Wikipedia

Module:Ordnance Survey coordinates

--[[ Ordnance Survey / Lat Long functions in Lua 

****** ORDNANCE SURVEY TO LAT LONG FUNCTIONS ******

Ported to Lua from PHP by Wikipedia User Hike395, 18 Aug 2019

found by RWH at http://www.megalithia.com/search/llfuncshighlight.php

With thanks to Andy, G4JNT for inspiration in GEOG, and to the OSGB for their white paper on coordinate transformation
describing the iterative method used
thanks to the Ordnance survey of Ireland for details of the true and false origins of the Irish grid

You may use and redistribute this code under the terms of the GPL see http://www.gnu.org/copyleft/gpl.html


Written by Richard
www.megalithia.com
v0.something 27/2/2000
v 1.01 28 June 2004
v 1.02 6 Aug 2004 line 89 add "0" to chars in ngr=stripcharsnotinbag Thx Andy
v 1.03 9 Mar 2005 Jan (Klingon) added conversion to WGS84 map datum and removed limitation of digits of the grid ref
v 1.04 10 Aug 2005 Richard correct error trapping (only manifest on malformed ngrs

This code is predicated on the assumption that your are ONLY feeding it Irish or UK Grid references.
It uses the single char prefix of Irish grid refs to tell the difference, UK grid refs have a two letter prefix.
We would like an even number of digits for the rest of the grid ref.
Anything in the NGR other than 0-9, A-Z, a-z is eliminated.
WARNING this assumes there are no decimal points in your NGR components.

The transformation from OSGB36/Ireland 1965 to WGS84 is more precise than 5 m.

The function is case insensitive

Lat/Long to Ordnance Survey conversion is at bottom of file, see further authorship there

]]

local oscoord = {}
local getArgs = require('Module:Arguments').getArgs
local yesno = require('Module:Yesno')
local namespace = mw.title.getCurrentTitle().namespace

local pow = math.pow
local sqrt = math.sqrt
local abs = math.abs
local floor = math.floor
local ceil = math.ceil
local sin = math.sin
local cos = math.cos
local tan = math.tan
local atan = math.atan
local deg2rad = math.rad
local rad2deg = math.deg



--[[ DATUM SHIFT USING HELMERT TRANSFORMATION
 *
 * height above the ellipsoid is ignored
 * latitude and longitude must be given in decimal degrees
 *
 * no transformation if abs(latitude)>89 or abs(longitude)>89
 * (lifting this restriction requires some more lines of code)
 *
 * Written in 2009 by user Telford at de.wikipedia
 * Based on math described in "A Guide to Coordinate Systems in Great Britain"
 * by the UK Ordnance Survey
 * URL: https://www.ordnancesurvey.co.uk/documents/resources/guide-coordinate-systems-great-britain.pdf
]]

-- Datum parameters

local OSGBglobe = {
	semimajor = 6377563.396,
	semiminor = 6356256.910,
	ecc = 0.006670539761597529073698869358812557054558,
	n1 = 0.00167322025032508731869331280635710896296,
	scale = 0.9996012717,
    e0 = 400000.0,
    n0 = -100000.0,
    lat0 = 49.0,
    lon0 = -2.0
}

local IEglobe = {
	semimajor = 6377340.189,
	semiminor = 6356034.447,
	ecc = 0.006670540293336110419293763349975612794125,
	n1 = 0.001673220384152058651484728058385228837777,
	scale = 1.000035,
	e0 = 200000.0,
	n0 = 250000.0,
	lat0 = 53.5,
	lon0 = -8.0
}

local WGSglobe = {
	semimajor = 6378137.0,
	semiminor = 6356752.3141,
	ecc = 0.00669438003551279089034150031998869922791
}

local WGS2OSGBparam = {
 -- Table 4, Section 6.6, Ordnance Survey document 
	semimajor_src = WGSglobe.semimajor,
	semiminor_src = WGSglobe.semiminor,
	ecc_src = WGSglobe.ecc,
	semimajor_dst = OSGBglobe.semimajor,
	semiminor_dst = OSGBglobe.semiminor,
	ecc_dst = OSGBglobe.ecc,
	tx = -446.448,
    ty = 125.157,
    tz = -542.060,
    s0 = 0.0000204894,
    rx = deg2rad ( -.1502/3600. ),
    ry = deg2rad ( -.2470/3600. ),
    rz = deg2rad ( -.8421/3600. )
}

