En este articulo veremos como crear funciones específicas para obtener las Coordenadas Geográficas a partir de las Coordenadas UTM.
Esto lograremos insertando código Javascript en la hoja mediante la interfaz Apps Script (Google Apps Script – GAS)
Ver instrucciones en el vídeo.
Codigo a insertar en la interfaz GAS del archivo:
function result(y) {
//var y ;
var alpha_ ;
var beta_ ;
var gamma_ ;
var delta_ ;
var epsilon_ ;
var n ;
var sm_a ;
var sm_b ;
//'var y ;
var result ;
sm_a = 6378137;
sm_b = 6356752.314;
//' /* Precalculate n (Eq. 10.18) */
n = (sm_a - sm_b) / (sm_a + sm_b);
// '/* Precalculate alpha_ (Eq. 10.22) */// //
//'/* (Same as alpha in Eq. 10.17) */
alpha_ = ((sm_a + sm_b) / 2) * (1 + (n ** 2) / 4) + (n ** 4) / 64;
// '/* Precalculate y_ (Eq. 10.23) */
var y_ = y / alpha_;
// '/* Precalculate beta_ (Eq. 10.22) */
beta_ = (3 * n / 2) + (-27 * (n ** 3) / 32) + (269 * (n ** 5) / 512);
// ' /* Precalculate gamma_ (Eq. 10.22) */
gamma_ = (21 * (n ** 2) / 16) + (-55 * (n ** 4) / 32);
// ' /* Precalculate delta_ (Eq. 10.22) */
delta_ = (151 * (n ** 3) / 96) + (-417 * (n ** 5) / 128);
// '/* Precalculate epsilon_ (Eq. 10.22) */
epsilon_ = (1097 * (n ** 4) / 512);
// '/* Now calculate the sum of the series (Eq. 10.21) */
result = y_ + (beta_ * Math.sin(2 * y_)) + (gamma_ * Math.sin(4 * y_)) + (delta_ * Math.sin(6 * y_)) + (epsilon_ * Math.sin(8 * y_));
return result;
// ' //echo $result;
}
function x_geo(x, y) {
var zone ;
var lamba0 ;
var phif ;
var Nf ;
var Nfpow ;
var nuf2 ;
var ep2 ;
var tf ;
var tf2 ;
var tf4 ;
var cf ;
var x1frac ;
var x2frac ;
var x3frac ;
var x4frac ;
var x5frac ;
var x6frac ;
var x7frac ;
var x8frac ;
var x2poly ;
var x3poly ;
var x4poly ;
var x5poly ;
var x6poly ;
var x7poly ;
var x8poly ;
var philambda ;
var philambda1 ;
var sm_a ;
var sm_b ;
// ' var x_geo ;
var UTMScaleFactor = 0.9996;
var zone = 21;
x = x - 500000;
x = x / UTMScaleFactor;
// ' /* If in southern hemisphere, adjust y accordingly. */
// ' /* if ($southhemi) */
y = y - 10000000;
y = y / UTMScaleFactor;
// ' // $cmeridian = UTMCentralMeridian ($zone); //
'//$lambda0 = ((-183.0 + ($zone * 6.0))/180) * 3.14159265358979 ;
lambda0 = ((-183 + (zone * 6)) / 180) * 3.141592654;
sm_a = 6378137;
sm_b = 6356752.314;
// '/* Get the value of phif, the footpoint latitude. */
phif = result(y);
// '/* Precalculate ep2 */
ep2 = (sm_a ** 2 - sm_b ** 2) / (sm_b ** 2);
// '/* Precalculate cos (phif) */
cf = Math.cos(phif);
// '/* Precalculate nuf2 */
nuf2 = ep2 * (cf ** 2)
// '/* Precalculate Nf and initialize Nfpow */
Nf = (sm_a ** 2) / (sm_b * Math.sqrt(1 + nuf2));
Nfpow = Nf;
// '/* Precalculate tf */
tf = Math.tan(phif);
tf2 = tf * tf;
tf4 = tf2 * tf2;
// '/* Precalculate fractional coefficients for x**n in the equations
// 'below to simplify the expressions for latitude and longitude. */
x1frac = 1 / (Nfpow * cf);
Nfpow = Nfpow * Nf ; /* now equals Nf**2) */
x2frac = tf / (2 * Nfpow);
Nfpow = Nfpow * Nf; /* now equals Nf**3) */
x3frac = 1 / (6 * Nfpow * cf);
Nfpow = Nfpow * Nf ; /* now equals Nf**4) */
x4frac = tf / (24 * Nfpow);
Nfpow = Nfpow * Nf ; /* now equals Nf**5) */
x5frac = 1 / (120 * Nfpow * cf);
Nfpow = Nfpow * Nf ; /* now equals Nf**6) */
x6frac = tf / (720 * Nfpow);
Nfpow = Nfpow * Nf; /* now equals Nf**7) */
x7frac = 1 / (5040 * Nfpow * cf);
Nfpow = Nfpow * Nf ; /* now equals Nf**8) */
x8frac = tf / (40320 * Nfpow);
//' /* Precalculate polynomial coefficients for x**n.
