Comparison of HEALPix with other tessellations, including the QuadCube, icosahedral tessellation of the sphere, and ECP or "geographic grid." The shaded areas illustrate the subsets of all pixels on the sky for which the associated Legendre functions have to be computed in order to perform the spherical harmonic transforms. This plot demonstrates why the isolatitude ECP and HEALPix point sets support faster computation of spherical harmonic transforms than the QuadCube, the icosahedral grid, and any nonisolatitude construction.