local OSGB2WGSparam = {
	semimajor_src = OSGBglobe.semimajor,
	semiminor_src = OSGBglobe.semiminor,
	ecc_src = OSGBglobe.ecc,
	semimajor_dst = WGSglobe.semimajor,
	semiminor_dst = WGSglobe.semiminor,
	ecc_dst = WGSglobe.ecc,
	tx = -WGS2OSGBparam.tx,
    ty = -WGS2OSGBparam.ty,
    tz = -WGS2OSGBparam.tz,
    s0 = -WGS2OSGBparam.s0,
    rx = -WGS2OSGBparam.rx,
    ry = -WGS2OSGBparam.ry,
    rz = -WGS2OSGBparam.rz,
}

local IE2WGSparam = {
	semimajor_src = IEglobe.semimajor,
	semiminor_src = IEglobe.semiminor,
	ecc_src = IEglobe.ecc,
	semimajor_dst = WGSglobe.semimajor,
	semiminor_dst = WGSglobe.semiminor,
	ecc_dst = WGSglobe.ecc,
	tx = 482.53,
	ty = -130.596,
	tz = 564.557,
	s0 = 8.15/1000000.0,
	rx = deg2rad( -1.042/3600.0 ),
	ry = deg2rad( -0.214/3600.0 ),
	rz = deg2rad( -0.631/3600.0 )
}

local function HelmertDatumShift ( latitude , longitude, param )
	-- latitude and longitude are in degrees
    -- return if latitude or longitude out of range 

    if abs(latitude) > 89. or abs(longitude) > 89. then
    	return {lat=latitude, lon=longitude}
    end

	param = param or WGS2OSGBparam

    -- parameters for ellipsoids
    -- Annex A.1, Ordnance Survey document --

    local a1 = param.semimajor_src
    local b1 = param.semiminor_src
    local e1 = param.ecc_src

    local a2 = param.semimajor_dst
    local b2 = param.semiminor_dst
    local e2 = param.ecc_dst

    -- convert latitude and longitude to cartesian coordinates
    -- math in Annex B.1, Ordnance Survey document
    local phi = deg2rad ( latitude )
    local lambda = deg2rad ( longitude )
    local cosphi = cos ( phi )
    local sinphi = sin ( phi )
    local coslambda = cos ( lambda )
    local sinlambda = sin ( lambda )

    local ny = a1 / sqrt ( 1. - e1*sinphi*sinphi )

    local x1 = ny * cosphi * coslambda
    local y1 = ny * cosphi * sinlambda
    local z1 = ny * ( 1. - e1 ) * sinphi
    -- the helmert transformation proper
    -- Equation 3, Section 6.2, Ordnance Survey document

    local x2 = x1 + param.tx + ( param.s0 * x1 - param.rz * y1 + param.ry * z1 )
    local y2 = y1 + param.ty + ( param.rz * x1 + param.s0 * y1 - param.rx * z1 )
    local z2 = z1 + param.tz + ( -param.ry *x1 + param.rx * y1 + param.s0 * z1 )
    -- convert cartesian coordinates to latitude and longitude
    -- math in Annex B.2, of Ordnance Survey document 

    lambda = atan ( y2 / x2 )

    local p2 = sqrt ( x2*x2 + y2*y2 )
    phi = atan ( z2 / p2*(1.-e2) )

    local n0 = 101

	local phi_alt
    repeat
	    phi_alt = phi
	    ny = a2 / sqrt ( 1. - e2 * sin(phi) * sin(phi) )
	    phi = atan ( (z2 + e2 * ny * sin(phi)) / p2 )
	    n0 = n0 - 1
    until abs ( phi - phi_alt ) <= 0.000000000001 or n0 <= 0

