UFOIce and water
22° and 46° haloes, sundogs, the parhelic circle, tangent, circumzenithal and circumhorizontal arcs: not one of those angles is stored. Each is derived from the refractive index of ice and the geometry of the crystal, which is what makes the whole display move together and stay consistent with the Sun's own height. Pyramid-ended crystals add the odd-radius haloes (9°, 20°, 35°), and plates free to turn about a level axis add Lowitz's arcs; the mix of crystals is stated by the recording, since no record counts them. Point at a ring, an arc or a sundog to have it named; hold Alt for what it is and what makes it.
The halo simulation was checked against Atmospheric Optics, the reference on these phenomena: the 22° halo (red edge at 21.7°) and the sundogs (about 22° from a low Sun) agree.
Rainbows and moonbows are ray-traced through a spherical drop for the same reason — the order of the colours, the gap between the two bows and the light inside the primary come out of the trace rather than being drawn in.
Every source is named where its data is reported, with the attribution its licence requires — and can be swapped for another. The picker is the credit. What is still missing, and what each item is waiting on, is on the roadmap.