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Math for converting coordinates

DuncanNisbett

I know that I can use the geometryService to convert between 2 different coordinate systems, but I'd like to reduce the number of calls made to the server to update coordinates. I'm trying to convert from wkid 32149 (NAD_1983_StatePlane_Washington_South_FIPS_4602) to Latitude/Longitude 4326. Does anyone know where I can find the math so I can create my own function to convert the coordinates? I've tried my Google Kung Fu, but come up dry.

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DavidKitten

I stumbled upon this old post while working on a similar project and was able to get Jeff's code to work for the first function(convertSPtoLL_LLC) by adding in the false northing variable and Y coordinate correction.

New lines are in red.

org.mymanatee.common.latlong.convertSPtoLL_LLC = function (uX,uY) {
var a = 20925604.48; //major radius of ellipsoid, map units (NAD 83)
var ec = 0.08181905782; //eccentricity of ellipsoid (NAD 83)
var angRad = 0.01745329252; //number of radians in a degree
var pi4 = Math.PI / 4; //Pi / 4
var p0 = 24.333333 * angRad; //latitude of origin
var p1 = 24.333333 * angRad; //latitude of first standard parallel
var p2 = 31.5 * angRad; //latitude of second standard parallel
var m0 = -82.000000 * angRad; //central meridian
var x0 = 656166.666667; //False easting of central meridian, map units
var y0 = value; //False northing of central meridian, map units
// Calculate the coordinate system constants.
with (Math) {
var m1 = cos(p1) / sqrt(1 - (pow(ec,2)) * pow(sin(p1),2));
var m2 = cos(p2) / sqrt(1 - (pow(ec,2)) * pow(sin(p2),2));
var t0 = tan(pi4 - (p0 / 2));
var t1 = tan(pi4 - (p1 / 2));
var t2 = tan(pi4 - (p2 / 2));
t0 = t0 / pow(((1 - (ec * (sin(p0)))) / (1 + (ec * (sin(p0))))),ec/2);
t1 = t1 / pow(((1 - (ec * (sin(p1)))) / (1 + (ec * (sin(p1))))),ec/2);
t2 = t2 / pow(((1 - (ec * (sin(p2)))) / (1 + (ec * (sin(p2))))),ec/2);
var n = log(m1 / m2) / log(t1 / t2);
var f = m1 / (n * pow(t1,n));
var rho0 = a * f * pow(t0,n);
// Convert the coordinate to Latitude/Longitude.
// Calculate the Longitude.
var uX = uX - x0;
var uY = uY - y0;
var pi2 = pi4 * 2;
var rho = sqrt(pow(uX,2) + pow((rho0 - uY),2));
var theta = atan(uX / (rho0 - uY));
var txy = pow((rho / (a * f)),(1 / n));
var lon = (theta / n) + m0;
var uX = uX + x0;
// Estimate the Latitude
var lat0 = pi2 - (2 * atan(txy));
// Substitute the estimate into the iterative calculation that
// converges on the correct Latitude value.
var part1 = (1 - (ec * sin(lat0))) / (1 + (ec * sin(lat0)));
var lat1 = pi2 - (2 * atan(txy * pow(part1,(ec/2))));
while ((abs(lat1 - lat0)) > 0.000000002) {
lat0 = lat1;
part1 = (1 - (ec * sin(lat0))) / (1 + (ec * sin(lat0)));
lat1 = pi2 - (2 * atan(txy * pow(part1,(ec/2))));
}
// Convert from radians to degrees.
var Lat = lat1 / angRad;
var Lon = lon / angRad;
//alert(Lat);
//alert(Lon);
//Round the latitude and longitude
//lat = (CLng(lat * 100000)) / 100000;
//lon = (CLng(lon * 100000)) / 100000;
Lat = Lat.toPrecision(7);
Lon = Lon.toPrecision(8);
return [Lat,Lon];
}
};
//End of Code for converting map units to decimal degrees.

DuncanNisbett

One of the original sources is John Snyder's Map Projections: A Working Manual. It also contains the state plane parameter values (NAD83 changes from NAD27 are listed in an appendix).

If you use Jeff Pace's code as a template, please note that the "map units" of the first section are in US survey feet, not meters.