	return {lat=rad2deg(phi),lon=rad2deg(lambda)}

end

--  LAT LONG TO OS GRID LIBRARY RESUMES HERE

local function northeast(lett,num,shift)
   -- split into northings and eastings
   local le=mw.ustring.len(num)
   if le%2 == 1 then
   	 return {err="Malformed numerical part of NGR"}
   end
   local pr=le/2
   local n = mw.ustring.sub(num,pr+1)
   local e = mw.ustring.sub(num,1,pr)
   -- Hack to move to center of square: append a 5 to northings and eastings
   shift = yesno(shift)
   if shift then
     n = n.."5"
     e = e.."5"
     pr = pr+1
   end
   -- end hack
   n = n == '' and 0 or n
   e = e == '' and 0 or e
   pr = pow(10.0,(5.0-pr))
   local T1 = mw.ustring.byte(mw.ustring.sub(lett,1,1))-65
   if T1>8 then
     T1 = T1-1
   end
   local T2 = nil
   if mw.ustring.len(lett)>1 then
     T2 = mw.ustring.byte(mw.ustring.sub(lett,2))-65
     if T2>8 then
       T2 = T2-1
     end
   end
   return {n=n,e=e,pr=pr,T1=T1,T2=T2}
end

local function EN2LL(e,n,datum)
   local a = datum.semimajor*datum.scale
   local b = datum.semiminor*datum.scale
   local lat0rad = deg2rad(datum.lat0)
   local n1 = datum.n1
   local n12 = n1*n1
   local n13 = n12*n1
   local k=(n-datum.n0)/a+lat0rad
   local nextcounter=0
   local j3, j4, j5, j6, m
   repeat
     nextcounter=nextcounter+1
     local k3=k-lat0rad
     local k4=k+lat0rad
     j3=(1.0+n1+1.25*n12+1.25*n13)*k3
     j4=(3.0*n1+3.0*n12+2.625*n13)*sin(k3)*cos(k4)
     j5=(1.875*n12+1.875*n13)*sin(2.0*k3)*cos(2.0*k4)
     j6=35.0/24.0*n13*sin(3.0*k3)*cos(3.0*k4)
     m=b*(j3-j4+j5-j6)
     k=k+(n-datum.n0-m)/a
   until abs(n-datum.n0-m)<=0.000000001 or nextcounter>=100
   local x = 1.0-datum.ecc*pow(sin(k),2.0)
   local v=a/sqrt(x)
   local r=v*(1.0-datum.ecc)/x
   local h2=v/r-1.0
   local y1=e-datum.e0
   local tank = tan(k)
   local tank2 = tank*tank
   local tank4 = tank2*tank2
   local tank6 = tank2*tank4
   local cosk = cos(k)
   local yv = y1/v -- dimensionless quantity in series expansion
   local yv2 = yv*yv
   local yv3 = yv*yv2
   local yv5 = yv3*yv2
   local yv7 = yv5*yv2
   j3=tank/(2.0*r)
   j4=tank/(24.0*r)*(5.0+3.0*tank2+h2-9.0*tank2*h2)
   j5=tank/(720.0*r)*(61.0+90.0*tank2+45.0*tank4)
   local k9=k-y1*(yv*j3+yv3*j4-yv5*j5)
   j6=1.0/(cosk)
   local j7=1.0/(cosk*6.0)*(v/r+2.0*tank2)
   local j8=1.0/(cosk*120.0)*(5.0+28.0*tank2+24.0*tank4)
   local j9=1.0/(cosk*5040.0)
   j9=j9*(61.0+662.0*tank2+1320.0*tank4+720.0*tank6)
   local long=datum.lon0+rad2deg(yv*j6-yv3*j7+yv5*j8-yv7*j9)
   local lat=rad2deg(k9)
   return {lat=lat,lon=long}
end

local function GBEN2LL(e,n)
   local latlong = EN2LL(e,n,OSGBglobe)
   local helmert = HelmertDatumShift ( latlong.lat, latlong.lon, OSGB2WGSparam)
   return {region="GB",lat=helmert.lat,long=helmert.lon}
end


