'direction-independent' originates from English, specifically the compounds 'direction' + 'independent', where 'direction' ultimately comes from Latin 'directio' (from 'dirigere') meaning 'a guiding or straightening' and 'independent' comes from Late Latin 'independens' meaning 'not hanging from' (in- 'not' + dependere 'to hang').

'direction' passed into English via Old French/Latin from Latin 'directio', and 'independent' developed from Late Latin 'independens' (formed from in- + dependere); the modern English compound 'direction-independent' is a straightforward combination of these two English words.

Initially the root words related to 'guiding/straightening' (for 'direction') and 'not hanging from/being free from dependence' (for 'independent'); combined in modern usage they mean 'not depending on direction', a technical sense that has emerged in physics and engineering.