モジュール:Ordnance Survey 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)=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)=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)=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)=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 = args1
if input == nil or string.len(input)==0 then
	return warning(nil)
end
local linktitle = args2
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(args2) then
if string.sub(args1,1,1) == 'i' then
local firstArg = string.sub(args1,2)
if alldigits(firstArg) then
LL = {IrishEN2LL(firstArg,args2)}
	    restargs = 3
	    if linktitle == nil or string.len(linktitle) == 0 then
linktitle=args1..'_'..args2
	    end
end
elseif alldigits(args1) then
LL = {GBEN2LL(args1,args2)}
restargs = 3
if linktitle == nil or string.len(linktitle) == 0 then
linktitle=args1..'_'..args2
end
end
else
LL = {NGR2LL(args1)}
restargs = 2
if linktitle == nil or string.len(linktitle) == 0 then
linktitle=args1
end
end
linktitle = trim(linktitle)
if LL2 ~= nil then
local html = linktitle
html = html..warning(LL2)
return html
end
local url = '..';'..LL4
for i = restargs,#args do
url = url..'_'..argsi
end
if string.find(input,"region") == nil then
url = url..'_region:'..LL1
end
if pagename ~= nil then
url = url..'?pagename='..pagename
end
url = url..' '..linktitle..
return url
end
return oscoord