'rectilinear-based' is built from 'rectilinear' (from Latin roots) combined with the English adjective-forming use of '-based' (from 'base'). 'rectilinear' originates from Latin elements 'rectus' and 'linea', where 'rectus' meant 'straight' and 'linea' meant 'line'.

'rectilinear' came into English via Late Latin/Neo-Latin formation from Latin 'rectus' + 'linea' to mean 'having straight lines'; the compound with English 'base/‑based' is a modern English formation attaching '‑based' to describe what something is founded on (e.g., 'X-based').

Initially the Latin roots conveyed the separate ideas 'straight' and 'line'; over time the combined form 'rectilinear' came to mean 'characterized by straight lines', and the modern compound 'rectilinear-based' now means 'based on or founded on straight-line (rectilinear) principles'.