Static cdshealpix::LAT_OF_SQUARE_CELL

pub static LAT_OF_SQUARE_CELL: f64

Latitude, in the equatorial region, for which the distance from the cell center to its four vertices is almost equal on the sky (i.e. the shape of the cell on the sky is close to a square). The larger the depth, the better the approximation (based on differential calculus).

dX = dY = 1 / nside (center to vertex distance) X = 4/pi * lon => dX = 4/pi dlon Y = 3/2 * sin(lat) => dY = 3/2 * cos(lat) dlat dlon * cos(lat) = dlat (same distance on the sky) => cos^2(lat) = 2/3 * 4/pi => lat = arccos(sqrt(2/3 * 4/pi)) ~= 22.88 deg ~= 0.39934 rad

use cdshealpix::{TRANSITION_Z, FOUR_OVER_PI, LAT_OF_SQUARE_CELL};
assert!(f64::abs(f64::acos(f64::sqrt(TRANSITION_Z * FOUR_OVER_PI)) - LAT_OF_SQUARE_CELL) < 1e-15_f64);