Melita

I admit to feeling a bit overwhelmed, this doesn't appear to be as straightforward a process as I had hoped. The PDF has a lot of information and am unable to process until I can really sit down and read it.

I took a look at the 5 functions that Jeff Pace included and no single function performs an accurate or even close conversion. Do I need to use a combination of these functions? If so, what combination should I be using?

JeffPace1

that is correct

MelitaKennedy

One of the original sources is John Snyder's Map Projections: A Working Manual. It also contains the state plane parameter values (NAD83 changes from NAD27 are listed in an appendix).

If you use Jeff Pace's code as a template, please note that the "map units" of the first section are in US survey feet, not meters.

Melita

DuncanNisbett

is washington south transverse mercator or lambert?

It's Lambert Conformal Conic

JeffPace1

also

    org.mymanatee.common.latlong.convertWebMercAuxtoLL = function (uX,uY) {
  //code completely borrowed from http://www.frosties.com/index.php?option=com_mojo&Itemid=45&p=7
   // lat and long backwards on link for some reason
   //alert("IN CONVERSION");
  var x = uX;
   // alert("IN CONVERSION2");
  var  y = uY;
   
 var num3 = x / 6378137.0;
 var num4 = num3 * 57.295779513082323;
 //alert("IN CONVERSION3");
 var num5 = Math.floor(((num4 + 180.0) / 360.0));
 var num6 = num4 - (num5 * 360.0);
 //alert("IN CONVERSION4");
var  num7 = 1.5707963267948966 - (2.0 * Math.atan(Math.exp((-1.0 * y) / 6378137.0)));
var lon  = num6;
var lat = num7*57.295779513082323;



   // alert([lat,lon]);


    return [lat,lon];
    };
    
        org.mymanatee.common.latlong.convertLLtoWebMercAux = function (lat,lon) {
  //code completely borrowed from Dr Bill Hazelton's HP-33S calculator
    // http://homepage.mac.com/nwjh/HP-33S/ 10-Feb-10

    //code completely borrowed from Dr Bill Hazelton's HP-33S calculator
    // http://homepage.mac.com/nwjh/HP-33S/ 10-Feb-10
var num = lon * 0.017453292519943295;
var x = 6378137.0 * num;
var a = lat * 0.017453292519943295;

var mercatorX = x;
var mercatorY = 3189068.5*Math.log((1.0 + Math.sin(a))/(1.0 - Math.sin(a)));

//    alert(londd);

    return [mercatorX,mercatorY];
    };

JeffPace1

I know that I can use the geometryService to convert between 2 different coordinate systems, but I'd like to reduce the number of calls made to the server to update coordinates. I'm trying to convert from wkid 32149 (NAD_1983_StatePlane_Washington_South_FIPS_4602) to Latitude/Longitude 4326. Does anyone know where I can find the math so I can create my own function to convert the coordinates? I've tried my Google Kung Fu, but come up dry.

is washington south transverse mercator or lambert?

/* 
 * To change this template, choose Tools | Templates
 * and open the template in the editor.
 */

dojo.provide("org.mymanatee.common.latlong");

dojo.require("dojo.string");

org.mymanatee.common.latlong.convertSPtoLL_LLC = function (uX,uY) {
var a = 20925604.48;     //major radius of ellipsoid, map units (NAD 83)
var ec = 0.08181905782;    //eccentricity of ellipsoid (NAD 83)
var angRad = 0.01745329252;   //number of radians in a degree
var pi4 = Math.PI / 4;   //Pi / 4
var p0 = 24.333333 * angRad;    //latitude of origin
var p1 = 24.333333 * angRad;    //latitude of first standard parallel
var p2 = 31.5 * angRad;   //latitude of second standard parallel
var m0 = -82.000000 * angRad;   //central meridian
var x0 = 656166.666667;   //False easting of central meridian, map units

