ECP pixelization   

GLCP pixelization:

A version of the cylindrical projection pixelization (or rather discretization) scheme (see e.g., Mucciacia, Natoli, & Vittorio, 1997) in which the polar angles, theta of the iso-latidudinal rings are determined according to the zeros of the Legendre polynomial of order nrings and with the quadrature weights assigned to each ring as defined by the Gauss-Legendre quadrature of the same order. The S2HAT pixelization structure, pixelization, of the type s2hat_pixeltypr, describing this scheme is set by calling

set_pixelization( PIXCHOICE_GLCP, pixpars, pixelization),

where PIXCHOICE_GLCP is a predefined S2HAT parameter (a 4-byte integer set to 3) and:
the field par1 of the pixpars variable is equal to nrings, i.e., a total number of iso-latitude rings
the field par2 of the pixpars variable is equal to nphi, i.e., a number of pixels per ring.

Check here or here to find more about the set_pixelization routine in Fortran 90 and C, respectively.

Brief description

The pixel centers are then located on the iso-latitude rings as given by,

theta_i, for i = 0, ..., nrings-1 are such that P_(l = nrings) ( cos( theta_i)) = 0, where P_l is the Legendre polynomial of order l;

and for each latitude their azimuths are given by,

phi_j = j dphi, for j = 0, ..., nphi-1 and dphi = 2 PI/nphi.

The global pixel numbers start at 0 at the North Pole and continue ring-by-ring and left-to-right.