First experiments with the shell script

1 files changed, 84 insertions, 0 deletions

diff --git a/harvesin.sh b/harvesin.sh
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+#!/bin/sh
+#-
+# © 2021 mirabilos Ⓕ CC0; implementation of Haversine GCD from public sources
+#
+# now developed online:
+# 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
+	echo >&2 "E: syntax: $0 lat1 lon1 lat2 lon2"
+	exit 1
+fi
+
+set -e
+
+# make GNU bc use POSIX mode and shut up
+BC_ENV_ARGS=-qs
+export BC_ENV_ARGS
+
+# assignment of constants, variables and functions
+# p: multiply with to convert from degrees to radians (π/180)
+# r: earth radius in metres
+# d: distance
+# h: haversine intermediate
+# i,j: (lat,lon) point 1
+# x,y: (lat,lon) point 2
+# k: delta lat
+# l: delta lon
+# m: sin(k/2) (square root of hav(k))
+# n: sin(l/2) (  partial haversine  )
+# n(x): arcsin(x)
+# r(x,n): round x to n decimal digits
+# v(x): sign (Vorzeichen)
+# w(x): min(1, sqrt(x)) (Wurzel)
+
+bc -l <<-EOF
+scale=64
+define n(x) {
+	if (x == -1) return (-2 * a(1))
+	if (x == 1) return (2 * a(1))
+	return (a(x / sqrt(1 - x*x)))
+}
+define v(x) {
+	if (x < 0) return (-1)
+	if (x > 0) return (1)
+	return (0)
+}
+define r(x, n) {
+	auto o
+	o = scale
+	if (scale < (n + 1)) scale = (n + 1)
+	x += v(x) * 0.5 * A^-n
+	scale = n
+	x /= 1
+	scale = o
+	return (x)
+}
+define w(x) {
+	if (x >= 1) return (1)
+	return (sqrt(x))
+}
+/* WGS84 reference ellipsoid: große Halbachse (metres), Abplattung */
+i = 6378137.000
+x = 1/298.257223563
+/* other axis */
+j = i * (1 - x)
+/* mean radius resulting */
+r = (2 * i + j) / 3
+/* coordinates */
+p = (4 * a(1) / 180)
+i = (p * $1)
+j = (p * $2)
+x = (p * $3)
+y = (p * $4)
+/* calculation */
+k = (x - i)
+l = (y - j)
+m = s(k / 2)
+n = s(l / 2)
+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