Module:Ordnance Survey coordinates

This module is rated as ready for general use. It has reached a mature form and is thought to be relatively bug-free and ready for use wherever appropriate. It is ready to mention on help pages and other Wikipedia resources as an option for new users to learn. To reduce server load and bad output, it should be improved by sandbox testing rather than repeated trial-and-error editing.

This module depends on the following other modules:

Usage

Converts a OS grid ref to a lat/long hyperlink to geohack.

{{#invoke:Ordnance Survey coordinates|main|SK135733}} ← Two-letter code interpreted as OS grid ref in Great Britain

{{#invoke:Ordnance Survey coordinates|main|O169318}} ← One-letter code interpreted as Irish OS grid ref

{{#invoke:Ordnance Survey coordinates|main|439668_1175316}} ← Two digit strings interpreted as easting/northing in meters in Great Britain

{{#invoke:Ordnance Survey coordinates|main|i88888_99999}} ← String starting with i is easting/northing in meters in Ireland

{{#invoke:Ordnance Survey coordinates|main|SK135733|Miller's Dale}} ← Second argument is used as link text

{{#invoke:Ordnance Survey coordinates|main|SK135733_scale:25000_region:GB-DBY}} ← extra underscored parameters passed to geohack

License

This work is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License Version 2 as published by the Free Software Foundation.
This work 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: Free Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA

-- Lat Long functions in Lua 

-- 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

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


local function northeast(lett,num,shift)
   -- split into northings and eastings
   local le=mw.ustring.len(num)
   if le%2 == 1 then
     return "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
   if shift ~= nil and shift > 0 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 = math.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 nil,n,e,pr,T1,T2
end       

local function GBEN2LL(e,n)
   local pow,sqrt,abs=math.pow,math.sqrt,math.abs
   local sin,cos,tan,atan=math.sin,math.cos,math.tan,math.atan
   local dr = math.deg(1.0)
   -- True Origin is 2 deg W
   local phi0uk=-2.0
   -- True Origin is 49 deg N
   local lambda0uk=49.0
   -- scale factor @ central meridian
   local F0uk=0.9996012717
   -- True origin in 400 km E of false origin
   local E0uk=400000.0
   --True origin is 100 km S of false origin
   local N0uk=-100000.0
   -- semi-major axis (in line to equator) 0.996012717 is yer scale @ central meridian
   local auk=6377563.396*F0uk
   --semi-minor axis (in line to poles)
   local buk=6356256.91*F0uk
   -- flatness=a1-b1/(a1+b1)
   local n1uk=0.00167322025032508731869331280635710896296
   -- first eccentricity squared=2*f-f^2where f=(a1-b1)/a1
   local e2uk=0.006670539761597529073698869358812557054558
   local k=(n-N0uk)/auk+lambda0uk/dr
   local nextcounter=0
   local j3, j4, j5, j6, m
   repeat
     nextcounter=nextcounter+1
     local k3=k-lambda0uk/dr
     local k4=k+lambda0uk/dr
     j3=(1.0+n1uk+1.25*pow(n1uk,2.0)+1.25*pow(n1uk,3.0))*k3
     j4=(3.0*n1uk+3.0*pow(n1uk,2.0)+2.625*pow(n1uk,3.0))*sin(k3)*cos(k4)
     j5=(1.875*pow(n1uk,2.0)+1.875*pow(n1uk,3.0))*sin(2.0*k3)*cos(2.0*k4)
     j6=35.0/24.0*pow(n1uk,3.0)*sin(3.0*k3)*cos(3.0*k4)
     m=buk*(j3-j4+j5-j6)
     k=k+(n-N0uk-m)/auk
   until abs(n-N0uk-m)<=0.000000001 or nextcounter>=100
   local v=auk/sqrt(1.0-e2uk*pow(sin(k),2.0))
   local r=v*(1.0-e2uk)/(1.0-e2uk*pow(sin(k),2.0))
   local h2=v/r-1.0
   local y1=e-E0uk
   j3=tan(k)/(2.0*r*v)
   j4=tan(k)/(24.0*r*pow(v,3.0))*(5.0+3.0*pow(tan(k),2.0)+h2-9.0*pow(tan(k),2.0)*h2)
   j5=tan(k)/(720.0*r*pow(v,5.0))*(61.0+90.0*pow(tan(k),2.0)+45.0*pow(tan(k),4.0))
   local k9=k-y1*y1*j3+pow(y1,4.0)*j4-pow(y1,6.0)*j5
   j6=1.0/(cos(k)*v)
   local j7=1.0/(cos(k)*6.0*pow(v,3.0))*(v/r+2.0*pow(tan(k),2.0))
   local j8=1.0/(cos(k)*120.0*pow(v,5.0))*(5.0+28.0*pow(tan(k),2.0)+24.0*pow(tan(k),4.0))
   local j9=1.0/(cos(k)*5040.0*pow(v,7.0))
   local j9=j9*(61.0+662.0*pow(tan(k),2.0)+1320.0*pow(tan(k),4.0)+720.0*pow(tan(k),6.0))
   local long=phi0uk+dr*(y1*j6-y1*y1*y1*j7+pow(y1,5.0)*j8-pow(y1,7.0)*j9)
   local lat=k9*dr
   local v=6377563.396/sqrt(1.0-e2uk*pow(sin(k),2.0))
   local cartxa=v*cos(k9)*cos(long/dr)
   local cartya=v*cos(k9)*sin(long/dr)
   local cartza=(1.0-e2uk)*v*sin(k9)
   -- Helmert-Transformation from OSGB36 to WGS84 map date
   local rotx=-0.1502/3600.0/dr
   local roty=-0.2470/3600.0/dr
   local rotz=-0.8421/3600.0/dr
   local scale=-20.4894/1000000.0
   local cartxb=446.448+(1.0+scale)*cartxa+rotz*cartya-roty*cartza
   local cartyb=-125.157-rotz*cartxa+(1.0+scale)*cartya+rotx*cartza
   local cartzb=542.06+roty*cartxa-rotx*cartya+(1.0+scale)*cartza
   -- convert Cartesian to long/lat
   local awgs84=6378137.0
   local bwgs84=6356752.3141
   local e2wgs84=0.00669438003551279089034150031998869922791
   local lambdaradwgs84=atan(cartyb/cartxb)
   long=lambdaradwgs84*dr
   local pxy=sqrt(pow(cartxb,2.0)+pow(cartyb,2.0))
   local phiradwgs84
   local phinewwgs84=atan(cartzb/pxy/(1.0-e2wgs84))
   nextcounter=0
   repeat
     phiradwgs84=phinewwgs84
     nextcounter=nextcounter+1
     v=awgs84/sqrt(1.0-e2wgs84*pow(sin(phiradwgs84),2.0))
     phinewwgs84=atan((cartzb+e2wgs84*v*sin(phiradwgs84))/pxy)
   until abs(phinewwgs84-phiradwgs84)<=0.000000000001 or nextcounter>=100
   lat=phinewwgs84*dr
   return "GB",nil,lat,long
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 err, n, e, pr, T1, T2 = northeast(lett,num,0)
   if err ~= nil then
     return "GB",err,0.0,0.0
   end
   -- use British definition of e and n
   e=500000.0*(T1%5)+100000.0*(T2%5)-1000000.0+e*pr
   n=1900000.0-500000.0*math.floor(T1/5)-100000.0*math.floor(T2/5)+n*pr
   return GBEN2LL(e,n)
end
   
