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--- georef [2018/10/10 22:57] – [Coordinate Conversion] allchin09
+++ georef [2021/03/11 00:31] (current) – [Coordinate Conversion] allchin09
@@ Line 60: / Line 60: @@
 {{ :agd_tm_p54.jpg | AGD Technical Manual - p54}}
+=== NTv2 Transformation Grids ===
+Another way to transform coordinates is through a transformation grid. This is essentially a fancy version of a 'block shift' where the change (dLat and dLong or dE and dN) between the two CRSs was specified over a large region. An example of a rough block shift is adding 100m to eastings, and 200m to northings when transforming between AMG66 and MGA94.
+A transformation grid uses the same principle but defines the shift at regular intervals throughout a region (eg, different values every minute). The NTv2 transformation grid is a specific file containing this information developed by Canada but now used throughout the world.
+In many cases, you can find an NTv2 grid for the transformation you wish to perform. ICSM has produced multiple grids to transform between GDA94 and GDA202 which they have made [[https://www.icsm.gov.au/datum/gda-transformation-products-and-tools/transformation-grids|freely available online]]. Grids for transforming between AGD66/84 and GDA94 also exist.
+If a grid file does not exist for the transformation you wish to perform, it is possible (but appears difficult) to create your own. Some information about process flows was discussed in 2013 on the [[http://lists.maptools.org/pipermail/proj/2013-January/006540.html|maptools mail list]].
+The Victorian land agency also appear to have a free tool perform transformations called [[https://www.propertyandlandtitles.vic.gov.au/surveying/geodetic-survey/geocentric-datum-of-australia|GDAit]]
+Killet Software has an [[http://www.killetsoft.de/p_ntta_e.htm|NTvtTools]] package for developing and processing NTv2 files in both binary and ASCII formats. A trial version is freely available and a full licence currently costs 160 EUR.
+A paper on the [[http://www2.unb.ca/gge/Personnel/Santos/Santos_SNB_Report_Grid_Shift-NAD27-NAD83.pdf|Generation of a NAD27-NAD83(CSRS) NTv2-type Grid Shift File for New Brunswick]] is also of interest.
+== An example - ANG to GDA94 ==
+The trial version of [[http://www.killetsoft.de/p_svpa_e.htm|SEVENPAR]] by Killet Software was used to produce local parameters for a 7 parameter Helmann transformation. The trial version is limited to only 25 common points (locations known in both source and target CRS) so ones near Sydney sourced from the NGRS were used.
+It's important to note the convention used (either Coordinate-Frame Rotation, or Position Vector) to define the three rotation parameters (signs are flipped between them).
+The output in position vector format was:
+^Parameter^Value^Units^
+|dx|195.056526|m|
+|dy|-112.959677|m|
+|dz|-172.456394|m|
+|rx|3.59354054|rad, seconds|
+|ry|5.39693644|rad, seconds|
+|rz|-1.34857381|rad, seconds|
+|s|-3.2756552|ppm|
+Combining these with the known values of the ellipsoid parameters of the ANS, a custom CRS can be defined in PROJ to allow transform between ANG and GDA94 coordinates. This can then be used in QGIS to 'reproject' ANG georeferenced rasters into a GDA94 CRS.
+The following PROJ string was used to define the ANG CRS:
+''+proj=longlat +a=6378339.78 +rf=294.26 +towgs84=195.056526,-112.959677,-172.456394,3.59354054,5.39693644,-1.34857381,-3.2756552 +no_defs''
+This CRS is then available to be applied to any raster.
 ==== Coordinate Conversion ====
-[[https://proj4.org/|PROJ]] is a useful program here.
+[[https://proj.org/|PROJ]] is a useful program here.
+Note that PROJ is being updated and dramatically changed - a useful overview [[https://www.gaia-gis.it/fossil/libspatialite/wiki?name=PROJ.6|here]].
