'curved-line-based' originates from Modern English, specifically the words 'curved' (from 'curve'), 'line' (from Latin 'linea') and 'based' (from 'base'), where 'curved' meant 'bent or shaped into a curve', 'line' meant 'a long narrow mark or band', and 'base' meant 'foundation or basis'.

'curve' changed from the Latin word 'curvare' through Old French and Middle English and eventually became the modern English word 'curve'; 'line' comes from Latin 'linea' via Old French and Middle English; 'base' comes from Late Latin 'basis' via Old French. In Modern English these components were combined as a compound adjective 'curved-line-based'.

Initially the components meant 'bent' (for 'curve'), 'a linear mark' (for 'line'), and 'foundation' (for 'base'); over time the compound came to be used specifically to describe something whose design or basis relies on curved lines—'based on curved lines.'