local function IrishEN2LL(e,n)
   local pow,sqrt,abs=math.pow,math.sqrt,math.abs
   local sin,cos,tan,atan=math.sin,math.cos,math.tan,math.atan
   local dr=math.deg(1.0)
   -- True Origin is 8 deg W
   local phi0ir=-8.0
   -- True Origin is 53.5 deg N
   local lambda0ir=53.5
   -- scale factor @ central meridian
   local F0ir=1.000035
   -- True origin in 200 km E of false origin
   local E0ir=200000.0
   --True origin is 250km N of false origin
   local N0ir=250000.0
   -- semi-major axis (in line to equator) 1.000035 is yer scale @ central meridian
   local air=6377340.189*F0ir
   --semi-minor axis (in line to poles)
   local bir=6356034.447*F0ir
   -- flatness=a1-b1/(a1 + b1)
   local n1ir=0.001673220384152058651484728058385228837777
   -- first eccentricity squared=2*f-f^2 where f=(a1-b1)/a1
   local e2ir=0.006670540293336110419293763349975612794125
   local k=(n-N0ir)/air+lambda0ir/dr
   local nextcounter=0
   local j3,j4,j5,j6,m
   repeat
     nextcounter=nextcounter+1
     local k3=k-lambda0ir/dr
     local k4=k+lambda0ir/dr
     j3=(1.0+n1ir+1.25*pow(n1ir,2.0)+1.25*pow(n1ir,3.0))*k3
     j4=(3.0*n1ir+3.0*pow(n1ir,2.0)+2.625*pow(n1ir,3.0))*sin(k3)*cos(k4)
     j5=(1.875*pow(n1ir,2.0)+1.875*pow(n1ir,3.0))*sin(2.0*k3)*cos(2.0*k4)
     j6=35.0/24.0*pow(n1ir,3.0)*sin(3.0*k3)*cos(3.0*k4)
     m=bir*(j3-j4+j5-j6)
     k=k+(n-N0ir-m)/air
   until abs(n-N0ir-m)<=0.000000000001 or nextcounter>=10000
   local v=air/sqrt(1.0-e2ir*pow(sin(k),2.0))
   local r=v*(1.0-e2ir)/(1.0-e2ir*pow(sin(k),2.0))
   local h2=v/r-1.0
   local y1=e-E0ir
   j3=tan(k)/(2.0*r*v)
   j4=tan(k)/(24.0*r*pow(v,3.0))*(5.0+3.0*pow(tan(k),2.0)+h2-9.0*pow(tan(k),2.0)*h2)
   j5=tan(k)/(720.0*r*pow(v,5.0))*(61.0+90.0*pow(tan(k),2.0)+45.0*pow(tan(k),4.0))
   local k9=k-y1*y1*j3+pow(y1,4.0)*j4-pow(y1,6.0)*j5
   j6=1.0/(cos(k)*v)
   local j7=1.0/(cos(k)*6.0*pow(v,3.0))*(v/r+2.0*pow(tan(k),2.0))
   local j8=1.0/(cos(k)*120.0*pow(v,5.0))*(5.0+28.0*pow(tan(k),2.0)+24.0*pow(tan(k),4.0))
   local j9=1.0/(cos(k)*5040.0*pow(v,7.0))
   local j9=j9*(61.0+662.0*pow(tan(k),2.0)+1320.0*pow(tan(k),4.0)+720.0*pow(tan(k),6.0))
   local long=phi0ir+dr*(y1*j6-y1*y1*y1*j7+pow(y1,5.0)*j8-pow(y1,7.0)*j9)
   local lat=k9*dr
   -- convert long/lat to Cartesian coordinates
   v=6377340.189/sqrt(1.0-e2ir*pow(sin(k),2.0))
   local cartxa=v*cos(k9)*cos(long/dr)
   local cartya=v*cos(k9)*sin(long/dr)
   local cartza=(1.0-e2ir)*v*sin(k9)
   -- Helmert-Transformation from Ireland 1965 to WGS84 map date
   local rotx=1.042/3600.0/dr
   local roty=0.214/3600.0/dr
   local rotz=0.631/3600.0/dr
   local scale=8.15/1000000.0
   local cartxb=482.53+(1.0+scale)*cartxa+rotz*cartya-roty*cartza
   local cartyb=-130.596-rotz*cartxa+(1.0+scale)*cartya+rotx*cartza
   local cartzb=564.557+roty*cartxa-rotx*cartya+(1.0+scale)*cartza
   -- convert Cartesian to long/lat
   local awgs84=6378137.0
   local bwgs84=6356752.3141
   local e2wgs84=0.00669438003551279089034150031998869922791
   local lambdaradwgs84=atan(cartyb/cartxb)
   long=lambdaradwgs84*dr
   local pxy=sqrt(pow(cartxb,2.0)+pow(cartyb,2.0))
   local phinewwgs84=atan(cartzb/pxy/(1.0-e2wgs84))
   local phiradwgs84
   nextcounter=0
   repeat
     phiradwgs84=phinewwgs84
     nextcounter=nextcounter+1
     v=awgs84/sqrt(1.0-e2wgs84*pow(sin(phiradwgs84),2.0))
     phinewwgs84=atan((cartzb+e2wgs84*v*sin(phiradwgs84))/pxy)
   until abs(phinewwgs84-phiradwgs84)<=0.000000000001 or nextcounter>=10000
   lat=phinewwgs84*dr
   return "IE",nil,lat,long
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 err, n, e, pr, T1 = northeast(lett,num,0)
   if err ~= nil then
     return "IE",err,0.0,0.0
   end
   -- use Irish definition of northing and easting
   local e=100000.0*(T1%5.0)+e*pr
   local n=n*pr+100000.0*(4.0-math.floor(T1/5.0))
   return IrishEN2LL(e,n)
end

