At 05:51 PM 6/11/02 -0800, Carl Schaefer wrote: >I'm looking for the calculations of grid convergence between UTM >grid north and true north given a specific Lat/Long. ...I need the math >behind >it.
From one perspective, the math is easier than you might think. In any programming environment where you can project points, you can readily compute all the local properties of a projection, including the convergence and the parameters of Tissot's indicatrix. These properties are defined in terms of partial derivatives of the projection, which in all practical cases are extremely well approximated by finite differences computed over distances of a few meters. Thus, for the convergence, simply create a short north-pointing geodesic centered at the point in question and project it. A few years ago I published working code to compute convergence using this technique (http://arcscripts.esri.com/details.asp?dbid=3C29F07E-7839-11D4-943200508B0CB419) . The bad news is that it was written for an ESRI product (ArcView) but the good news is that the code is transparent and simple enough that you should have no problem porting it. Here are the guts of the calculation. The first three executable lines do all the work; the rest is a routine angle calculation. Input is a point object in lat-lon, ptU, and a projection object, thePrj: ' ' Create an "infinitesimal" north-pointing geodesic, ' project it, and obtain the projected direction vector. ' ptW = 0@ (1/111000) ' A displacement of about one meter, measured in degrees linNorth = Line.Make(ptU - ptW, ptU + ptW).ReturnProjected(thePrj) ptV = linNorth.Along(100) - linNorth.Along(0) ' Vector from start to end of the projected geodesic ' ' Compute the angle made with grid east. ' t = ptV.GetY/ptV.GetX ' Tangent radA = t.ATan ' Between -pi/2 and pi/2 angA = radA / Number.GetPi * 180 ' Between -90 and 90 if (ptV.GetX < 0) then angA = angA + 180 ' Between 90 and 270 end ' ' Convert to the convergence angle (degrees east of north) ' for the grid north relative to true north. ' angA = angA - 90 ' Between -180 and 180 ' end of example --Bill Huber --------------------------------------------------------------------- List hosting provided by Directions Magazine | www.directionsmag.com | To unsubscribe, e-mail: [EMAIL PROTECTED] For additional commands, e-mail: [EMAIL PROTECTED]
