Module:OS coordinates

-- 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 namespace = mw.title.getCurrentTitle.namespace;

local function northeast(lett,num,shift) -- split into northings and eastings local le=string.len(num) if le%2 == 1 then return "Malformed numerical part of NGR" end local pr=le/2 local n = string.sub(num,pr+1) local e = string.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 if string.len(n) == 0 then n = 0 end if string.len(e) == 0 then e = 0 end pr = math.pow(10.0,(5.0-pr)) local T1 = string.byte(string.sub(lett,1,1))-65 if T1>8 then T1 = T1-1 end local T2 = nil if string.len(lett)>1 then T2 = string.byte(string.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 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 NGR2LL(ngr) -- returns a country,error,lat,long list ngr = string.gsub(string.upper(ngr),"[^%d%u]","") local lett = string.gsub(ngr,"[^%u]","") local num = string.gsub(ngr,"[^%d]","") if string.len(lett) == 1 then return Irish2LL(lett,num) end if string.len(lett) == 2 then return GB2LL(lett,num) end return nil,"Malformed NGR",0.0,0.0 end

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

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

local function alldigits(s) return string.find(s,"%D") == nil end

local function warning(errmsg) local frame = mw.getCurrentFrame:getParent local html = "" local msg = errmsg if errmsg == nil then msg = "Empty OS grid ref" end if frame:preprocess( "" ) == "" then html = ' Warning: '..msg html = html..' (this message is shown only in preview) ' end if namespace == 0 and errmsg ~= nil then html = html..'' end return html end

function oscoord.main(frame) local args = getArgs(frame,{parentFirst=true,parentOnly=false,frameOnly=false}) local input = args[1] if input == nil or string.len(input)==0 then return warning(nil) end local linktitle = args[2] 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 string.sub(args[1],1,1) == 'i' then local firstArg = string.sub(args[1],2) if alldigits(firstArg) then LL = {IrishEN2LL(firstArg,args[2])} restargs = 3 if linktitle == nil or string.len(linktitle) == 0 then linktitle=args[1]..'_'..args[2] end end elseif alldigits(args[1]) then LL = {GBEN2LL(args[1],args[2])} restargs = 3 if linktitle == nil or string.len(linktitle) == 0 then linktitle=args[1]..'_'..args[2] end end else LL = {NGR2LL(args[1])} restargs = 2 if linktitle == nil or string.len(linktitle) == 0 then linktitle=args[1] end end linktitle = trim(linktitle) if LL[2] ~= nil then html = linktitle html = html..warning(LL[2]) return html end local url = '..';'..LL[4] for i = restargs,#args do   url = url..'_'..args[i] end if string.find(input,"region") == nil then url = url..'_region:'..LL[1] end if pagename ~= nil then url = url..'?pagename='..pagename end url = url..' '..linktitle..']' return url end

return oscoord