# Point Coordinates Conversion with unknown system

I've been using QGis for few weeks now. Although this site always came very helpful, I can't find solution to my recent problem:

I have few points, and know their coordinates in "WGS-84" and "ISN-93" systems. Those points also have specified coordinates in "Local" system.

The problem is that there are also few points that only have "Local" coordinates, and I would like to find their "ISN-93" coordinates.

How can I do it?

*for example:

point1 ISN93 (685320.253,420614.733) Local (-3537.239,2284.487)

point2 ISN93 (685841.253,420586.536) Local (-3016.528,2248.842)

point3 ISN93 (?,?) Local (-5187.996,2584.508)

I was trying to use simple geometry, but when I measure distance between points, ISN93 system gives slightly different lengths than Local (difference vary between lengths to up to 0,01% of its value), so it's no use.

• Do you have access to the surveyor or other person who created the local grid? Sometimes they also have the transformation values to convert to a more well-known coordinate reference system. Otherwise, you might have to use something like georeferencing, but for vector data. – mkennedy Jul 10 '15 at 16:20

A very simple brute force approach:

1. take the first points coordinates and convert them from ISN93 / Lambert 1993 to WGS84 degrees using cs2cs in the OSGEO4W shell

`cs2cs +init=epsg:3057 +to +init=epsg:4326 -f "%%.8f" <ISN93.txt >WGS84.txt`

2. build a local omerc CRS on that point, with the "local coordinates" as false Easting and Northing

3. convert the point coordinates into this custom CRS

`cs2cs +init=epsg:3057 +to +proj=omerc +lonc=-15.1778877053125 +lat_0=64.2376322211738 +alpha=0.01 +gamma=0 +k=1.0 +x_0=-3537.239 +y_0=2284.487 +datum=WGS84 +units=m +no_defs -f "%%.8f" <ISN93.txt >local.txt`

4. calculate the offset X and Y in meters for the second point

5. play with `+alpha` and `+k` values to minimize the offsets

This way I get with an offset of 2mm:

``````+proj=omerc +lonc=-15.1778877053125 +lat_0=64.2376322211738 +alpha=2.646 +gamma=0 +k=1.00032 +x_0=-3537.239 +y_0=2284.487 +datum=WGS84 +units=m +no_defs
``````

I assume your coordinates are in East-North order, and you don't have to care about tectonic moves between ISN93 and WGS84. On an Openstreetmap background, your local grid looks like this: 