/// <param name="k">resolution, 9 is 5-arc min, 11 is 1-arc min</param>
public HealpixManager(int k)
{
Neibors = new NeighborManager(this);
K = k;
Nside = 1 << k;
Npix = 12 * Nside * Nside;
EquatorPixelsCount = (2 * Nside - 1) * 4 * Nside;
PolarPixelsCount = (4 + 4 * Nside) * Nside / 2;
OmegaPix = Math.PI / (3 * Nside * Nside);
ThetaPix = Math.Sqrt(OmegaPix);
}