Openstreetmap rectangular grid for whole planet

Question

I`m trying to generate rectangular grid for whole world with fixed cell size in 350 meters (width and height are equals).

What i tried to do:

1) in main loop iterate trough longitude in range [-180; 180]

2) in nested loop iterate trough latitude in range [-85.06; 85.06] (Web mercator bounds)

3) increment cells bound to 350 meters on East (in main loop) and North (in nested loop) using Java GeographicLib Geodesic.WGS84.Direct().

Java code:

double lon_min = -180;
double lon_max = 180;
double lat_min = -85.06;
double lat_max = 85.06;

double lon_max_c = lon_min;
double lon_min_c = lon_min;

int grid_x = 0;
int grid_y = 0;
int cell_id = 0;

while(lon_max_c < lon_max)
{
    double lat_min_c = lat_min;
    double lat_max_c = lat_min;

    lon_min_c = lon_max_c;
    GeodesicData g = Geodesic.WGS84.Direct(lat_min_c, lon_min_c, 90, 350);

    boolean isXlast = g.lon2 > lon_max || (lon_min_c > 0 && g.lon2 < 0);
    lon_max_c = isXlast? lon_max : g.lon2;

    grid_y = 0;

    while(lat_max_c < lat_max)
    {
        lat_min_c = lat_max_c;

        GeodesicData g1 = Geodesic.WGS84.Direct(lat_min_c, lon_min_c, 0, 350);

        boolean isYlast = g1.lat2 > lat_max;
        lat_max_c = isYlast? lat_max : g1.lat2;

        System.out.print("\rid: " +  cell_id + " lon: " + lon_max_c + " lat: " + lat_max_c);

        grid_y = grid_y + 1;
        cell_id = cell_id + 1;
    }
    grid_x = grid_x + 1;
}

As a result, ~530 million cells were generated. Howewer, area of whole planet is ~510M squared kilometers. So, the total number of cells should be about 4 billion. I'm pretty new to geodesic math, so what is wrong? What should I do to generate this grid correctly?

Answer 1

rectangular grid for whole world with fixed cell size in 350 meters (width and height are equals)

What you are trying to do is impossible as Earth is not a rectangle. See https://en.wikipedia.org/wiki/Map_projection for starting point to learn more.

While this effect can be ignored for small areas, on scale like "longitude in range [-180; 180]", "latitude in range [-85.06; 85.06]" ignoring it is not feasible.