 Handy tables of parameters can be found [[https://en.wikibooks.org/wiki/PROJ.4|here]]
-'Clarke Coordinate' have the following parameters
+=== Coordinate coversion for 1 inch to the mile millitary maps (ANG) ===
+'Clarke Coordinates' or the 'ANG' (Australian National Grid) have the following parameters:
 ^Parameter       ^ Value         ^ Units        ^
 | ellipsoid      | Clarke 1858   |              |
 | a              | 20,926,348    | british feet |
-| a              |  6,378,339.78 | metres       |
+| a              | 6,378,339.78  | metres       |
-| b              |  20,855,233   | british feet |
+| b              | 20,855,233    | british feet |
-| b              |  6,356,663.92 | metres       |
+| b              | 6,356,663.92  | metres       |
-| 1/f            |        294.26 |              |
+| 1/f            | 294.26        |              |
 | projection     | transverse mercator|         |
-| false easting  |    400,000    | yards        |
+| false easting  | 400,000       | yards        |
-| false easting  |    365,759.36 | metres       |
+| false easting  | 365,759.36    | metres       |
-| false northing |    800,000    | yards        |
+| false northing | 800,000       | yards        |
-| false northing |    731,518.73 | metres       |
+| false northing | 731,518.73    | metres       |
-| zones          |        1 to 8 |              |
+| zones          | 1 to 8        |              |
-| zone width     |          5    | degrees      |
+| zone width     | 5             | degrees      |
 | zone 1 central meridian| 116E  | degrees      |
-| zone latitude origin |    34S  | degrees      |
+| zone latitude origin | 34S     | degrees      |
-| scale factor   |          1    |              |
+| scale factor   | 1             |              |
+On these maps, Sydney Observatory was used as a datum for triangulation, with the following values:
+^Format ^Latitude          ^Longitude         ^
+|DMS    |S 33d 51m 41.10s  |E 151d 12m 17.85s |
+|DD     |S 33.861417d      |E 151.204958d     |
+The [[http://www.ga.gov.au/ngrs/imf.jsp?site=ngrs|NGDB]] provides the following values of the observatory in different datums:
+^Datum  ^Latitude            ^Longitude           ^Easting       ^Northing   ^
+|Clarke |S33°51' 41.107"     |E151°12' 17.993"    |420746.19     |816789.65  |
+|AGD66  |S33°51' 40.2924"    |E151°12' 12.3136"   |333809.38     |6251769.51 |
+|AGD84  |S33°51' 40.3241"    |E151°12' 12.2557"   |333807.91     |6251768.51 |
+|GDA94  |S33°51' 34.610232"  |E151°12' 16.470597" |333913.76     |6251959.42 |
 Note:
@@ Line 91: / Line 149: @@
     * Tasmania apparently used the Clarke foot which equalled 0.3047972654 meters
     * Others appear to use today's standard conversion of 0.3048
-  * Need to confirm what the approporiate conversion factor for the yards used in the false easting and northing should be (3*british foot or 0.9144)
+  * PROJ units:
-    * PROJ allows you to specify your output units, however, it doesn't allow you to define them. It defines yd=0.9144 so I've supplied the false e/n using in metres using the same conversion factor. Testing shows that the conversion is approximately correct near the true origin, however, I think it will grow larger the further away. Using the british feet conversion factor for both false e/n and output should correct this.
+    * Input parameter values (eg, for ellipsoid or false origin)
+      * Appears that they can only be specified in metres
+      * If using other units, convert to metres before supplying parameter
+    * Output values (eg, eastings, northings, heights, lat, long)
+      * Allows you to specify your output units using +units-parameter, where the value is chosen from a set list (see ''proj -lu'', default is metres)
+      * Alternatively, use the ''+to_meter-parameter'' instead and specify the value you multiple your unit by to get 1 metre (eg, ''+to_meter=100'' would output centimetres)
+As an example, the below PROJ code will convert a lat,long (S 33.75, E 151.5) to E,N for zone 8 (cm=151e) of the ANG:
+''echo 151d30e 33d45s | proj +proj=tmerc +lat_0=34s +lon_0=151e +k_0=1 +a=6378339.78 +rf=294.26 +to_meter=0.91439841 +x_0=365759.36 +y_0=731518.73''
+Which returns: E=450,666.78 N=830,202.64
+An explaination of parameters is as follows:
+=== Parameters ===
-Using these details, the below PROJ code will convert lat,long to E,N for a given zone.
