1

I have the longitude and latitude of a known point O(x,y) where x and y are obtained from transforming the longitude and latitude from EPSG 4326 to EPSG 32635. This is the observer point. I have another point A(x1, y1) whose coordinates I don't know, but I know the distance from O to A in meters and the azimuth from O to A in radians.

How can I compute the coordinates of A knowing only these?

A function in Qgis in C++ would be the most useful, or at least a mathematical formula would be great.

Improve this question
4
  • Can you treat the measurements to be on a plane or do you need geodesic calculations?
    – bugmenot123
    Commented Nov 6, 2018 at 9:43
  • I think with EPSG 32635 (UTM 35N) we are on a plane anyway.
    – Andreas Müller
    Commented Nov 6, 2018 at 9:45
  • This plugin seems to do it, may be you have to chage your radians to degrees: northrivergeographic.com/qgis-azimuth-distance-plugin
    – Andreas Müller
    Commented Nov 6, 2018 at 9:54
  • For reference: on a plane (projection) use Pythagoras, on a spheroid (e.g. WGS84) refer to the Direct Problem of Vincenty's formulae.
    – geozelot
    Commented Nov 6, 2018 at 13:18

2 Answers 2

Reset to default
1

If QGIS Field calculator is an option;

enter image description here

INPUTS

  • x_32635: your input x-coordinate on EPSG:32645
  • y_32635: your input y-coordinate on EPSG:32645
  • d_m: your input distance in meters
  • az_rad: your input azimuth in radians (nb. clockwise from north)

Calculation

x_new (x-coordinate of new point on UTM35N)

x(translate(geom_from_wkt('POINT('||"x_32635"||' '||"y_32635"||')'),
            "d_m"*sin("az_rad"), "d_m"*cos("az_rad")))

y_new (y-coordinate of new point on UTM35N)

y(translate(geom_from_wkt('POINT('||"x_32635"||' '||"y_32635"||')'),
            "d_m"*sin("az_rad"), "d_m"*cos("az_rad")))

x_4326 (longitude of new point)

x(transform(translate(geom_from_wkt('POINT('||"x_32635"||' '||"y_32635"||')'), 
                       "d_m"*sin("az_rad"), "d_m"*cos("az_rad")), 
            'EPSG:32635', 'EPSG:4326'))

y_4326 (latitude of new point)

y(transform(translate(geom_from_wkt('POINT('||"x_32635"||' '||"y_32635"||')'), 
                       "d_m"*sin("az_rad"), "d_m"*cos("az_rad")), 
            'EPSG:32635', 'EPSG:4326'))
Improve this answer
0
0

Thank you everyone for your suggestions. I found the solution to be

y1 = asin(sin(y1) * qCos(d/R) + cos(y) * sin(d/R) * cos(a));

x1 = x + atan2(sin(a) * sin(d/R) * cos(y), cos(d/R) - sin(y) * sin(y1));

where R is the radius of Earth , d is the distance OA and a is the azimuth.

Improve this answer
2
  • 2
    This is only an approximation because the Earth is not a perfect sphere.
    – AndreJ
    Commented Nov 14, 2018 at 7:23
  • Besides that, the distance in that formula is supposed to be ellipsoidal, not planimetric.
    – Gabriel De Luca
    Commented Jan 14, 2019 at 16:40

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.