local function GB2LL(lett,num)
   -- British OS to Lat+Long
   -- first caclulate e,n
   -- computing e and n exactly, to get SW corner of box
   local ne = northeast(lett,num)
   if ne.err then
   	 return {region="GB",err=ne.err}
   end
   -- use British definition of e and n
   local e=500000.0*(ne.T1%5)+100000.0*(ne.T2%5)-1000000.0+ne.e*ne.pr
   local n=1900000.0-500000.0*floor(ne.T1/5)-100000.0*floor(ne.T2/5)+ne.n*ne.pr
   local result = GBEN2LL(e,n)
   result.prec = 0.8165*ne.pr
   return result
end
   
local function IrishEN2LL(e,n)
   local latlong = EN2LL(e,n,IEglobe)
   local helmert = HelmertDatumShift ( latlong.lat, latlong.lon, IE2WGSparam)
   return {region="IE",lat=helmert.lat,long=helmert.lon}
end

local function Irish2LL(lett,num)
   -- Irish OS to Lat+Long
   -- first caclulate e,n
   -- computing e and n exactly, to get SW corner of box
   local ne = northeast(lett,num)
   if ne.err then
   	 return {region="IE", err=ne.err}
   end
   -- use Irish definition of northing and easting
   local e=100000.0*(ne.T1%5.0)+ne.e*ne.pr
   local n=ne.n*ne.pr+100000.0*(4.0-floor(ne.T1/5.0))
   local result = IrishEN2LL(e,n)
   result.prec = 0.8165*ne.pr  -- useful @ Commons
   return result
end

local function empty(s)
  return not s or s == ''
end

local function NGR2LL(ngr)
  local result = {}
  ngr, _ = mw.ustring.gsub(mw.ustring.upper(ngr),"[%s%p]","")
  local first, last, lett, num = mw.ustring.find(ngr,"^([A-Z]+)(%d+)$")
  if not first or empty(lett) or empty(num) or mw.ustring.len(lett) > 2 then
  	return {err="Malformed NGR"}
  end
  if mw.ustring.len(lett) == 1 then
    return Irish2LL(lett,num)
  end
  return GB2LL(lett, num)
end

local function split(s,sep)
-- split a string s into chunks, separated by sep
  sep = sep or "%s"
  local t = {}
  for chunk in mw.ustring.gmatch(s,"([^"..sep.."]+)") do
    table.insert(t,chunk)
  end
  return t
end

local function trim(s)
  s, _ = mw.ustring.gsub(s,"^%s+","")
  s, _ = mw.ustring.gsub(s,"%s+$","")
  return s
end

local function alldigits(s)
  return not mw.ustring.find(s,"%D")
end

local function warning(errmsg)
  local preview = require('Module:If preview')
  local msg = errmsg or 'Empty OS grid ref'

  local html = preview._warning({ msg })

  if namespace == 0 and errmsg then
  	html = html..'[[Category:Pages with malformed OS coordinates]]'
  end
  return html
end

function oscoord._main(args)
  local input = args[1]
  if empty(input) then
  	return warning(nil)
  end
  local linktitle = args[2]
  local namearg = args["name"]
  local rawurl = yesno(args["rawurl"])
  local args = split(input,'_')
  local LL
  local restargs = 1
  local current_page = mw.title.getCurrentTitle()
  local pagename = mw.uri.encode( current_page.prefixedText, 'WIKI' )
  if #args >= 2 and alldigits(args[2]) then
    if mw.ustring.sub(args[1],1,1) == 'i' then
      local firstArg = mw.ustring.sub(args[1],2)
      if alldigits(firstArg) then
        LL = IrishEN2LL(firstArg,args[2])
	    restargs = 3
	    if empty(linktitle) then
          linktitle=args[1]..'_'..args[2]
	    end
      end
    elseif alldigits(args[1]) then
      LL = GBEN2LL(args[1],args[2])
      restargs = 3
      if empty(linktitle) then
        linktitle=args[1]..'_'..args[2]
      end
    end
  else
    LL = NGR2LL(args[1])
    restargs = 2
    if empty(linktitle) then
      linktitle=args[1]
    end
  end
  linktitle = trim(linktitle)
  if not empty(LL.err) then
    return linktitle ..warning(LL.err)
  end
  -- https://geohack.toolforge.org/geohack.php?pagename=Mount_Whitney&params=36.578580925_N_118.29199495_W_type:mountain_region:US-CA_scale:100000_source:NGS
  local url = ''
  if not rawurl then
  	url = url..'['
  end
  url = url..'https://geohack.toolforge.org/geohack.php?'
  if not empty(pagename) then
  	url = url..'pagename='..pagename..'&'
  end
  LL.lat = LL.lat or 0
  LL.long = LL.long or 0
  LL.lat = ceil(LL.lat*1000000)/1000000
  LL.long = ceil(LL.long*1000000)/1000000
  url = url..'params='..mw.ustring.format('%.6f',LL.lat)..'_N_'
  if LL.long < 0 then
  	url = url..mw.ustring.format('%.6f',-LL.long)..'_W'
  else
  	url = url..mw.ustring.format('%.6f',LL.long)..'_E'
  end
  for i = restargs,#args do
  	url = url..'_'..args[i]
  end
  if not mw.ustring.find(input,"region") and LL.region then
    url = url..'_region:'..LL.region
  end
  if not mw.ustring.find(input,"scale") and
     not mw.ustring.find(input,"type") and
     not mw.ustring.find(input,"dim") and LL.prec then
     	url = url..'_dim:'..floor(50*LL.prec+0.5)..'m'
  end
  if not empty(namearg) then
    url = url .. "&title=" .. mw.uri.encode(namearg)
  end
  if not rawurl then
	url = url..' '..linktitle..']'
  end
  return url
end

