GPS Manager User Manual -- Projections and coordinate grids

|  |  | Projections and coordinate grids

## Projections and coordinate grids

### Selecting and defining projections

Selecting the map projection is done by using the second (from the left) menu-buttons on the bottom of the map window if the map window is the main window, or the `Projection` menu-button if the lists window is the main window.

If a background image is to be loaded the projection and the datum should be set to the projection and datum used in the image (see above for the details on this). If there is no image, the map projection should be selected according to the map scale and the geometry of the region to be covered.

World maps and small-scale maps need suitable projections, such as Mercator. Using projections that were developed for large-scale maps, such as the Transverse Mercator will give strange results or even errors. With small-scale maps the following should also be noted:

- a map cannot have overlapping parts; this implies that for each point on the Earth the projection procedure will give a single projected point;
- for projections having a central longitude or false longitude parameter, GPSMan converts any longitude value to the range from -180 to 180 (inclusive) centred on that central/false longitude; this means that it may happen that a point created too far to the West (or East) of this longitude will be mapped to the East (or West) of it, causing lines (routes, tracks or polylines) to be displayed in a wrong way; it is therefore very important that the central or false longitude be given an appropriate value;
- when initializing a map projection the default value for the central/false longitude in GPSMan is the average of longitudes of the points that are to be displayed then; if the option on asking for confirmation of projection parameters is set, the user will have the opportunity to change it;
- measuring distances on a small-scale map as explained above can yield wrong values for points too distant from each other.

Projections can be either predefined or user-defined. There are a small set of predefined projections. Some of them admit particular cases, in the sense that they have parameters whose values can be fixed. The user may define such particular cases along with a coordinates grid associated to it.

Each projection has an associated coordinates grid that will be used as default position format for displaying the map cursor coordinates and when a waypoint is created from the map. This position format and the associated datum can be changed from the map window (menu-buttons near the cursor coordinates). If the position format is a grid requiring a fixed datum, the datum will be set automatically when the format is changed and cannot be changed.

When defining a projection, the user may also define a new coordinates grid User-defined grids cannot have more than one zone.

User-defined projections and grids are automatically saved in a file in the GPSMan user directory, and will be loaded when GPSMan is started.

To define/change a projection there are the appropriate entries under the `Definitions` menu-button.

When defining a new projection, which is necessarily a particular case of a general projection, the user must select first the general projection to use, along with a name and short name. The short name, that can not have blanks, is for internal use and will also serve as the coordinates grid name, if the user associates one to the new projection. The values of the projection parameters must be then given. The user may either associate to the new projection an existing grid, or create a new grid by selecting a distance unit (currently either metres or feet), by giving the values for the false easting and northing (for some projections these parameters are in fact the easting/northing of the false origin or of the projection centre), sensible bounds to the coordinates, and by choosing whether or not a fixed datum must be used with the grid. The bounds given will be used to check that the grid is not used outside its intended scope. All values of latitudes and longitudes must be given either in the datum of the grid if there is a fixed one, or in the datum being used for the map.

An user-defined grid cannot be forgotten if it is currently associated to another projection or in use for displaying the map coordinates. Changing the definition of a user-defined grid may cause inconsistencies in previously projected data.

### Predefined projections and grids

With the UTM/UPS (Universal Transverse Mercator/Universal Polar Stereographic) projection a single UTM zone is used, that of the first point displayed. Points in different zones will be projected into the same zone what may produce some deformation. There are no parameters that can be changed by the user.

The Transverse Mercator projection, also known as Gauss or Gauss-Kruegger projection is used with large scale maps and is not suitable for longitude ranges larger than about 6 degrees. It has 3 parameters: the latitude and longitude of the centre and the scale factor at the central meridian. The first two are computed as the averages of the latitudes/longitudes of the first points being mapped, while the third one has the default value of 0.9996 (used for UTM).

Particular cases of the Transverse Mercator projection are used in several maps usually for a certain country or region. Besides UTM, GPSMan predefines the following ones:

