value

1 if the mode is MODE_ACCURATE, 0 if the mode is MODE_FAST.

Math::dvec3 getNEDSurfacePoint ( const Math::dvec3 & geodetic_origin, const Math::dvec3 & tangent_point ) #

Returns surface point by using tangent point coordinates.

NoticeThe Down-axis direction in NED points downward along the ellipsoid normal, while in UNIGINE implementation of NED it goes through the Earth's center.

Arguments

const Math::dvec3 & geodetic_origin - The origin in ellipsoid coordinates (latitude (degrees), longitude (degrees) and altitude (meters).
const Math::dvec3 & tangent_point - Tangent point coordinates to converted (curved) to surface coordinates (offset related to point of junction).

Return value

Surface point coordinates.

Math::dvec3 getNEDTangentPoint ( const Math::dvec3 & geodetic_origin, const Math::dvec3 & surface_point ) #

Returns tangent point NED coordinates based on the geographical coordinates.

NoticeThe Down-axis direction in NED points downward along the ellipsoid normal, while in UNIGINE implementation of NED it goes through the Earth's center.

Arguments

const Math::dvec3 & geodetic_origin - The origin in ellipsoid coordinates (latitude (degrees), longitude (degrees) and altitude (meters).
const Math::dvec3 & surface_point - Surface point coordinates to be converted (flatten) to tangent point (offset related to point of junction).

Return value

Tangent point coordinates.

Math::quat getNEDWorldRotation ( const Math::dvec3 & geodetic_origin ) #

Returns the world rotation quaternion in NED coordinates.

NoticeThe Down-axis direction in NED points downward along the ellipsoid normal, while in UNIGINE implementation of NED it goes through the Earth's center.

Arguments

const Math::dvec3 & geodetic_origin - The origin in ellipsoid coordinates (latitude (degrees), longitude (degrees) and altitude (meters).

Return value

World rotation in NED coordinates.

Math::dmat4 getNEDWorldTransform ( const Math::dvec3 & geodetic_origin ) #

Returns the world transformation matrix in NED coordinates.

NoticeThe Down-axis direction in NED points downward along the ellipsoid normal, while in UNIGINE implementation of NED it goes through the Earth's center.

Arguments

const Math::dvec3 & geodetic_origin - The origin in ellipsoid coordinates (latitude (degrees), longitude (degrees) and altitude (meters).

Return value

World transformation matrix in NED coordinates.

void setSemimajorAxis ( double axis ) #

Sets new semimajor axis of the ellipsoid.

Arguments

double axis - Semimajor axis length in units.

double getSemimajorAxis ( ) #

Returns semimajor axis length of the ellipsoid in units.

Return value

Semimajor axis of the ellipsoid.

double getSemimajorEccentricitySqr ( ) #

Returns the squared eccentricity calculated along the semimajor axis.

Return value

Squared eccentricity calculated along the semimajor axis.

double getSemiminorAxis ( ) #

Returns semiminor axis of the ellipsoid in units.

Return value

Semiminor axis of the ellipsoid in units.

double getSemiminorEccentricitySqr ( ) #

Returns the squared eccentricity calculated along the semiminor axis.

Return value

Squared eccentricity calculated along the semiminor axis.

Math::dvec3 solveGeodeticDirect ( const Math::dvec3 & geodetic_start, double bearing, double distance ) #

Solves the direct geodetic problem: calculates end point coordinates on the ellipsoid by using given start point, distance between points, and bearing value.

Arguments

const Math::dvec3 & geodetic_start - Start point on the ellipsoid.
double bearing - Bearing value.
double distance - Distance between two points on the ellipsoid.

void solveGeodeticInverse ( const Math::dvec3 & geodetic_start, const Math::dvec3 & geodetic_end, double & bearing, double & distance ) #

Solves the inverse geodetic problem: calculates distance and bearing values by using given start and end points on the ellipsoid.

Arguments

const Math::dvec3 & geodetic_start - Start point on the ellipsoid.
const Math::dvec3 & geodetic_end - End point on the ellipsoid.
double & bearing - Variable to save the calculated bearing value.
double & distance - Variable to save the calculated distance value.

Math::dvec3 toECF ( const Math::dvec3 & geodetic_coords ) #

Converts geodetic coordinates to Cartesian (ECF).

Arguments

const Math::dvec3 & geodetic_coords - Ellipsoid coordinates (latitude (degrees), longitude (degrees) and altitude (meters)) to be converted to Cartesian.

Return value

Cartesian coordinates.

Math::dvec3 toENU ( const Math::dvec3 & geodetic_origin, const Math::dvec3 & geodetic_coords ) #

Converts geodetic coordinates to ENU (East, North, Up).

NoticeThe Up-axis (Z+) direction in ENU points upward along the ellipsoid normal, while in UNIGINE implementation of ENU it goes from the Earth's center.

Arguments

const Math::dvec3 & geodetic_origin - The origin in ellipsoid coordinates (latitude (degrees), longitude (degrees) and altitude (meters).
const Math::dvec3 & geodetic_coords - Coordinates to be converted to ENU.

Return value

ENU coordinates.

Math::dvec3 toGeodetic ( const Math::dvec3 & ecf_coords, int need_alt = 1 ) #

Converts Cartesian (ECF) coordinates to Ellipsoid.

Arguments

const Math::dvec3 & ecf_coords - Cartesian ECF coordinates to be converted.
int need_alt - Flag indicating if altitude is to be calculated. 1 to calculate altitude, 0 - to skip altitude calculation.The default value is 1.

Return value

Ellipsoid coordinates (latitude (degrees), longitude (degrees) and altitude (meters)

Math::dvec3 toNED ( const Math::dvec3 & geodetic_origin, const Math::dvec3 & geodetic_coords ) #

Converts geodetics coordinates to NED (North, East, Down).

NoticeThe Down-axis direction in NED points downward along the ellipsoid normal, while in UNIGINE implementation of NED it goes through the Earth's center.

Arguments

const Math::dvec3 & geodetic_origin - The origin in ellipsoid coordinates (latitude (degrees), longitude (degrees) and altitude (meters).
const Math::dvec3 & geodetic_coords - Coordinates to be converted to NED.

Return value

NED coordinates.

Last update: 13.12.2021

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