Coordinate System

Units

Model units may be either meters (m, default) or kilometers (km), this can be selected when creating a model.
You can check the units using Preferences (Edit → Preferences), in the Units Tab:

IGMAS+ is using the following coordinate system (ENU system):

• x positive to the East
• y positive to the North
• z positive to the top (Up)

Projections

For the modelling it is not necessary to use a special geographical projection, the only prerequisite is an orthogonal coordinate system - which may be any projection.

However, if you plan to visualize the model and the anomaly fields using WorldWind, you have to specify the correct projection.

Use the Property editor tab of the Object Tree entry Model to get the projection definition:

Projection: unknown

Use this default setting, if you don't know the projection being used, if you use local coordinates (not referred to world coordinates) or if you are not interested in visualization with WorldWind.

Projection: Universal Transverse Mercator

The Universal Transverse Mercator (UTM) projection uses the Hayford Ellipsoid/

The parameters are: Ref. meridian, UTM Zone, Hemisphere, East - Delta and North - Delta:

Ref. meridian:

The central meridian (in IGMAS+ called reference meridian) varies between -177° and +177° according to the table:

UTM Zone	Central Meridian	UTM Zone	Central Meridian
1	-177° W	31	3° E
2	-171° W	32	9° E
3	-165° W	33	15° E
4	-159° W	34	21° E
5	-153° W	35	27° E
6	-147° W	36	33° E
7	-141° W	37	39° E
8	-135° W	38	45° E
9	-129° W	39	51° E
10	-123° W	40	57° E
11	-117° W	41	63° E
12	-111° W	42	69° E
13	-105° W	43	75° E
14	-99° W	44	81° E
15	-93° W	45	87° E
16	-87° W	46	93° E
17	-81° W	47	99° E
18	-75° W	48	105° E
19	-69° W	49	111° E
20	-63° W	50	117° E
21	-57° W	51	123° E
22	-51° W	52	129° E
23	-45° W	53	135° E
24	-39° W	54	141° E
25	-33° W	55	147° E
26	-27° W	56	153° E
27	-21° W	57	159° E
28	-15° W	58	165° E
29	-9° W	59	171° E
30	-3° W	60	177° E

UTM Zone:

The UTM Zone varies between 1 and 60 and is linked to the central meridian via the following equation:

$$\mathrm{Zone} = (\mathrm{Central~Meridian} + 183)/6$$

UTM Zones 1 to 30 cover the western hemisphere (west of Greenwich).
UTM Zones 31 to 60 cover the eastern hemisphere (east of Greenwich).

Each UTM zone spans 6 degrees of longitude, with the central meridian located in the middle of the zone.

Hemisphere:

Either North or South (Default: North)

North and South UTM Zones refer to the division of UTM zones based on the hemisphere:

• UTM North (N) Zones:
  - Cover the northern hemisphere (from the equator to 84°N).
  - Zone numbers range from 1N to 60N.
  - Latitude values are positive, starting at 0 m at the equator and increasing northward.

• UTM South (S) Zones:
  - Cover the southern hemisphere (from the equator to 80°S).
  - Zone numbers range from 1S to 60S.
  - Latitude values are negative, starting at 0 m at the equator and increasing southward.
  - To avoid negative coordinates, false northing of 10,000,000 meters is applied at the equator.

East Delta:

This value (in meters, default is 0) will be added to the model $x$-coordinates before transformation into geographical coordinates.

East Delta:

This value (in meters, default is 0) will be added to the model $y$-coordinates before transformation into geographical coordinates.

Projection: Gauss-Krueger

The Gauss-Krueger (Gauß-Krüger) projection uses the Bessel Ellipsoid.

The system is similar to the UTM (Universal Transverse Mercator) system but the central meridians of the Gauss-Krueger zones are only 3° apart, as opposed to 6° in UTM.