// Calculate the coordinate system constants.
with (Math) {
var m1 = cos(p1) / sqrt(1 - (pow(ec,2)) * pow(sin(p1),2));
var m2 = cos(p2) / sqrt(1 - (pow(ec,2)) * pow(sin(p2),2));
var t0 = tan(pi4 - (p0 / 2));
var t1 = tan(pi4 - (p1 / 2));
var t2 = tan(pi4 - (p2 / 2));
t0 = t0 / pow(((1 - (ec * (sin(p0)))) / (1 + (ec * (sin(p0))))),ec/2);
t1 = t1 / pow(((1 - (ec * (sin(p1)))) / (1 + (ec * (sin(p1))))),ec/2);
t2 = t2 / pow(((1 - (ec * (sin(p2)))) / (1 + (ec * (sin(p2))))),ec/2);
var n = log(m1 / m2) / log(t1 / t2);
var f = m1 / (n * pow(t1,n));
var rho0 = a * f * pow(t0,n);

// Convert the coordinate to Latitude/Longitude.

// Calculate the Longitude.
var uX = uX - x0;
var pi2 = pi4 * 2;

var rho = sqrt(pow(uX,2) + pow((rho0 - uY),2));
var theta = atan(uX / (rho0 - uY));
var txy = pow((rho / (a * f)),(1 / n));
var lon = (theta / n) + m0;
var uX = uX + x0;

// Estimate the Latitude
var lat0 = pi2 - (2 * atan(txy));

// Substitute the estimate into the iterative calculation that
// converges on the correct Latitude value.
var part1 = (1 - (ec * sin(lat0))) / (1 + (ec * sin(lat0)));
var lat1 = pi2 - (2 * atan(txy * pow(part1,(ec/2))));

while ((abs(lat1 - lat0)) > 0.000000002) {
  lat0 = lat1;
  part1 = (1 - (ec * sin(lat0))) / (1 + (ec * sin(lat0)));
  lat1 = pi2 - (2 * atan(txy * pow(part1,(ec/2))));
  }

// Convert from radians to degrees.
var Lat = lat1 / angRad;
var Lon = lon / angRad;

//alert(Lat);
//alert(Lon);

//Round the latitude and longitude
//lat = (CLng(lat * 100000)) / 100000;
//lon = (CLng(lon * 100000)) / 100000;

Lat = Lat.toPrecision(7);
Lon = Lon.toPrecision(8);

return [Lat,Lon];

}
};
//End of Code for converting map units to decimal degrees.


//COnversion to LL from State Plane for Florida West (Transverse mercator, not Lamberic
org.mymanatee.common.latlong.convertSPtoLL_TM = function (uX,uY) {

    //code completely borrowed from Dr Bill Hazelton's HP-33S calculator
    // http://homepage.mac.com/nwjh/HP-33S/ 10-Feb-10
 var    metconv = 1200/3937; //exact survey feet to meters
 var    uXm = uX*metconv;
 var    uYm = uY*metconv;

  var   a = 6378137.000000000000000000; // semimajor axis from ESRI
 var    b =  6356752.314140356100000000; // semiminor axis from ESRI
 var    e2 = ((a*a)-(b*b))/(a*a);//ellipsoid
 var    p0 = 24.333333;    //latitude of origin
 var    m0 = -82.000000;   //central meridian in degrees
 var    x0 = 656166.666667;  //False easting of central meridian, map units
 var    y0 = 0; //False Northing
 var    k0 = 0.999941;    //central scale factor k0
 var    x0m = x0*metconv;
 var    y0m = y0*metconv;

 var    p0rad = p0*Math.PI/180;
 var    m0rad = m0*Math.PI/180;
 var    e = Math.sqrt(e2);


 var    b = a * Math.sqrt(1-e2);
 var    n = (a - b)/(a + b);
 var    G = a*(1-n)*(1-(n*n))*(1+2.25*(n*n)+225/64*(n*n*n*n))*Math.PI/180;
 var    A0 = 1-e2/4-3*(e2*e2)/64-5*(e2*e2*e2)/256;
 var    A2 = 3/8*(e2+(e2*e2)/4+15*(e2*e2*e2)/128);
var     A4 = 15/256*((e2*e2)+0.75*(e2*e2*e2));
var     A6 = 35*(e2*e2*e2)/3072;
var     lat0 = p0rad;
 var    m0atlat0 = a*(A0*lat0-A2*Math.sin(2*lat0)+A4*Math.sin(4*lat0)-A6*Math.sin(6*lat0))
 var    NminusNo = uYm - y0m;