- the Austrian "Bundesmeldenetz" (BMN) projection. Parameters: central latitude `0`, central longitude in three zones of 3 degrees named `M28`, `M31` and `M34` and centred at `10.3333333`, `13.3333333` and `16.3333333E`, scale factor `1`. The datum to be used is called "Austrian (MGI)". Coordinates in the BMN grid have a false northing of 0 and a false easting that depends on the zone: 150km in zone `M28`, 460km in `M31`, and 750km in `M34`.
- the British National Grid (BNG) projection. Parameters: central latitude `49`, central longitude `-2`, scale factor `0.9996012717`. The datum to be used is called "Ordnance Survey Great Britain". Coordinates in this grid correspond to a false easting of 400km and a false northing of 100km.
- the British West Indies projection. Parameters: central latitude `0`, central longitude `-62`, scale factor `0.9995`. The datum to be used should be based on the "Clarke 1880" ellipsoid. Coordinates in this grid correspond to a false easting of 400km.
- the projection used in the Italian Carta Tecnica Regionale (CTR). Parameters: central latitude `0`, central longitude in two zones of 6 degrees centred at `9` and `15E`, scale factor `0.9996`. Coordinates in the CTR grid have a false northing of 0 and a false easting that depends on the zone: 1500km in the first zone, and 2520km in the second one.
- the German Grid projection (GKK: Gauss-Krueger-Koordinatensystem). Parameters: central latitude `0`, central longitude in zones of 6 degrees centred at `0`, `3`, `6`, `9`, `12`, and `15E`, scale factor `1`. Coordinates in the GKK grid have a false easting of z×1000 + 500 km, where z is the zone number.
- the Irish Transverse Mercator Grid (ITM) projection. Parameters: central latitude `53.5`, central longitude `-8`, scale factor `1.000035`. The datum to be used is called "Ireland 1965". Coordinates in this grid correspond to a false easting of 200km and a false northing of 250km.
- the Portuguese Military Maps projection, used in 1:25000 maps published by the Portuguese Army Geographic Institute. Parameters: central latitude `39.66666666666667`, central longitude `-8.13190611111111`, scale factor `1`. The datum to be used is called "Lisboa". Military coordinates in these maps correspond to a false easting of 200km and a false northing of 300km.
- the Swedish Grid (SEG) projection. Parameters: central latitude `0`, central longitude `15.808277777778`, scale factor `1`. Coordinates in this grid correspond to a false easting of 1500km.
- the Taiwan Grid projection (TWG). Parameters: central latitude `0`, central longitude in 6 zones of 2 degrees centred at `115`, `117`, ..., `125`, and scale factor `0.9999`. Coordinates in the TWG grid have a false easting of 250km. This grid is usually employed with either the "Hu-Tzu-Shan" datum (also known as "TWD67"), or the "TWD97" datum (whose definition could not be found for inclusion in GPSMan).
- the Uniform Finnish Grid (KKJY) projection. Parameters: central latitude `0`, central longitude `27`, scale factor `1`. Coordinates in this grid correspond to a false northing of 500km. There is a single zone named `27E`.
- the Basic Finnish Grid (KKJP) projection. Parameters: central latitude `0`, central longitude in zones of 6 degrees centred at `21`, `24`, `27`, and `30E`, scale factor `1`. Coordinates in the KKJP grid have a false easting of z×1000 + 500 km, where z is the zone number.

The Swiss Oblique Mercator projection is a particular case of an Oblique Mercator projection, which in turn differs from the Mercator and Transverse Mercator projections in that the central line with true scale is neither the equator (as in the Mercator), nor a meridian (as in the Transverse Mercator), and is chosen to suit the region to be mapped. In the Swiss Oblique Mercator this line has an azimuth of 90 degrees and contains the centre of the projection. There are three parameters: the latitude and longitude of the centre, and the scale factor, the default values being the averages of latitudes and of longitudes of the first points to be projected and 1, respectively.

The Swiss LV03 Grid projection is a particular case of the Swiss Oblique Mercator projection with centre at Bern, N46.9524055556, E7.43958333333 degrees in the "CH-1903" datum, and a scale factor of 1.

The Swiss LV03 grid has false easting and northing of 600km and 200km, and use the "CH-1903" datum.

The Uniform Hungarian National projection (EOV: Egységes országos vetület) is a reduced oblique Mercator projection that has no parameters and should be used with the "Hungarian Datum 1972". Coordinates in the associated grid are by definition presented in the order northing then easting but this convention is not followed here. They correspond to a false easting of 650km and a false northing of 200km. Acceptable ranges of values are: 400000-950000m for easting, 0-400000m for northing, 45-49 degrees for latitude, and 16-23 degrees for longitude.

The Lambert Conic Conformal projection has two variants: single standard parallel (under the name `Lambert Conic Conf 1` in GPSMan), and two standard parallels (called in GPSMan `Lambert Conic Conf 2`).

The former has 3 parameters: the latitude and longitude of the centre and the scale factor at the natural origin. The first two are computed as the averages of the latitudes/longitudes of the first points being mapped, while the third one has the default value of 1 (corresponding to a tangent cone; a value of less than 1 stands for a secant cone).

The latter has 4 parameters: latitudes of the two standard parallels (along which the cone intersects the geoid) and of the false origin, and longitude of the false origin. The first two default to the extremes of latitudes of the first points being mapped, and the position of the false origin defaults to the average of the positions of these points.

The Iceland Grid projection is a particular case of the Lambert Conic Conformal projection with 2 standard parallels at N64.75 and N64.25 degrees, a false origin at N65, W19 degrees and the "WGS 84" datum.

The Iceland grid has a false easting and a false northing of 500km.

