How to convert a bing maps quadkey to mercator coordinates

Question

How do you convert a bing maps quad key, such as "03200320023" to coordinates in mercator virtual earth (epsg 3857) coordinate system?

I've got an algorithm to convert to coordinates in latitude longitude (e.g. the quad key above comes to "-84.19921875,33.7243385314941,-84.0234375,33.8704147338867"). I could then convert from latitude longitude to mercator coordinate, but that smells far too expensive in processing power.

The mercator virtual earth result I'm looking for given the above quadkey is: "-9373014,4011415,-9353446,4030983"

Some more context. I'm using bing maps and adding layers that I'm serving using mapserver from IIS using fastcgi. I basically want to convert the bing maps quadkey request for 256x256 tiles to a mapserver wms query in epsg 3857. It works in epsg 4326 (wgs84) and also when I convert from wgs84 to epsg 3857. However the performance is not what I want due to the two stage conversion.

I've also asked the question on gis.stackexchange.com which has now been answered

Your algorithm is already converting it to coordinates in mercator coordinate system. What is your question? — Micromega
The algorithm converts it to lat lon in wgs84 - or am I mistaken? — Nick Randell
I've edited the question to say mercator virtual earth (epsg 3857) — Nick Randell
IMO mercantor projection isn't that costly and do you have the algorithm to convert from mercantor to quadkey? — Micromega
There's no option to migrate it automatically, but you might consider asking on the GIS StackExchange. — erickson

Nick Randell Nick Randell · Accepted Answer · 2011-04-28T11:49:42

For completeness, here is the F# code I'm using to solve this problem.

let quadKeyToVE key =
let offset,x,y =
    key
    |> Seq.fold (fun (offset,x,y) ch ->
        let x',y' = 
            match ch with
            | '0' -> x-offset,y+offset
            | '1' -> x+offset,y+offset
            | '2' -> x-offset,y-offset
            | '3' -> x+offset,y-offset
            | _ -> failwith "Invalid quadkey"
        offset/2.0,x',y'
        ) (InitialOffset,0.0,0.0)

let offset = offset * 2.0
let west = x - offset
let north = y + offset
let east = x + offset
let south = y - offset
west,south,east,north

How to convert a bing maps quadkey to mercator coordinates

1 Answers