We show that the geometry of motions in atmospheric boundary-layer time series exhibits considerable independence from scale in spite of changing physics. The scale-independence of structure shapes is shown by using a simple technique to extract basic shapes from the time series for timescales between 3 s and 2 h. A set of predefined basic shapes is chosen subjectively as those that occur most frequently in the time series: sine, step, ramp-cliff and cliff-ramp. The frequency of occurrence of shapes changes with the timescale, with a pronounced minimum at scales between 2 and 10 min depending on the stability and the shape function. This is in accordance with the minimum of kinetic energy between turbulence and mesoscales. However, the ratios of occurrences between different shapes are approximately scale-independent. What shapes are preferred depends only on the variable examined. The physics of different shapes and scales is examined from characteristics of individual shapes. Steep edges of shapes seem to be predominantly related to downward transport of heat and momentum, which weakens with increasing scale. Sine shapes on the other hand seem to be related to turbulent eddies and shear instability at small scales, and to internal gravity waves at larger scales with stable stratification. Therefore, the physics of individual shapes is shown to change with scale, while the geometry seems to remain approximately scale-independent.