Data update

Task/Haversine-formula/Bc/haversine-formula.bc

@@ -1,8 +1,11 @@
 #!/bin/sh
 #-
-# © 2021 mirabilos Ⓕ CC0; implementation of Haversine GCD from public sources
+# © 2021 mirabilos Ⓕ CC0 or MirBSD
 #
-# now developed online:
+# implementation of Haversine GCD from public sources
+# output is in metres (rounded to millimetres), error < ¼%
+#
+# now developed online: (user/pass public)
 # https://evolvis.org/plugins/scmgit/cgi-bin/gitweb.cgi?p=useful-scripts/mirkarte.git;a=blob;f=geo.sh;hb=HEAD
 
 if test "$#" -ne 4; then
@@ -23,8 +26,8 @@ export BC_ENV_ARGS
 # h: haversine intermediate
 # i,j: (lat,lon) point 1
 # x,y: (lat,lon) point 2
-# k: delta lat
-# l: delta lon
+# k: delta lat/ΔΦ
+# l: delta lon/Δλ
 # m: sin(k/2) (square root of hav(k))
 # n: sin(l/2) (  partial haversine  )
 # n(x): arcsin(x)
@@ -32,7 +35,7 @@ export BC_ENV_ARGS
 # v(x): sign (Vorzeichen)
 # w(x): min(1, sqrt(x)) (Wurzel)
 
-bc -l <<-EOF
+exec bc -l <<-EOF
 scale=64
 define n(x) {
 	if (x == -1) return (-2 * a(1))
@@ -59,7 +62,8 @@ define w(x) {
 	return (sqrt(x))
 }
 /* WGS84 reference ellipsoid: große Halbachse (metres), Abplattung */
-i = 6378137.000
+/* (6378137 in WGS84); this radius from Astronomical Almanac 2021 */
+i = 6378136.600
 x = 1/298.257223563
 /* other axis */
 j = i * (1 - x)
@@ -80,5 +84,3 @@ h = ((m * m) + (c(i) * c(x) * n * n))
 d = 2 * r * n(w(h))
 r(d, 3)
 EOF
-
-# output is in metres, rounded to millimetres, error < ¼% in WGS84