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update easting and northing using distance and bearing

Posted on 2009-07-09
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Hi,
Could anyone suggest a formula / method for updating eastings and northings using a distance and a bearing?
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Question by:gardnerw
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by:Jaime Olivares
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at a first approach, I think you must always operate coordinates as latitude/longitude and then apply conversion to UTM
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by:oobayly
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When you say Northing & Easting, do you mean Lat/Lon or in some kind of projection?

The following page is one I've gotten a lot of information from. To project a point a given distance & bearing from a given coordinate, you could use the equations to determine destination using Rhumb lines.
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by:oobayly
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by:gardnerw
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Hi sorry for such a late response to your posts,

The data is on OSGB70 projection, it would be sitting within a variety of GIS applications. Ideally i would like to be able to export it to a xls, csv or  dxf then specify a bearing and a distance to update specific points.

Many Thanks
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oobayly earned 500 total points
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Unfortunately I'm not familiar with OSGB70, as I normally deal with OSGB70 & WGS84. However:

OSGB70 & ODGB36 share the same ellipsoid:
OSGB70: http://www.eye4software.com/products/coordinatecalculator/datum/175/
OSGB36: http://www.eye4software.com/products/coordinatecalculator/datum/12/

This page gives you some idea of how to do the transformation:
http://www.linz.govt.nz/geodetic/conversion-coordinates/geodetic-datum-conversion/datum-transformation-equations/index.aspx

The nice thing is that as the transformation and rotation parameters are all zero (for WGS84 & OSGB70), you only have to convert your coordinates in OSGB70 to Cartesian (using the Airy ellipsoid), and then straight back to WGS84 coordinates (using the WGS84 ellipsoid).
Actually, I'm guessing that your data is already cartesian coordinates as you mentioned Eastings & Northings, so you should only have to use the ToWGS84 method.

Then operating on the WGS84 using the equations in the 1st set of links I posted.

private static void FromOSGB70(double lat, double lon, double h,

  out double x, out double y, out double z) {

  // WGS coordinates in radians

  double phi = lat * Math.PI / 180;

  double lambda = lon * Math.PI / 180;

 

  // Airy 1830 ellipsoid parameters

  // http://www.eye4software.com/products/coordinatecalculator/datum/175/

  // Semi-major axis

  double a = 6377563.396;

  // Flattening

  double f = 1 / 299.3249646;

  // Eccentricity squared

  double e2 = (2 * f) - (f * f);

 

  double nu = a / Math.Sqrt(1 - e2 * Math.Pow(Math.Sin(phi), 2));

 

  x = (nu + h) * Math.Cos(phi) * Math.Cos(lambda);

  y = (nu + h) * Math.Cos(phi) * Math.Sin(lambda);

  z = ((nu * (1 - e2)) + h) * Math.Sin(phi);

}

 

private static void ToWGS84(double x, double y, double z,

  out double lat, out double lon, out double h) {

  // WGS84 ellipsoid parameters

  // http://www.eye4software.com/products/coordinatecalculator/datum/7/

  // Semi-major axis

  double a = 6378137;

  // Flattening

  double f = 1 / 298.257223563;

  // Eccentricity squared

  double e2 = (2 * f) - (f * f);

   

  double p = Math.Sqrt((x * x) + (y * y));

  double r = Math.Sqrt((p * p) + (z * z));

  double mu = Math.Atan2(

    z * ((1 - f) + (e2 * a / r)),

    p

    );

 

  double lambda= Math.Atan2(y, x);

  double phi = Math.Atan2(

    (z * (1 - f)) + (e2 * a * Math.Pow(Math.Sin(mu), 3)),

    (1 - f) * (p - (e2 * a * Math.Pow(Math.Cos(mu), 3)))

    );

  h = (p * Math.Cos(phi)) + (z * Math.Sin(phi)) -

    (a * Math.Sqrt(1 - (e2 * Math.Pow(Math.Sin(phi), 2))));

 

  lat = phi * 180 / Math.PI;

  lon = lambda * 180 / Math.PI;

}

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Author Closing Comment

by:gardnerw
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Cheers!
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