Sketching the method for mapping stellar surfaces, part 1: spot-free light curve. Upper panel: 12 consecutive (synthetic) transit light curves. Noise levels are comparable with what is expected to be routinely achieved by the Transiting Exoplanet Survey Satellite (TESS), see Sect. 3.1. Lower panel: 12 transits phase-folded (red dots) and median-combined (blue diamonds). The best fit to the median-combined light curve is shown as a solid green line. The input model used to synthesize the light curves is shown as a dashed black line.