var     m = m0atlat0+NminusNo/k0;
var     s = (m/G)*Math.PI/180;
 var    fpl1 = (1.5*n-27*(n*n*n)/32)*Math.sin(2*s);
  var   fpl2 = (21*(n*n)/16-55*(n*n*n*n)/32)*Math.sin(4*s);
 var    fpl3 = 151*(n*n*n)/96*Math.sin(6*s);
 var    fpl4 = 1097*(n*n*n*n)/512*Math.sin(8*s);
  var   footptlat = (s+fpl1+fpl2+fpl3+fpl4);
  var   rho = a*(1-e2)/Math.pow((1-e2*Math.sin(footptlat)*Math.sin(footptlat)),1.5);
 var    nu = a/(Math.sqrt(1-e2*Math.sin(footptlat)*Math.sin(footptlat)));
 var    psi = nu/rho;
  var   t = Math.tan(footptlat);
 var    E = uXm-x0m;
 var    x = E/k0/nu;

 var    lat1 = x*E/2;
 var    lat2 = (x*x*x)*E/24*(-4*psi*psi+9*psi*(1-t*t)+12*t*t);
  var   lat3 = (x*x*x*x*x)*E/720*(8*(psi*psi*psi*psi)*(11-24*(t*t))-12*(psi*psi*psi)*(21-71*(t*t))+15*(psi*psi)*(15-98*(t*t)+15*(t*t*t*t))+180*psi*(5*(t*t)-3*(t*t*t*t))+360*(t*t*t*t));
 var    lat4 = (x*x*x*x*x*x*x)*E/40320*(1385+3633*(t*t)+4095*(t*t*t*t)+1575*(t*t*t*t*t*t));
 var    lat = footptlat-(t/k0/rho)*(lat1-lat2+lat3-lat4);
 var    latdd = lat*180/Math.PI;

 var    w1 = x/Math.cos(footptlat);
 var    w2 = Math.pow(-1*x,3)/6*(psi+2*t*t)/Math.cos(footptlat);
 var    w3 = Math.pow(x,5)/120/Math.cos(footptlat)*(-4*(psi*psi*psi)*(1-6*(t*t))+(psi*psi)*(9-68*(t*t))+72*(psi)*(t*t)+24*(t*t*t*t));
 var    w4 = Math.pow(-1*x,7)/5040/Math.cos(footptlat)*(61+662*(t*t)+1320*(t*t*t*t)+720*(t*t*t*t*t*t));
 var    w = w1+w2+w3+w4;
 var    lon = (-1*m0)*Math.PI/180-w;
 var    londd = (-1*lon)*180/Math.PI;


//    alert(londd);

    return [latdd,londd];
    };

org.mymanatee.common.latlong.convertLLtoSP_TM = function (lat,lon) {
   var metconv = 1200/3937; //exact survey feet to meters

   var a = 6378137.000000000000000000; // semimajor axis from ESRI
   var b =  6356752.314140356100000000; // semiminor axis from ESRI
   var e2 = ((a*a)-(b*b))/(a*a);//ellipsoid
   var p0 = 24.333333;    //latitude of origin
   var m0 = -82.000000;   //central meridian in degrees
   var x0 = 656166.666667;  //False easting of central meridian, map units
   var y0 = 0; //False Northing
   var k0 = 0.999941;    //central scale factor k0
   var e = Math.sqrt(e2);
    
