Slippy map coordinates

Polymaps has the ability to easily pull in raster tiles from various sources to make Slippy maps. I have code that lets me use tiles made by Google, Cloudmade, Bing, GDAL’s tile script, even Minecraft. I have no idea how it works, though. The underlying thing I don’t understand is Polymaps’ internal coordinate representation. Here’s an example, for a map tile centered on San Francisco.

This tells me Polymaps is natively using Google’s coordinate system. TMS is similar but numbered differently, here’s my cargo cult code to work with it. Mike tells me 1 << c.zoom is the number of tiles at the given zoom level, which explains why it’s used as a modulus everywhere.

    // Set X to c.column, but wrapped around in the range [0, numTiles)
    var x = c.column % (1 << c.zoom);
    if (x < 0) {
      x = x + (1 << c.zoom)
    // Set Y to numTiles - c.row, to account for TMS doing lat backwards
    var y = (1 << c.zoom) - c.row - 1;
    var url = "" + c.zoom + "/" + y + "/" + x + ".jpg";

More info: interactive coordinate exploration tool, Google docs, OSM / TMS docs.