function oscoord._oscoord(args)
	local output = '<span class="plainlinks nourlexpansion" style="white-space: nowrap">' .. oscoord._main(args) .. '</span>'
	if namespace == 0 then
		output = output .. '[[Category:Articles with OS grid coordinates]]'
	end
	return output
end

function oscoord.main(frame)
	local args = getArgs(frame)
	return oscoord._main(args)
end

function oscoord.oscoord(frame)
	local args = getArgs(frame)
	return oscoord._oscoord(args)
end

--[[
 ******  LAT/LONG CONVERSION TO OS GRID REF FUNCTIONS *****
 *  Uses the WGS-84 ellipsoid and only works for GB grid ref
 *
 *  See also:
 *  http://www.posc.org/Epicentre.2_2/DataModel/ExamplesofUsage/eu_cs34h.html
 *  http://kanadier.gps-info.de/d-utm-gitter.htm
 *  http://www.gpsy.com/gpsinfo/geotoutm/
 *  http://www.colorado.edu/geography/gcraft/notes/gps/gps_f.html
 *  http://search.cpan.org/src/GRAHAMC/Geo-Coordinates-UTM-0.05/
 *  UK Ordnance Survey grid (OSBG36): http://www.gps.gov.uk/guidecontents.asp
 *  Swiss CH1903: http://www.gps.gov.uk/guidecontents.asp
 *
 *  ----------------------------------------------------------------------
 *
 *  Copyright 2005, Egil Kvaleberg <egil@kvaleberg.no>
 *
 *  This program is free software; you can redistribute it and/or modify
 *  it under the terms of the GNU General Public License as published by
 *  the Free Software Foundation; either version 2 of the License, or
 *  (at your option) any later version.
 *
 *  This program is distributed in the hope that it will be useful,
 *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 *  GNU General Public License for more details.
 *
 *  You should have received a copy of the GNU General Public License
 *  along with this program; if not, write to the Free Software
 *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
 
 Converted to Lua by User:Hike395 on 2023-12-15
]]


local function find_M ( lat_rad )
	local e = OSGBglobe.ecc
	local e2 = e*e
	local e3 = e*e*e

	return OSGBglobe.semimajor * ( ( 1 - e/4 - 3 * e2/64
			      - 5 * e3/256
			    ) * lat_rad
			  - ( 3 * e/8 + 3 * e2/32
			      + 45 * e3/1024
			    ) * sin(2 * lat_rad)
			  + ( 15 * e2/256 +
			      45 * e3/1024
			    ) * sin(4 * lat_rad)
			  - ( 35 * e3/3072
			    ) * sin(6 * lat_rad) )
end