   var lat0rad_lat0=p0*Math.PI/180;
   var latrad_lat=lat*Math.PI/180;
   var rho_lat=a*(1-e2)/Math.pow((1-e2*Math.sin(latrad_lat)*Math.sin(latrad_lat)),1.5);
 //   rho_lat0=a*(1-e2)/Math.pow((1-e2*Math.sin(lat0rad_lat0)*Math.sin(lat0rad_lat0)),1.5); not used
 var   nu_lat=a/(Math.sqrt(1-e2*Math.sin(latrad_lat)*Math.sin(latrad_lat)));
 //   nu_lat0=a/(Math.sqrt(1-e2*Math.sin(lat0rad_lat0)*Math.sin(lat0rad_lat0))); not used
  var  omega_lat=((lon)*Math.PI/180)-((m0)*Math.PI/180); //provide negative lon so no negative multiplier
 //   omega_lat0=""; not used
 var   psi_lat=nu_lat/rho_lat;
 //   psi_lat0=""; not used
  var  t_lat=Math.tan(latrad_lat);
  //  t_lat0=""; not used
  var  a0_lat=1-e2/4-3*e2*e2/64-5*e2*e2*e2/256;
  var  a2_lat=3/8*(e2+e2*e2/4+15*e2*e2*e2/128);
  var  a4_lat=15/256*(e2*e2+0.75*e2*e2*e2);
  var  a6_lat=35*e2*e2*e2/3072;
  var  mlat_lat=a*(a0_lat*latrad_lat-a2_lat*Math.sin(2*latrad_lat)+a4_lat*Math.sin(4*latrad_lat)-a6_lat*Math.sin(6*latrad_lat));
  var  mlat_lat0=a*(a0_lat*lat0rad_lat0-a2_lat*Math.sin(2*lat0rad_lat0)+a4_lat*Math.sin(4*lat0rad_lat0)-a6_lat*Math.sin(6*lat0rad_lat0));
 var   e1_lat=nu_lat*omega_lat*Math.cos(latrad_lat);
 var   e2_lat=nu_lat*omega_lat*omega_lat*omega_lat/6*Math.cos(latrad_lat)*Math.cos(latrad_lat)*Math.cos(latrad_lat)*(psi_lat-t_lat*t_lat);
 var   e3_lat=nu_lat*Math.pow(omega_lat,5)/120*Math.pow(Math.cos(latrad_lat),5)*(4*psi_lat*psi_lat*psi_lat*(1-6*t_lat*t_lat)+psi_lat*psi_lat*(1+8*t_lat*t_lat)-psi_lat*2*t_lat*t_lat+Math.pow(t_lat,4));
  var  e4_lat=nu_lat*Math.pow(omega_lat,7)/5040*Math.pow(Math.cos(latrad_lat),7)*(61-479*t_lat*t_lat+179*Math.pow(t_lat,4)-Math.pow(t_lat,6));
 var   e_lat=k0*(e1_lat+e2_lat+e3_lat+e4_lat);
 var   n1_lat=(omega_lat*omega_lat)/2*Math.cos(latrad_lat);
 var   n1_lat0=n1_lat*nu_lat*Math.sin(latrad_lat);
 var   n2_lat=(Math.pow(omega_lat,4)/24)*(Math.pow(Math.cos(latrad_lat),3))*(4*psi_lat*psi_lat+psi_lat-t_lat*t_lat);
 var   n2_lat0=n2_lat*nu_lat*Math.sin(latrad_lat);
 var   n3_lat=(Math.pow(omega_lat,6)/720)*(Math.pow(Math.cos(latrad_lat),5))*(8*Math.pow(psi_lat,4)*(11-24*t_lat*t_lat)-28*Math.pow(psi_lat,3)*(1-6*t_lat*t_lat)+psi_lat*psi_lat*(1-32*t_lat*t_lat)-2*psi_lat*t_lat*t_lat+Math.pow(t_lat,4));
  var  n3_lat0=n3_lat*nu_lat*Math.sin(latrad_lat);
 var   n4_lat=(Math.pow(omega_lat,8)/40320)*(Math.pow(Math.cos(latrad_lat),7))*(1385-3111*t_lat*t_lat+543*Math.pow(t_lat,4)-Math.pow(t_lat,6));
 var   n4_lat0=n4_lat*nu_lat*Math.sin(latrad_lat);
 var   n_lat=k0*(mlat_lat+nu_lat*Math.sin(latrad_lat)*(n1_lat+n2_lat+n3_lat+n4_lat));
 var   n_lat0=k0*mlat_lat0;
 var   no=n_lat-n_lat0;
  var  x=e_lat+x0*metconv;
 var   y=(n_lat-n_lat0)+y0*metconv;
//    alert(n_lat);
//    alert("x="+x+"y="+y);
  //  alert("a0="+a0_lat+"a2="+a2_lat+"a4="+a4_lat+"a6="+a6_lat);
 var   xft=x/metconv;
 var   yft=y/metconv;
 //   alert("x="+xft+"y="+yft);
  return [xft,yft];
    }

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