spherical-coordinates 0.0.0

Install

pip install spherical_coordinates

Transformations

CORSIKA uses mainly two representations for directions in three dimensional space. First, the azimuth-zenith representation, and second cartesian direction vectors of length 1.

The azimuth-zenith representation uses two floats (azimuth_rad and zenith_rad). The cartesian vector uses three floats (cx, cy, and cz).

In equations within CORSIKA’s documents, the azimuth angle is represented by greek letter Phi and the zenith angle is represented by greek letter Theta. Here, we use CORSIKA’s explicit names ‘azimuth’ and ‘zenith’ as they are used in the text body of e.g. CORSIKA’s manual.

import spherical_coordinates

cx, cy, cz = spherical_coordinates.az_zd_to_cx_cy_cz(
    azimuth_rad=0.2,
    zenith_rad=0.3,
)
print(cx, cy, cz)
0.28962947762551555 0.058710801693826566 0.955336489125606

az, zd = spherical_coordinates.cx_cy_cz_to_az_zd(cx=cx, cy=cy, cz=cz)
print(az, zd)
0.20000000000000015 0.30000000000000016

import spherical_coordinates

cx, cy = spherical_coordinates.az_zd_to_cx_cy(
    azimuth_rad=0.2,
    zenith_rad=0.3,
)
print(cx, cy, cz)
0.28962947762551555 0.058710801693826566

az, zd = spherical_coordinates.cx_cy_to_az_zd(cx=cx, cy=cy)
print(az, zd)
0.20000000000000015 0.30000000000000016

import spherical_coordinates

zenith_below_xy_plane_rad = 2.0
cx, cy = spherical_coordinates.az_zd_to_cx_cy(
    azimuth_rad=0.2,
    zenith_rad=zenith_below_xy_plane_rad,
)
az, zd = spherical_coordinates.cx_cy_to_az_zd(cx=cx, cy=cy)
print(zd)
1.1415926535897933
# zd is now the projection into the upper hemisphere

import spherical_coordinates

cz = spherical_coordinates.restore_cz(cx=0.1, cy=0.2)
print(cz)

Angles Between

Quickly estimate the angle between two pointings.

import spherical_coordinates

delta = spherical_coordinates.angle_between_cx_cy_cz(
    cx1=0.5, cy1=0.5, cz1=0.7071, cx2=0.7071, cy2=0.0, cz2=0.7071
)
print(delta*180/3.14159, "DEG")
31.399818557245204 DEG

delta = spherical_coordinates.angle_between_cx_cy(
    cx1=0.5, cy1=0.5, cx2=0.7071, cy2=0.0
)
print(delta*180/3.14159, "DEG")
31.399818557245204 DEG

delta = spherical_coordinates.angle_between_az_zd(
    azimuth1_rad=1.2, zenith1_rad=0.2, azimuth2_rad=-0.5, zenith2_rad=0.7
)
print(delta*180/3.14159, "DEG")
42.852624700439804 DEG

Azimuth Range

From my experience, some parts in CORSIKA expect the azimuth angle to be in the so called ‘least absolute residue’. This is:

For this spherical_coordinates has a range limiter:

import spherical_coordinates

az = spherical_coordinates.azimuth_range(azimuth_rad=123.4)
print(az*180/3.1415, "DEG")
-129.7046334064967 DEG