local function empty(s)
  return s == nil or s == ''
end

local function NGR2LL(ngr)
-- returns a country,error,lat,long list
  ngr = mw.ustring.gsub(mw.ustring.upper(ngr),"[%s%p]","")
  local first, last, lett, num = mw.ustring.find(ngr,"^([A-Z]+)(%d+)$")
  if first == nil or empty(lett) or empty(num) or mw.ustring.len(lett) > 2 then
  	return nil,"Malformed NGR",0.0,0.0
  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 mw.ustring.find(s,"%D") == nil
end

local function warning(errmsg)
  local msg = errmsg or 'Empty OS grid ref'
  
  local html = preview._warning({ msg })

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

function oscoord.main(frame)
  local args = getArgs(frame,{parentFirst=true,parentOnly=false,frameOnly=false})
  local input = args[1]
  if empty(input) then
  	return warning(nil)
  end
  local linktitle = args[2]
  local namearg = args["name"]
  local rawurl = 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[2]) then
    return linktitle ..warning(LL[2])
  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 yesno(rawurl) then
  	url = url..'['
  end
  url = url..'https://geohack.toolforge.org/geohack.php?'
  if not empty(pagename) then
  	url = url..'pagename='..pagename..'&'
  end
  url = url..'params='..LL[3]..'_N_'
  if LL[4] < 0 then
  	url = url..(-LL[4])..'_W'
  else
  	url = url..LL[4]..'_E'
  end
  for i = restargs,#args do
  	url = url..'_'..args[i]
  end
  if mw.ustring.find(input,"region") == nil then
    url = url..'_region:'..LL[1]
  end
  if not empty(namearg) then
    url = url .. "&title=" .. mw.uri.encode(namearg)
  end
  if not yesno(rawurl) then
	url = url..' '..linktitle..']'
  end
  return url
end

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

return oscoord

Module:Ordnance Survey coordinates

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