// ' -- x**1 does not have a polynomial coefficient. */
x2poly = -1 - nuf2;
x3poly = -1 - 2 * tf2 - nuf2;
x4poly = 5 + 3 * tf2 + 6 * nuf2 - 6 * tf2 * nuf2 - 3 * (nuf2 * nuf2) - 9 * tf2 * (nuf2 * nuf2);
x5poly = 5 + 28 * tf2 + 24 * tf4 + 6 * nuf2 + 8 * tf2 * nuf2;
x6poly = -61 - 90 * tf2 - 45 * tf4 - 107 * nuf2 + 162 * tf2 * nuf2;
x7poly = -61 - 662 * tf2 - 1320 * tf4 - 720 * (tf4 * tf2);
x8poly = 1385 + 3633 * tf2 + 4095 * tf4 + 1575 * (tf4 * tf2);
// ' /* Calculate latitude */
philambda = phif + x2frac * x2poly * (x * x) + x4frac * x4poly * x ** 4 + x6frac * x6poly * x ** 6 + x8frac * x8poly * x ** 8;
// ' /* Calculate longitude */
philambda1 = lambda0 + x1frac * x + x3frac * x3poly * x ** 3 + x5frac * x5poly * x ** 5 + x7frac * x7poly * x ** 7
// '// return $philambda;
x_geo = (philambda / 3.141592654) * 180;
// '$y_geo= (($philambda1)/3.141592654) * 180.0;
// 'Return
return x_geo;
}
function y_geo(x, y) {
var zone ;
var lamba0 ;
var phif ;
var Nf ;
var Nfpow ;
var nuf2 ;
var ep2 ;
var tf ;
var tf2 ;
var tf4 ;
var cf ;
var x1frac ;
var x2frac ;
var x3frac ;
var x4frac ;
var x5frac ;
var x6frac ;
var x7frac ;
var x8frac ;
var x2poly ;
var x3poly ;
var x4poly ;
var x5poly ;
var x6poly ;
var x7poly ;
var x8poly ;
var philambda ;
var philambda1 ;
var sm_a ;
var sm_b ;
// ' var x_geo ;
var UTMScaleFactor = 0.9996;
var zone = 21;
x = x - 500000;
x = x / UTMScaleFactor;
// ' /* If in southern hemisphere, adjust y accordingly. */
// ' /* if ($southhemi) */
y = y - 10000000; y = y / UTMScaleFactor;
// ' // $cmeridian = UTMCentralMeridian ($zone);
// '//$lambda0 = ((-183.0 + ($zone * 6.0))/180) * 3.14159265358979 ;
lambda0 = ((-183 + (zone * 6)) / 180) * 3.141592654;
sm_a = 6378137;
sm_b = 6356752.314;
// '/* Get the value of phif, the footpoint latitude. */
phif = result(y);
// '/* Precalculate ep2 */
ep2 = (sm_a ** 2 - sm_b ** 2) / (sm_b ** 2);
// '/* Precalculate cos (phif) */
cf = Math.cos(phif);
// '/* Precalculate nuf2 */
nuf2 = ep2 * (cf ** 2);
// '/* Precalculate Nf and initialize Nfpow */
Nf = (sm_a ** 2) / (sm_b * Math.sqrt(1 + nuf2));
Nfpow = Nf;
// '/* Precalculate tf */
tf = Math.tan(phif);
tf2 = tf * tf;
tf4 = tf2 * tf2;
// '/* Precalculate fractional coefficients for x**n in the equations
// 'below to simplify the expressions for latitude and longitude. */
x1frac = 1 / (Nfpow * cf);
Nfpow = Nfpow * Nf /* now equals Nf**2) */
x2frac = tf / (2 * Nfpow);
Nfpow = Nfpow * Nf; /* now equals Nf**3) */
x3frac = 1 / (6 * Nfpow * cf);
Nfpow = Nfpow * Nf ; /* now equals Nf**4) */
x4frac = tf / (24 * Nfpow);
Nfpow = Nfpow * Nf; /* now equals Nf**5) */
x5frac = 1 / (120 * Nfpow * cf);
Nfpow = Nfpow * Nf ; /* now equals Nf**6) */
x6frac = tf / (720 * Nfpow);
Nfpow = Nfpow * Nf ; /* now equals Nf**7) */
x7frac = 1 / (5040 * Nfpow * cf);
Nfpow = Nfpow * Nf ; /* now equals Nf**8) */
x8frac = tf / (40320 * Nfpow);
//' /* Precalculate polynomial coefficients for x**n.
// ' -- x**1 does not have a polynomial coefficient. */
x2poly = -1 - nuf2;
x3poly = -1 - 2 * tf2 - nuf2;
x4poly = 5 + 3 * tf2 + 6 * nuf2 - 6 * tf2 * nuf2 - 3 * (nuf2 * nuf2) - 9 * tf2 * (nuf2 * nuf2);
x5poly = 5 + 28 * tf2 + 24 * tf4 + 6 * nuf2 + 8 * tf2 * nuf2;
x6poly = -61 - 90 * tf2 - 45 * tf4 - 107 * nuf2 + 162 * tf2 * nuf2;
x7poly = -61 - 662 * tf2 - 1320 * tf4 - 720 * (tf4 * tf2);
x8poly = 1385 + 3633 * tf2 + 4095 * tf4 + 1575 * (tf4 * tf2);
//' /* Calculate latitude */
philambda = phif + x2frac * x2poly * (x * x) + x4frac * x4poly * x ** 4 + x6frac * x6poly * x ** 6 + x8frac * x8poly * x ** 8;
// ' /* Calculate longitude */
philambda1 = lambda0 + x1frac * x + x3frac * x3poly * x ** 3 + x5frac * x5poly * x ** 5 + x7frac * x7poly * x ** 7;
// '// return $philambda;
// 'x_geo = (philambda / 3.141592654) * 180
y_geo = ((philambda1) / 3.141592654) * 180;
return y_geo;
}