The Lambert 93 grid projection is a particular case of the Lambert Conic Conformal projection with 2 standard parallels at N44 and N49 degrees, a false origin at N46.5 E3 degrees and a datum based on the "GRS 80" ellipsoid. The "WGS 84" datum can be used for applications with handheld GPS receivers.

The Lambert 93 grid has a false easting of 700km and a false northing of 6600km.

The Lambert NTF grid projection has 4 zones, named `I`, `II`, `III` and `IV`, each corresponding to a particular case of the Lambert Conic Conformal projection with 2 standard parallels with the following parameters (in degrees):

zone |  | I |  | II |  | III |  | IV
1st parallel |  | 50.3959116667 |  | 45.8989188889 |  | 43.1992913889 |  | 41.5603877778
2nd parallel |  | 48.5985227778 |  | 47.6960144444 |  | 44.9960938889 |  | 42.0000593542
lat f origin |  | 49.5 |  | 46.8 |  | 44.1 |  | 42.165

the longitude of the false origin being that of the Paris meridian at E2.3372083333 degrees, and the "NTF (Nouvelle Triangulation de France)" datum.

The Lambert NTF grid has for zones `I` to `III` a false easting of 600km and a false northing of 200km, and for zone `IV` a false easting of 234.358m and false northing of 185861.369m.

The Lambert NTF étendue grid projection is the same as the projection for zone `II` of the Lambert NTF grid projection.

The Lambert NTF étendue grid has a false easting of 600km and a false northing of 2200km.

Lambert Equal Area Conic projection is a conic, equal-area projection. It has four parameters: the latitude of a standard parallel, the polar aspect (either `north` or `south`), and the latitude and longitude of the centre.

The Albers Equal Area projection is a conic, equal-area projection. It has four parameters: the latitudes of the two standard parallels, and the latitude and longitude of the centre.

The Teale Albers grid projection is a particular case of the Albers Equal Area projection with standard parallels at 34 and 40.5 degrees North, and centre at the equator, 120 degrees West.

The Teale Albers grid uses this projection with the `NAD27 CONUS` datum, false easting of 0 and false northing of -4000km. Note that coordinate values may be negative.

The Mercator projection can be defined as a Lambert Conic Conformal projection either with the equator as its single standard parallel, or with the two standard parallels at equal North and South latitudes (i.e., symmetrical with respect to the equator).

This leads to two variants: single standard parallel (named in GPSMan `Mercator 1`), and two standard parallels (named in GPSMan `Mercator 2`).

The former has 2 parameters: the longitude of the centre and the scale factor at the natural origin. They are taken as the average of the longitudes of the first points being mapped, and as 1, respectively.

The latter has 3 parameters: the latitudes of one of the two standard parallels and of the false origin, and longitude of the false origin. The first default to the maximum of the absolute values of the latitudes of the first points being mapped, the position of the false origin defaults to the average of the positions of these points.

The Stereographic projection is an azimuthal conformal projection used both for large scale and small scale mapping. There are 3 possible aspects: polar, oblique and equatorial, which are dealt with automatically by GPSMan. A particular case of this projection is the Universal Polar Stereographic that is used in the UTM/UPS.

The Stereographic projection has three parameters: the latitude and the longitude of the centre (tangent point) and a scale factor. By default the scale factor is 1 and the coordinates of the centre are taken as the average of the latitudes of the first points to be mapped.

The Schreiber double projection is a variant of the Stereographic projection, in which each point in the ellipsoid is first projected in a sphere and the resulting point projected in a plane that intersects the sphere. This projection must be used with a datum based on the "Bessel 1841" ellipsoid, usually the "Rijks Driehoeksmeting" datum. If the given datum is for a different ellipsoid, GPSMan will change the datum to "Rijks Driehoeksmeting". All parameters for this projection are fixed: the centre is at N52 09 22.178 E5 23 15.5 in the "Rijks Driehoeksmeting" datum (coordinates of the Amersfoot OLV church), the scale factor is 0.9999079, and the constants for the conversions between the isometric latitudes in the ellipsoid and in the sphere are n=1.00047585668 and m=0.003773953832.

The Netherlands grid uses the Schreiber dual projection with a false easting of 155km and a false northing of 463km, and the "Rijks Driehoeksmeting" datum. Acceptable ranges of values are: 0-290000m for x, 290000-630000m for y, 50.3-53.45 degrees for latitude, and 3-7.45 degrees for longitude.

The Cassini-Soldner projection is a neither conformal nor equal-area projection used in the 19th century. It is still used for mapping areas with a small E-W extent. Scale is true along a central meridian and distortion increases significantly with distance from it. It has two parameters: the latitude and the longitude of the natural origin. These parameters are taken as the averages of the latitudes and longitudes of the first points being mapped.

The American Polyconic projection is also a neither conformal nor equal-area projection used before the computer era. It has a single parameter: the standard latitude, whose default value is taken as the average of the latitudes of the first points to be mapped.

|  |  | Projections and coordinate grids