Proposal for using Polygonal Validity Scopes in NTv2 grid files

An attempt for meaningful supplement of the NTv2 standard.

(firmenpresse) - By means of NTv2 grid files it is possible to transform points from one coordinate reference system to another with very high accuracy. An NTv2 file contains one or more quasi-rectangular coordinate grids which are defined in the NTv2 headers. Instead of a rectangular area only an embedded polygonal area should and must be covered, for example, a state territory within the country borders. How can outside of a polygonal administrative area located coordinates be excluded from the coordinate transformations and reference system transitions (datum shifts) and thereby localization errors be suppressed? The author presents a simple but effective solution for this problem. The article matches GIS developers who generate NTv2 files for accurate reference system transitions in administrative areas. It also addresses GIS users who perform coordinate transformations and reference system transitions using NTv2 files.

NTv2 was developed in Canada in the mid-nineties and means ordinate grids of the NTv2 files contain the required shifts between both reference systems. Using bilinear interpolation, the exact coordinates of points in the source reference system are calculated to the target reference system.

The NTv2 file is composed of one or several parent and child coordinate grids in hierarchical structure. With compacted grid meshes optional child coordinate grids improve subareas of the parent coordinate grids lying below. In a hierarchical way child grids can appear as parent grids to further child grids lying above (see figure 3). Most grid files, e.g. the German Beta2007, only contain one single parent coordinate grid.

The NTv2 file begins with a main header (left) in which general information, the names of the used reference systems and the particular ellipsoid parameters are stored. Parent and child coordinate grids follow and each begins with a sub header (right). Therein validity scopes of the coordinate grids are specified by southern and northern latitudes and western and eastern longitudes.

Each sub header is followed by grid meshes with two values for longitudinal and latitudinal shifts as well as two values for accuracy. Shifts between reference systems are mostly specified in seconds, but can also be stored as minutes or degrees. Optionally the accuracy can be specified in meters for the mean error of the longitudinal and latitudinal shifts.

Thus, the rectangular validity scope of a NTv2 file is defined by one or several quasi-rectangular coordinate grids. Therefore, the limitation to the actually required polygonal area, e.g. defined by national frontiers, is not possible. As a result, all coordinate transformations outside of the polygonal validity scope are incorrect. To solve this problem you could fill grid meshes that lie outside of the desired polygonal area with certain values. These values are called

Figure 1: NTv2 grid with rectangular validity scope.
This rectangular coordinate grid of a common NTv2 file covers the state territory of the Federal Republic of Germany. Coordinate transformations outside of the state territory, which is provided for the reference system transition, will inevitably cause errors.

The first option for implementing polygonal structures is the use of exopolygonal entries for accuracy values of the grid meshes. In most NTv2 files, accuracy values are set to 0 or -1 to indicate that there is no information about accuracy available. Empirically, there are no NTv2 files in which accuracy values are specified by plausible numbers. There is no known GIS software that includes accuracy values in calculations.

Grid meshes that are supposed to be excluded are marked as invalid, in case you determine both of their accuracy values by an exopolygonal entry of -99. So labeled grid meshes are excluded from the calculations of reference system transitions. The number -99 is proper for the mark because it cannot be found as a value pair for plausible accuracies.

Figure 2: NTv2 grid with polygonal validity scope.
This example addresses the area of the Federal Republic of Germany as polygonal validity scope. The red grid meshes are marked by exopolygonal entries and thus excluded from reference system transitions. The white grid meshes are border areas in which reference system transitions have to occur.

The second option is the exopolygonal entry -99 in both longitudinal and latitudinal shifts of the grid meshes. Again it applies, that this value pair cannot be found for plausible longitudinal or latitudinal shifts.

The example on the left shows both methods for the implementation of polygonal validity scopes. The shifts of two grid meshes marked yellow and the accuracy values of two further grid meshes marked blue have exopolygonal entries. Consequently, these four grid meshes are outside of the polygonal validity scope.

To implement polygonal validity scopes, a GIS software can query exopolygonal entries in the four shift and accuracy values of the grid meshes. During the calculation of reference system transitions, the coordinates that are to be transformed are examined for their association with such grid meshes. It is crucial whether the grid mesh is part of a parent coordinate grid or of a therein contained child coordinate grid. In case it lies in a child grid, the attempt is to continue the calculation in the parent grid lying below. When grid meshes fitting to a coordinate are marked by exopolygonal entries in all hierarchically stacked child and parent grids, then the coordinate is outside of the polygonal validity scope. It is excluded from the calculation of the reference system transition and a note is generated.

Figure 3: Testing coordinates on polygonal validity.
In this example, three coordinate grids are arranged one upon the other. Only when a coordinate falls through all exopolygonal grid meshes it lies outside of the polygonal validity and is excluded from the reference system transition.