--[[
*  Convert latitude, longitude in decimal degrees to
*  Transverse Mercator Easting and Northing based on a GB origin
*
*  return nil if problems
]]
local function LatLonOrigin2TM( latitude, longitude )
	if longitude < -180 or longitude > 180 or latitude < -80 or latitude > 84 then
		return nil
	end

	local longitude2 = longitude - floor((longitude + 180)/360) * 360

	local lat_rad = deg2rad( latitude )

	local e = OSGBglobe.ecc
	local e_prime_sq = e / (1-e)

	local v = OSGBglobe.semimajor / sqrt(1 - e * sin(lat_rad)*sin(lat_rad))
	local tank = tan(lat_rad)
	local T = tank*tank
	local T2 = T*T
	local C = e_prime_sq * pow( cos(lat_rad), 2)
	local A = deg2rad( longitude2 -OSGBglobe.lon0 ) * cos(lat_rad)
	local A2 = A*A
	local A3 = A2*A
	local A4 = A2*A2
	local A5 = A3*A2
	local A6 = A3*A3
	local M = find_M( lat_rad )
	local M0 = 0.0
	if latitude_origin ~= 0 then
		M0 = find_M(deg2rad( OSGBglobe.lat0 ))
	end

	local northing = OSGBglobe.n0 + OSGBglobe.scale *
			    ( (M - M0) + v*tan(lat_rad) * 
			      ( A2/2 
				+ (5 - T + 9*C + 4*C*C) * A4/24
				+ (61 - 58*T + T2
				+ 600*C - 330*e_prime_sq) * A6/720 ))

	local easting = OSGBglobe.e0 + OSGBglobe.scale * v *
			   ( A 
			     + (1-T+C)*A3/6
			     + (5 - 18*T + T2 + 72*C 
				- 58 * e_prime_sq)*A5/120 )

	return {northing=northing,easting=easting}
end

--[[
*  Convert latitude, longitude in decimal degrees to
*  OSBG36 Easting and Northing
]]
local function LatLon2OSGB36( latlon, prec )
	local tm = LatLonOrigin2TM(latlon.lat, latlon.lon)
	if not tm then return '' end
	if not tonumber(prec) then prec = 5 end
	prec = floor(prec+0.5)
	if prec > 5 then prec = 5 end
	if prec < 1 then prec = 1 end

	-- fix by Roger W Haworth
	local grid_x = floor( tm.easting / 100000 )
	local grid_y = floor( tm.northing / 100000 )
	if grid_x < 0 or grid_x > 6 or grid_y < 0 or grid_y > 12 then return '' end
	--               0000000001111111111222222
	--               1234567890123456789012345
	local letters = "ABCDEFGHJKLMNOPQRSTUVWXYZ"
	
	local indx1 = 18-floor(grid_y/5)*5+floor(grid_x/5)
	local indx2 = 21-(grid_y%5)*5+grid_x%5
	local c1 = mw.ustring.sub(letters,indx1,indx1)
	local c2 = mw.ustring.sub(letters,indx2,indx2)

	local easting = tm.easting%100000
	local northing = tm.northing%100000
	local grid = pow(10.0,5.0-prec)
	easting = floor(easting/grid)
	northing = floor(northing/grid)
	local fmt = '%0'..prec..'d'
	local e = mw.ustring.format(fmt, easting)
	local n = mw.ustring.format(fmt, northing)

	return c1..c2..e..n

end

function oscoord._WGS2OSGB(lat,lon,prec)
	return LatLon2OSGB36(HelmertDatumShift(lat,lon,WGS2OSGBparam),prec)
end

function oscoord.WGS2OSGB(frame)
	local args = getArgs(frame)
	return args[1] and args[2] and oscoord._WGS2OSGB(args[1],args[2],args[3]) or ''
end

function oscoord.LL2OS(frame)
	local args = getArgs(frame)
	if not args[1] or not args[2] then return '' end
	local gridRef = oscoord._WGS2OSGB(args[1],args[2],args.prec)
	if not gridRef or #gridRef == 0 then return '' end
	if args[3] then
		gridRef = gridRef..'_'..args[3]
	end
	return oscoord._oscoord({gridRef,args.linktitle,name=args.name})
end

return oscoord
Retrieved from "https://en.wikipedia.org/w/index.php?title=Module:Ordnance_Survey_coordinates&oldid=1190359893"