TileProvider method getTile - need to translate x and y to lat/long

Question

I’m porting an iOS app to Android, and using Google Maps Android API v2. The application needs to draw a heatmap overlay onto the map.

So far, it looks

Answer 1

On zoom level 0, there is only one tile (x=0,y=0). On next zoom level number of tiles are quadrupled (doubled on x and y).

This means on zoom level W, x may be a value in range <0, 1 << W).

From documentation:

The coordinates of the tiles are measured from the top left (northwest) corner of the map. At zoom level N, the x values of the tile coordinates range from 0 to 2N - 1 and increase from west to east and the y values range from 0 to 2N - 1 and increase from north to south.

You can achieve this using simple calculations.

For longitude this is straightforward :

double longitudeMin = (((double) x) / (1 << zoom)) * 360 - 180;
double longitudeMax = (((double) x + 1) / (1 << zoom)) * 360 - 180;
longitudeMax = Double.longBitsToDouble(Double.doubleToLongBits(longitudeMax) - 1); // adjust

Here x is first scaled into <0,1), then into <-180,180).

The max value is adjusted, so it doesn't overlap with the next area. You may skip this.

For latitude this will be a bit harder, because Google Maps use Mercator projection.

First you scale y just like it was in range <-180,180). Note that the values need to be reversed.

double mercatorMax = 180 - (((double) y) / (1 << zoom)) * 360;
double mercatorMin = 180 - (((double) y + 1) / (1 << zoom)) * 360;

Now you use a magical function that does Mercator projection (from SphericalMercator.java):

public static double toLatitude(double mercator) {
    double radians = Math.atan(Math.exp(Math.toRadians(mercator)));
    return Math.toDegrees(2 * radians) - 90;
}

latitudeMax = SphericalMercator.toLatitude(mercatorMax);
latitudeMin = SphericalMercator.toLatitude(mercatorMin);
latitudeMin = Double.longBitsToDouble(Double.doubleToLongBits(latitudeMin) + 1);

This was was typed from memory and was not tested in any way, so if there is an error there, please put a comment and I will fix it.