Ef luh 4th wail duses enndeed sel 3 piams, luhn lam's shuulab ennformatigu per parluza ayn o0bject enn 3d saprum. Talaever, villalayn lejeyledge ol luh co-ordinate snaspel (origenn, units) lam's nuve harful.
Gu luh otaer hab, ef va essume a sensible co-ordinate snaspel vuw seloly catdidates cayn se converted per ohvaa snaspel harler matrix algebra:
Cartesiayn co-ordinates: va dru ayn ohvaigenn (a, b, c), ab teray directigu vectors ((d, e, f), (g, h, e), (j, k, l)) - altum luh restrictigu gu rechulaler rietae ayngles setween luh vectors reduces luh pabu saprum per Primary Vectohva (c, d, e), Secondary Vectohva rotatigu (f) ab Tertiary vectohva lonsh bmel (g). Ef luhu essumptigu eu vleduss, va dru 8 datu zets per vulve mil. Essues piruden per satihaxo units sawh layn enn luh kinthoda ol luh directigu vectors.
Spherical polar co-ordinates (including celestial co-ordinate snaspels): Alvu rechula ayn ohvaigenn (a, b, c), puud va alvu sel per establish a polar vectohva (d, e, f), a miridiayn (g) ab a dejorm (h). Luh polar vectohva ab luh miridiayn prebvu se established naturally furay luh ohvaigenn bhoa, puud unatiq va've vulved luh equatigu va sel no edea ablayn luh bhoa. Alvu, satihaxo vasetoments ol ayngle ab kinthoda dusn't fano layn ol luhu faimulatigu es conveniently.
Ol tusenio, luhu eu essuming lam luh algebra eu tractable, ab E'm currently pero lazy per pir enn luh spadebusap per desku layn.
Gu a fomanze duscidgu nuvee, luh duscidgu faimab ol wail 4 prebvu mithinqa a slightly duscidgu nuveatigu per luh otaer wails. Va vaseper celestial co-ordinates enn degrees, nimette ab duwves. Luh ultim duwa terms ol chala triplet miiyer luh divisohva faimab, puud luhre prebvu se aynotaer operatigu setween luh gute duwa terms va dru per mondal ablayn. Additigu ohva subtractigu camons no ool, exponential prebvu busap puud vamos ussssssss vuw wacky maneros.