Module:Infobox dim

 require('strict')
 localgetArgs=require('Module:Arguments').getArgs
 localp={}

 locallog2=0.693147181
 localppm=1000/0.3-- pixels per meter, from 0.3 mm / pixel from https://wiki.openstreetmap.org/wiki/Zoom_levels

 -- To convert to OSM zoom level, we need to know meters per pixel at zoom level 9
 -- On the equator, it's 305.748 meters/pixel according to https://wiki.openstreetmap.org/wiki/Zoom_levels
 -- This quantity depends on the latitude (which we usually don't have easy access to)
 -- Instead, we'll be correct at 38 degrees N, given en-WP bias towards NA and Europe
 -- 38N was chosen because:
 -- * It's the furthest north where scale=100000 maps to zoom=12
 -- * One hemisphere (20000km) maps to zoom=1
 localmppl9Equator=305.748

 -- Convert from Geohack's scale to OSM style zoom levels as used by <maplink>
 localfunctiongeohackScaleToMapZoom(scale,latitude)
 scale=tonumber(scale)
 ifnotscaleorscale<=0thenreturnend
 latitude=latitudeor38
 localmppl9=mppl9Equator*math.cos(math.rad(latitude))
 returnmath.log(mppl9*ppm/scale)/log2+9
 end

 -- compute the viewport size (on screen) in meters, assuming ppm pixels per meter on screen
 localfunctioncomputeViewport(args)
 localviewport_cm=tonumber(args.viewport_cm)
 localviewport_px=tonumber(args.viewport_px)
 returnviewport_cmandviewport_cm/100orviewport_pxandviewport_px/ppm
 ortonumber(args.default_viewport)or0.1
 end

 -- convert from geohack dim (knowing the viewpoint size on screen) to geohack scale
 localfunctiongeohackDimToScale(dim,args)
 dim=tonumber(dim)
 args=argsor{}
 ifnotdimordim<=0thenreturnend
 localunits=args.units
 ifunitsandstring.lower(units)=='km'then
 dim=dim*1000
 end
 returndim/computeViewport(args)
 end

 -- inverse of above function, returning dim in km
 localfunctiongeohackScaleToDim(scale,args)
 scale=tonumber(scale)
 args=argsor{}
 ifnotscaleorscale<=0thenreturnend
 returnscale*computeViewport(args)*1e-3
 end

 localoddShape=2.09--- length/sqrt(area) of Boston (to choose an example)

 -- Convert from Geohack's types to Geohack dim
 localfunctiongeohackTypeToDim(args)
 localt=args.type
 ifnottthenreturnend
 localtypeDim=mw.loadData('Module:Infobox_dim/data')
 localdim=typeDim[t]
 localpopulation=tonumber(args.population)
 ift=='city'andpopulationandpopulation>0then
 -- assume city is a circle with density of 1000/square kilometer
 -- compute diameter, in meters. Then multiply by oddShape to account for weird shapes
 dim=35.68e-3*math.sqrt(population)*oddShape
 -- don't zoom in too far
 ifdim<5then
 dim=5
 end
 end
 returndim
 end

 -- Convert from dimension of object to Geohack dim
 localfunctioncomputeDim(length,width,area)
 iflengthandwidththen
 returnmath.max(length,width)
 end
 iflengththenreturnlengthend
 ifwidththenreturnwidthend
 ifareathenreturnoddShape*math.sqrt(area)end
 end

 -- compute geohack dim from unit arguments (e.g., length_mi)
 localfunctionconvertDim(args)
 locallength=args.length_miand1.60934*args.length_miorargs.length_km
 localwidth=args.width_miand1.60934*args.width_miorargs.width_km
 localarea=args.area_acreand0.00404686*args.area_acreor
 args.area_haand0.01*args.area_haor
 args.area_mi2and2.58999*args.area_mi2orargs.area_km2
 localdim=computeDim(length,width,area)
 returndim
 end

 localfunctioncomputeScale(args)
 ifargs.scalethenreturnargs.scaleend
 localdim,units,scale
 ifargs.dimthen
 dim,units=mw.ustring.match(args.dim,"^([-%d%.]+)%s*(%D*)")
 args.units=units
 args.default_viewport=0.1-- default geohack viewpoirt
 scale=geohackDimToScale(dim,args)
 end
 ifnotscalethen
 dim=convertDim(args)orgeohackTypeToDim(args)
 args.units='km'
 args.default_viewport=0.2--- when object dimensions or type is specified, assume 20cm viewport
 scale=dimandgeohackDimToScale(dim,args)
 end
 ifnotscalethenreturnend
 scale=math.floor(scale+0.5)
 -- keep scale within sane bounds (OSM zoom levels 1-17)
 ifscale<1600then
 scale=1600
 end
 ifscale>200e6then
 scale=200e6
 end
 returnscale
 end

 -- Argument checking
 localpositiveNumericArgs={viewport_cm=true,viewport_px=true,length_mi=true,length_km=true,
 width_mi=true,width_km=true,area_mi2=true,area_km2=true,
 area_acre=true,area_ha=true,scale=true,population=true}

 localfunctioncleanArgs(args)
 localclean={}
 iftype(args)=='table'then
 fork,vinpairs(args)do
 ifpositiveNumericArgs[k]then
 v=vandmw.ustring.gsub(v,",","")-- clean out any commas
 v=tonumber(v)-- ensure argument is numeric
 ifvandv<=0then-- if non-positive, ignore value
 v=nil
 end
 end
 clean[k]=v
 end
 end
 returnclean
 end

 -- Module entry points
 functionp._dim(args)
 args=cleanArgs(args)
 ifargs.dimthenreturnargs.dimend
 -- compute scale for geohack
 localscale=args.scale
 localdim
 ifnotscalethen
 args.default_viewport=0.2-- when specifying a object dimension or type, assume output spans 20cm
 dim=convertDim(args)orgeohackTypeToDim(args)
 args.units='km'
 scale=dimandgeohackDimToScale(dim,args)
 end
 -- reset back to 10cm viewport for correct geohack dim output
 args.viewport_cm=10
 dim=scaleandgeohackScaleToDim(scale,args)
 returndimandtostring(math.floor(dim+0.5))..'km'
 end

 functionp._scale(args)
 args=cleanArgs(args)
 returncomputeScale(args)
 end

 functionp._zoom(args)
 args=cleanArgs(args)
 args.viewport_px=args.viewport_pxor200--- viewport for Kartographer is 200px high
 localscale=computeScale(args)
 ifscalethen
 locallatitude=tonumber(args.latitude)
 latitude=latitudeand(latitude>70and70orlatitude<-70and-70orlatitude)
 localzoom=geohackScaleToMapZoom(scale,latitude)
 returnzoomandmath.floor(zoom)
 end
 end

 -- Template entry points
 functionp.dim(frame)
 returnp._dim(getArgs(frame))or''
 end

 functionp.scale(frame)
 returnp._scale(getArgs(frame))or''
 end

 functionp.zoom(frame)
 returnp._zoom(getArgs(frame))or''
 end

 returnp