Plotting points using x,y coordinates from point on map in QGIS?

Question

In my line of work, fieldworkers measure specific drilling points and give us x,y coordinates from easily identifiable reference points (the corner of a house for example).

Is it possible to plot their reference point on a map (say a satellite image), define an axis and then insert the x,y coordinates they provided (in meters) to find the point they plotted on the map?

I'm using QGIS.

Answer 1

You need to know the coordinate reference system (CRS) in which they're providing x,y coordinates. This could be an EPSG code. Then add your x,y points in QGIS; here's some guidance on that. Finally, you can use "Reproject Layer" in the Processing Toolbox to project your x,y coordinates to EPSG:4326 (most common lat/lon spheroid).

Personally, I would use Python:

import ogr, osr
import numpy as np
def transform_coordinates(xs, ys, inputEPSG, outputEPSG):

    if inputEPSG == outputEPSG:
        return xs, ys

    # Create an ogr object of multipoints
    points = ogr.Geometry(ogr.wkbMultiPoint)
    for i in range(len(xs)):
        point = ogr.Geometry(ogr.wkbPoint)
        point.AddPoint(float(xs[i]), float(ys[i]))
        points.AddGeometry(point)

    # Create coordinate transformation
    inSpatialRef = osr.SpatialReference()
    inSpatialRef.ImportFromEPSG(inputEPSG)

    outSpatialRef = osr.SpatialReference()
    outSpatialRef.ImportFromEPSG(outputEPSG)

    coordTransform = osr.CoordinateTransformation(inSpatialRef, outSpatialRef)

    # transform point
    points.Transform(coordTransform)

    xyout = np.array([0,0,0])
    for i in range(len(xs)):
        xyout = np.vstack((xyout, points.GetGeometryRef(i).GetPoints()))
    xyout = xyout[1:,0:2]

    return xyout[:,0], xyout[:,1]

Answer 2

1. Find the given reference point using satellite imagery and find its coordinates in the appropriate UTM zone. UTM is based on meters, and makes this process a little tidier. We'll refer to this point as ( x' , y' ).
2. Make sure you know the azimuth of the positive direction of the y axis of the field grid, which we'll refer to as α. If your field workers were nice, this is should hopefully line up with true north. Whatever the bearing, cross your fingers that they were accounting for declination.

3. Open your site coordinates table in QGIS (assuming X and Y values are in their own fields) and perform the following in the Field Calculator. This will assign coordinates that correspond to the reference point, as well as apply a rotational matrix to account for any rotation of the grid.

   1. Create new field "Eastings" with the expression
      "Field_X" * cos(radians(-α)) - "Field_Y" * sin(radians(-α)) + x'

   2. Create new field "Northings" with the expression
      "Field_X" * sin(radians(-α)) + "Field_Y" * cos(radians(-α)) + y'

4. Your new fields will be virtual ones, so save the table as a new CSV to make them permanent.

5. In the Processing toolbox, select QGIS geoalgorithms > Vector creation tools > Points layer from table.

6. Use your new CSV as the input, select Eastings as X field, Northings as Y field, and match the Target CRS to the coordinates of your reference point.

You should now have your points properly georeferenced. Below is an example of this process, using a random reference point, a 5m x 20m grid, rotated at sixty degrees. Any points from within this grid, run through the same process, will now have a proper coordinate reference.