There are two methods for the implementation of polygonal validity scopes resulting from the use of exopolygonal entries in shift or in accuracy values. Both methods have different effects.

Figure 4: Usage of accuracy values for the exclusion of one single grid mesh.

Method 1: Exopolygonal entry in accuracy values of a grid mesh.

Exactly one grid mesh is addressed that has a grid spacing LAT_INC in northern direction and a grid spacing LON_INC in western direction from the grid point. Exactly this grid mesh is defined by the grid point and addressed regarding the interpolation of a coordinate that lies within. This grid mesh is excluded from the polygonal validity scope of the NTv2 grid.

Figure 5: Usage of shift values for the exclusion of four adjacent grid meshes.

Method 2: Exopolygonal entry in longitudinal and latitudinal shifts of a grid mesh.

With a bilinear interpolation the four adjacent grid points of a coordinate are used. Each may contain exopolygonal entries. So, all in all four grid meshes are addressed and each has one grid spacing LAT_INC in northern and southern direction and one grid spacing LON_INC in western and eastern direction from the grid point. These are the four grid meshes that are arranged around the grid point. Exactly these four grid meshes are excluded from the polygonal validity scope of the NTv2 grid. Thereby grid meshes may also be excluded from polygonal validity in an overlapping order.

Method 1 should be preferred because every single grid mesh in the NTv2 file can be excluded from polygonal validity. Method 2 should be applied when the GIS software used for the creation of a NTv2 grid file does not allow access to accuracy values. In case method 2 is used, an overlap region has to be taken into consideration due to the quadruple size of the addressed area. Both methods can be used separately or together without any special precautions.

The polygonal validity scope is specified by the developer while creating a NTv2 file or subsequently. Therefore the developer inserts exopolygonal entries into the shift or accuracy values of the outside of the required polygon lying grid meshes. The evaluating software then must be so constituted that it can identify the exopolygonal entries and declare them as void.

KilletSoftand parent coordinate grids. On hits the software generates a message, that the coordinate is located outside of the polygonal validity scope of the NTv2 grid file. Common NTv2 files without polygonal validity scopes still work as usual.

In August 2018, the version 18.10 of the Geodetic Development Kit GeoDLL was supplemented with a function that uses shape files to add polygonal validity scopes to any NTv2 files. At the same time, the stand-alone program NTv2Poly was released by KilletSoft, which also adds polygonal validity scopes with the help of shape files to any NTv2 files. In such a shape file, for example, the border outline of a country representing the polygonal validity scope for the NTv2 file used in that country may be available. With the software offered by KilletSoft, every GIS user now can benefit from the advantages of using polygonal scopes in their GIS calculations.

It depends on GIS developers and GIS users whether polygonal validity scopes will be implemented in NTv2 files in the future. A few if-statements and an additional loop structure in the source code of programs with NTv2 support are sufficient for implementing polygonal validity scopes. KilletSoft would like to support developers who are interested in this idea.

Summary
The author presents a simple method for realizing polygonal validity scopes in NTv2 files. Thereby the structure of the NTv2 file remains unchanged. When generating NTv2 files, grid meshes that are located outside of the polygonal validity can be labeled with exopolygonal entries. The benefit of this method is the exclusive addressing of grid meshes inside the intended administrative area and thus the exclusion of localization errors. Software developers can implement the consideration of polygonal validity scopes in GIS software by a few changes in the source code. KilletSoft already provides GIS software which supports polygonal validity scopes. KilletSoft also offers software that allows inserting polygonal validity scopes into existing NTv2 files.

List of figures
Figure 1:NTv2 grid with rectangular validity scope
Author: Fred Killet
Figure 2:NTv2 grid with polygonal validity scope
Author: Fred Killet
Figure 3:Testing coordinates on polygonal validity
Author: Fred Killet
Figure 4:Usage of accuracy values for the exclusion of one single grid mesh
Author: Fred Killet
Figure 5:Usage of shift values for the exclusion of four adjacent grid meshes
Author: Fred Killet

Figures 1 to 5 were generated by the program IncScape 0.91 equipped with a

Author / Writer
Dipl.-Ing. Fred Killet
Escheln 28a
47906 Kempen, Germany
http://www.killetsoft.de/homee.htm

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Datum: 22.09.2018 - 11:39 Uhr
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Dear Sir or Madam,

I ask to make the here described feature article available to our readers by publishing it on your media.

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A ZIP file with the article as MS-WORD file and as PDF file and with all images in different resolutions and graphic formats for the purpose of publication in a print or online medium can be downloaded from the address http://www.killetsoft.de/zip/presse/pr1706_e.zip.

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