Orient and origin

The word Orient, or the East, is where the sun "is born", from Latin orior (to be born), thence origin, originator, original, etc. I recently found out that Hungarian uses the same concept to express the idea of originate and Orient. Kelet is East, Orient, and keletkezik is originate. I was somewhat surprised because Hungarian is the only non-Indo-European language I've come across that does that. I wonder if it is a calque. But from what language? German doesn't do that, at least I can't think of such words. Maybe from a Slavic language, like Czech východ (east), východ slunce (sunup, sunrise), vycházet (to go/come out).