Angular Data and Symmetry

Coordinate Systems

Type-A, Type-B and Type-C use different angular conventions; identical angle pairs do not generally describe identical Cartesian directions in different conventions. HEALPix uses a different sampling representation.

In Type-C data, C identifies the plane around the photometric axis and gamma identifies the conic angle. The full domain is C from 0 to 360 degrees and gamma from 0 to 180 degrees. C = 0 and C = 360 describe coincident directions.

Changing displayed coordinates differs from resampling stored data. See Photometry Type and Resolution.

Sampling

A denser angular grid does not recover detail absent from the measurement. Narrow peaks and sharp cutoffs need sufficient source resolution. Resampling or modifying a distribution can change its integrated flux; check the result rather than assuming conservation.

Symmetry

Command API code	Symmetry
0	No symmetry
1	C0-C180 plane symmetry
2	C90-C270 plane symmetry
3	Quadratic symmetry
4	Rotational symmetry

A rotationally symmetric distribution can be stored with a single C plane. A full-domain calculation must still include the complete azimuthal solid angle. Shared boundaries and the repeated C = 360 plane must not be counted twice.

Numerically symmetric samples and an explicit symmetry setting are different. Applying symmetry can modify the distribution; it is not merely a report label. See Symmetrize.