The black-hole X-ray transient MAXI J1820+070 (=ASSASN-18ey) discovered in March 2018 was one of the optically brightest ever seen, which has resulted in very detailed optical outburst light-curves being obtained. We combine them here with X-ray and radio light-curves to show the major geometric changes the source undergoes. We present a detailed temporal analysis which reveals the presence of remarkably high amplitude (>0.5 mag) modulations, which evolve from the superhump (16.87 h) period towards the presumed orbital (16.45 h) period. These modulations appear ~87d after the outburst began, and follow the Swift/BAT hard X-ray light-curve, which peaks 4 days before the radio flare and jet ejection, when the source undergoes a rapid hard to soft state transition. The optical modulation then moves closer to the orbital period, with a light curve peak that drifts slowly in orbital phase from ~0.8 to ~0.3 during the soft state. We propose that the unprecedentedly large amplitude modulation requires a warp in the disc in order to provide a large enough radiating area, and for the warp to be irradiation-driven. Its sudden turn-on implies a change in the inner disc geometry which raises the hard X-ray emitting component to a height where it can illuminate the warped outer disc regions.
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