The fundamental sinusoidal components of a chequerboard pattern are oriented at 45 degrees to the orientation of the chequerboard edges. Removal of one of the fundamental sinusoids (at +45 degrees) creates a useful pattern for studying the mechanisms of visual analysis. Close up, the pattern appears to be oriented +45 degrees, although there is no global energy at that orientation, implying local analysis. At a distance, the perceived diagonality switches to -45 degrees implying access to global information. Measurements show that contrast thresholds for seeing diagonality at +45 degrees follow closely those for detecting the 5th harmonic component of the pattern, over a wide range of spatial frequencies and luminances. Low pass filtering also causes the pattern to be perceived according to its global energy, provided that the cutoff frequency is set to remove the fifth harmonic. We conclude that, at least for this particular stimulus, the visual system performs a local analysis if the fifth harmonic is visible and a global analysis if not.