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Map Datum Convert Demo

Goal

Demo utility that converts Rijksdriehoeksmeting coordinates to WGS84 and vice versa. It also demonstates the map projections Mercator, Web Mercator, Transverse Mercator and Oblique Stereographic (the latter is used for RD). I wrote it for own understanding of RD in Oziexplorer and get hands on experience with map projections. It contains the methods for Map Datum Conversion, a method for each step.

The code can be used as library, but it also contains a simple, quick and dirty demo that projects the 'landsdeel_gegeneraliseerd' data (the outline of the Netherlands) from the PDOK dataset 'gebiedsindeling'. The demo allows for comparison of two projectons. On the image below: Mercator vs Web Mercator.

projections

Background

Coordinates in the real world are expressed in [latitude, longitude, height], with respect to an Ellipoid that fits the globe or part of the globe. These values can be projected on a 2D plane by means of a Map Projection. This results in [Easting, Northing] in meter, or [x, y] or [y,x] coordinates. For Map Datum conversion [latitude, longitude, height] are converted to Carthesian coordinates [X, Y, Z] which are coordinates in 3D space. These coordinates can be converted by rotation and translation.

Code

The main flow for Map Datum conversion is shown in the diagram, in this case RD to WGS84 conversion. Step 1 is the the reverse map projection (Easting, Northing -> latitude, longitude) and is implemented in the class StereographicProjection. The remaining steps are implemented in MapDatumConvert. Step 2 converts latitude/longitude on on the ellipsoid to Carthesian coordinates, Step 3 is the actual conversion, in casu RD to WGS84. Step 4 converts the converted Carthesian coordinates to latitude/longtitude.

FLow

Design

Main methods that execute a full conversion in MapDatumConvert are rdToWgs84() and wgs84ToRd(). Both map conversion classes implement the interface MapProjection, which contain the methods latLonToMapDatum() and mapDatumToLatLon().

Ellipsoid implements an ellipoid representation. It contains the popular WGS84 and Bessel 1841 ellipsoid representations.

The software is provided with Unit Test classes, that can be used as example.

Comparison of projections

OziExplorer uses the Transverse Mercator projection for Dutch topographic RD maps, since Oblique Stereographic doesn't seem to be supported. One could wonder what the error is of applying the 'wrong' projection.

The Main class contains a demo. It uses MainView, which implement the demo projections. It calculates the difference in Map Datum coordinates (in meter) of the Martinitoren in Groningen, given the two projections to compare.

Note: the required data (the outline of the Netherlands) is downloaded on the fly from a PDOK Web Feature Service API (WFS). The code also contains a method to read the data from file, but it is not used.

References used

  1. A document of the Johannes Postgroep
  2. Geodetic reference frames in the Netherlands (chapter 6)
  3. The stereographic double projection
  4. Map Projections, a working manual
  5. OGP Surveying and Positioning Guidance Note Number 7, part 2 - 2009
  6. Geomatics Guidance Note Number 7, part 2: Coordinate Conversions and Transformations including Formulas