I have a list of WGS84 and Gauss coordinates, but how to convert another WGS84 coordinates.
I want to use PROJ for conversion.
What is PROJ string like?
| Name | x | y | H | Lat(N) | Lon(E) |
|------|-----------|----------|---------|-------------|-------------|
| X1 | -1676.071 | 4056.312 | 10.4167 | 31.2203175 | 121.5097212 |
| X2 | -1180.277 | 6330.704 | 10.4985 | 31.22477859 | 121.533594 |
| X3 | 472.067 | 6226.347 | 10.4846 | 31.23968209 | 121.5325094 |
| X4 | -73.008 | 4895.714 | 10.4383 | 31.23477255 | 121.5185389 |
| X5 | -646.523 | 5682.03 | 10.4711 | 31.22959614 | 121.5267891 |
| X6 | -398.196 | 5181.716 | 10.4711 | ? | ? |
Best Answer
First, let's see what the mapping between a Y-X plane and a Lon-Lat plane would look like:
Notes:
Y-X-H coordinates are Cartesian ones.
Since you named it Gaussian coordinates, it is suposed to Y and X are Transverse Mercator projections of the geodetic coordinates.
I am assuming that Y coordinates are Eastings and X coordinates are Northings. Also, H coordinates seems to be orthometric heights. But in a projected system we can go from the ellipsoid to a 2D plane and vice versa.
If you had also ellipsoidal heights we can try a transformation between Cartesian geocentric coordinates (X-Y-Z) and a X-Y-H Cartesian system. Or we can try the projection but using a vertical datum to transform altitudes in heights. For now, we can only discard H coordinates.
Then, we generate the text files to be processed by PROJ:
lonlat.txt:
yx.txt:
Let's try the most simple way to estimate the projection: Using one given point as the center of the projection plane. We will use X4 point because its relative spatial location:
We are defining a custom Transverse Mercator projection, centered on X4, with the X4 coordinates defining false Easting a Northing.
We can see indeterminations in the order of the meter. Analyzing the errors for each point, I think we could calculate the coordinates of X6 with an indeterminacy close to half a meter.
So, I think that X6 is almost a half meter away from LonLat = (121.52154084 31.23183955).
We can start playing with tests. For example, in a projection centered in X4, with X4 coordinates as false Easting and Northing, where is the Y-X = (0 0) point located?
So, can we use LonLat = (121.46715049 31.23542076) as the center of the projection without false Easting and Northing?
We are seeing very good approximations in the Y coordinate, but very bad in the X.
This must be because when moving away from the central meridian, the latitudes deform. But I recognize that I was surprised by the magnitude of these deformation (also, by the accuracy in the Y outputs).
We could try assuming that the projection center is at Y = 5000? In a projection centered in X4, with X4 coordinates as false Easting and Northing, where is the Y-X = (5000 0) point located?
Let's see then project using that center with false Easting 5000:
Ok, very similar than project centered in X4.
Conclusion:
We can easily estimate a custom projection with an indetermination of the order of one meter, with and for the data given.
Accuracy in Eastings and unaccuracy in Northings, when moving away the central meridian, attracts attention. An analysis is still pending in order to find a better solution to the problem.
The recommended action is to consult the information provider about the type of transformation and the parameters used.