The parameters are: Ref. meridian, Hemisphere, East - Delta and North - Delta:

Zones of the Gauss-Krueger projections are defined by the central meridian (parameter Ref. meridian).
Each GK zone spans 3 degrees of longitude, with the central meridian located in the middle of the zone.

Ref. meridian:

The central meridian (in IGMAS+ reference meridian) varies between -177° and +177°.

Hemisphere:

Either North or South (Default: North)

East Delta:

This value (in meters, default is 0) will be added to the model $x$-coordinates before transformation into geographical coordinates.

East Delta:

This value (in meters, default is 0) will be added to the model $y$-coordinates before transformation into geographical coordinates.

Projection: European Petroleum Survey Group (EPSG)

The European Petroleum Survey Group (EPSG) established a system to define and access all geodetic coordinate projections used worldwide.
The website http://epsg.io may be used to find the EPSG code for a special projection.

The parameters are: EPSG - Code and Proj4 Definition:

By specifying the appropriate EPSG code code in the field EPSG - Code you can set up any projection.

Examples:

EPSG code	Description
3857	WGS 84 / Pseudo-Mercator - Spherical Mercator, Google Maps, OpenStreetMap, Bing, ArcGIS, ESRI
31466	DHDN, Gauß-Krüger Zone 2, Germany
31467	DHDN, Gauß-Krüger Zone 3, Germany
31468	DHDN, Gauß-Krüger Zone 4. Germany
24819	PSAD56, UTM Zone 19, Chile

Note

If the EPSG code is used, the model coordinates have to be in meters, and there is no additional offset for the locations possible.

PROJ.4 Definition

PROJ (formerly PROJ.4) is an open-source software library used for cartographic projections and coordinate transformations.
The ideas is that each projection may be defined by a number of parameters and thus described by a single line definition using PROJ syntax.

The PROJ definition is given for each projection on the EPSG website, in addition it is always shown in the IGMAS+ EPSG projection settings (see the previous figure).
You may alter the value under Proj4 Definition to define your own projection. (the EPSG - Code value is then set to 0).

Example

The Proj4 definition of the EPSG code 24819 (UTM zone 19N) is:

+proj=utm +zone=19 +ellps=intl +towgs84=-288,175,-376,0,0,0,0 +units=m +no_defs

See also this archive article for more information.

Mercator projection

The Mercator projection is the easiest way to transfer spherical (geographical) coordinates into plane (orthogonal) coordinates.
Use the following transfer functions - they are exact and easy to use:

Forward (spherical into orthogonal):

$$x = (\lambda - \lambda_0)$$

$$y = 0.5 \cdot \ln \left(\dfrac{1+\sin(\varphi)} {1-\sin(\varphi)}\right)$$

Here $\lambda$ and $\varphi$ are given in radians. $x$ and $y$ are normalized with the Earth radius, so multiply x and y with 6378137 to get meters or 6378.137 to get kilometers.

Reverse (orthogonal into spherical):

$$\lambda = \lambda_0 + x$$

$$\varphi = \arcsin (\tanh(y))$$

Note

The Mercator projection (used for rendering maps in Google Maps, OpenStreetMap, Bing etc.) is most accurate in the area of low latitudes, it cannot be used in polar regions.

The EPSG code of this projection is 3857.

Projection: GeoTools Projection

GeoTools is another open-source Java library designed for geospatial data processing. It supports projections and coordinate transformations by leveraging standards like OGC and EPSG codes. GeoTools is widely used in GIS applications to handle vector and raster data, offering robust tools for reprojecting spatial data between coordinate reference systems (CRS).

There is only one parameter, EPSG - Code:

However, it is possible to provide information about the custom projection using the WKT format by loading files with *.wrt and .prj extensions (Import WKT button).

Example

A typical WKT string for WGS84 (EPSG:4326) looks like this:

GEOGCS["WGS 84",
DATUM["WGS_1984",
    SPHEROID["WGS 84",6378137,298.257223563]],
PRIMEM["Greenwich",0],
UNIT["degree",0.0174532925199433]]