+== +proj ==
+  * Description: Projection name
+  * Value: tmerc
+  * Value description:
+    * [[https://proj.org/operations/projections/tmerc.html|Transverse mecator]]
+    * Projection used by ANG from June 1936
+    * Note: prior to 1936, a polyconic projection was used
-''+proj=tmerc +south +lat_0=-34 +lon_0=[ZONE CM] +k_0=1 +a=6378339.78 +b=6356663.92 +units=yd +x_0=365760 +y_0=731520''
+== +lat_0 ==
+  * Description: Latitude of projection centre or true origin (TO) of projection.
+  * Value: 34s
+  * Value description:
+    * The true origin of ANG is 34 degrees south
+    * This is consistant across all 8 zones in Australia
-As an example, converting the lat,long (S 33.75, E 151.5) to E,N for zone 8:
+== +lon_0 ==
+  * Description: Longitude of projection centre or true origin (TO) of projection. Also called central meridian (CM).
+  * Value: 151e (for zone 8 only)
+  * Value description:
+    * Each zone has a different CM. ANG has 8 zones covering the width of Australia
+    * Zone 8 covers the East of NSW
+    * Zones and their CM values can be found in the table below
+    * Each zone is 5 degrees wide in longitude, starting at 113d30e and ending at 153d30e
-''echo 151.5 -33.75 | proj +proj=tmerc +lat_0=34s +lon_0=151 +k_0=1 +a=6378339.78 +b=6356663.92 +units=yd +x_0=365760 +y_0=731520''
+^Zone Number  ^Western Longitude   ^Eastern Longitude ^Zone Central Meridian^
+|1            |113d30e             |118d30e           |116de                |
+|2            |118d30e             |123d30e           |121de                |
+|3            |123d30e             |128d30e           |126de                |
+|4            |128d30e             |133d30e           |131de                |
+|5            |133d30e             |138d30e           |136de                |
+|6            |138d30e             |143d30e           |141de                |
+|7            |143d30e             |148d30e           |146de                |
+|8            |148d30e             |153d30e           |151de                |
-Returns: E=450,666.69 N=830,202.59
+== +k_0 ==
+  * Description: Scale factor at the central meridian
+  * Value: 1 (default value for tmerc in PROJ)
+  * Value description:
+    * ANG has a scale factor (SF) of 1 at the central meridian
+    * This means that on the CM, a measured distance on earth will equal the corresponding grid distances
+    * East and west of the CM, a measured distance on earth will be less than the corresponding grid distances
-A more accurate version when converting points a further distance away from the true origin makes use of the -m (multiply) flag for the PROJ command to scale the output to the correct yard units.
+== +a ==
+  * Description: Semimajor radius of the ellipsoid axis
+  * Value: 6378339.78
+  * Value description:
+    * Based on Clarke 1858 ellposid with a defined as 20,926,348 british feet
+    * A conversion factor of 0.30479947 metres per british foot = 6,378,339.78m
-''echo 151.5 -33.75 | proj +proj=tmerc +south +lat_0=34s +lon_0=151 +k_0=1 +a=6378339.78 +b=6356663.92 +x_0=365759.36 +y_0=731518.73 -m 1.0936152''
+== +rf ==
+  * Description: Inverse flattening of the ellipsoid
+  * Value: 294.26
+  * Value description:
+    * Based on Clarke 1858 ellposid where the inverse flattening was defined as 294.26
-Returns: E=450,666.78 N=830,202.64
+== +to_meter ==
+  * Description: Horizontal unit value for output coordinates
+  * Value: 0.91439841
+  * Value description:
+    * The ANG coordinates are in yards
+    * 1 yard = 3 british feet = 0.30479947 * 3 = 0.91439841 yards per metre
+== +x_0 ==
+  * Description: False easting
+  * Value: 365759.36
+  * Value description:
+    * ANG has a false easting of 400,000 yards west of the true origin
+    * Converting into metres is 400,000 / 0.91439841 = 365,759.36 metres
+== +y_0 ==
+  * Description: False northing
+  * Value: 731518.73
+  * Value description:
+    * ANG has a false northing of 800,000 yards south of the true origin
+    * Converting into metres is 800,000 / 0.91439841 = 731,518.73 metres