All calculations on this page are based on the reference ellipsoid of the WGS84 system. WGS84 uses 2 coordinate systems to specifiy a position on earth:

• Latitude/Longitude/Height (LLH) Geodetic coordinates (angles in degree)
• X/Y/Z in Earth Centered Earth Fixed (ECEF) coordinates in meters. The X-axes points to latitude = 0 and longitude = 0, the Y-Axes points to latitude = 0 and longitude = 90 and the Z-axes points to the North Pole.

In the panels you can enter a location either Geodetic LLH or in ECEF coordinates. The other coordinates are automatically computed from the input.

All calculations use the earth parameters as defined in [1].

Vector Origin-Target Input

The following panels can be used to convert between ECEF (earth centered, earth fixed) coordinates and LLH (latitude, longitude, height) too.

Use the following panels to compute data from the Origin Refrence Point to a Target Point. The Results are displayed at Vector Origin-Target Calculations. Some values are expressed in a local coordinate system positioned at Origin Point. The Local Coord Orientation Reference Point defines the orientation of the local coordinate system in such a way, that the y axes (North) is pointing from Origin to the Orientation Reference Point, the x axes is poining to the right of y (East) and the z axes is pointing away from the surface (Up).

Don't change the Reference Point or set lat = 90 if you want the local coordinate system to be a East/North/Up system. If you want to get Target Point local coordinates with respect to another target point Ref2, enter the coordinates of Ref2 above.

Vector Origin-Target Calculations

The values shown in the following panel are the result of a vector from Origin Point to Target Point, both in ECEF and local coordinates.

All data is calculated using the WGS84 ellipsoid model. ECEF = Earth Centered, Earth Fixed coordinates. Local coordinates are coordinates with respect to the local coordinate system at the Origin point. This is calculated in such a way, that Z is the perpendicular to the reference ellipsoid of the Origin point, Y is in direction to the Reference point and X points to the right wrt. Y.

Create Computer Model Data

The following form was used to convert the ECEF coordinates to the data format used in the Computer Model . Insert the ECEF Data from CurveAppData.csv into the field and click Create Curve App Data. The Computer Model needs the distance of the targets from the Origin and the Side Position from the center line.

The first line must specify the Origin point and the second line must specify the Reference Point. The center line is the line from the Origin to the Refrence Point.

The Data must have the following format for each line: ID, X, Y, Z, Description
where X, Y, Z are in ECEF (Earth Centered, Earth Fixed) coordinates.

Create Curve App Data

WGS84 Coordinate System

The WGS 84 Coordinate System is a Conventional Terrestrial Reference System (CTRS). The definition of this coordinate system follows the criteria outlined in the International Earth Rotation Service (IERS) Technical Note 21 [2]. These criteria are repeated below:

• It is geocentric, the center of mass being defined for the whole Earth including oceans and atmosphere
• Its scale is that of the local Earth frame, in the meaning of a relativistic theory of gravitation
• Its orientation was initially given by the Bureau International de l’Heure (BIH) orientation of 1984.0
• Its time evolution in orientation will create no residual global rotation with regards to the crust

The WGS 84 Coordinate System is a right-handed, Earth-fixed orthogonal coordinate system and is graphically depicted in Figure 2.1.

The origin and axes are defined as follows:

Origin

Earth’s center of mass

Z-Axis

The direction of the IERS Reference Pole (IRP). This direction corresponds to the direction of the BIH Conventional Terrestrial Pole (CTP) (epoch 1984.0) with an uncertainty of 0.005"

X-Axis

Intersection of the IERS Reference Meridian (IRM) and the plane passing through the origin and normal to the Z-axis. The IRM is coincident with the BIH Zero Meridian (epoch 1984.0) with an uncertainty of 0.005"

Y-Axis

Completes a right-handed, Earth-Centered Earth-Fixed (ECEF) orthogonal coordinate system

The WGS 84 Coordinate System origin also serves as the geometric center of the WGS 84 Ellipsoid and the Z-axis serves as the rotational axis of this ellipsoid of revolution. [1]

Converting ellipsoidal to ECEF coordinates

To convert from ellipsoidal latitude, longitude, height to ECEF cartesian coordinates, the formulas published in Wikipedia are used [3].

To convert latitude and longitude from degrees into radian, multiply them by π/180°.

Converting ECEF to ellipsoidal coordinates

To convert from ECEF cartesian coordinates to ellipsoidal latitude, longitude, height, the formulas published in Wikipedia are used [3]. This transformation can only be calculated iteratively. The calculator on this page uses the Newton method.

The longitude can be calculated directly. The calculator uses vector geometry to accomplish this. If the X and Y components are 0 then the longitude is undefined and set to 0. Otherwise longitude is calculated as folows:

To convert latitude and longitude from radian into degrees, multiply them by 180°/π.

If the X and Y components are 0 then latitude is +90° for Z > 0 or −90° for Z < 0. If Z is 0 then latitude is 0°. In all other cases the latitude has to be calculated iteratively:

The function to find the root for is:

If latitude $\varphi$ is +90° or −90° then the ellipsoid height is:

If latitude $-90° \lt \varphi \lt 90°$ then the ellipsoid height is:

References