Projected random patterns have been used to measure the shape of discontinuous objects. A sequence of independent random patterns are projected onto the object. These images are analyzed by use of the technique called temporal digital speckle photography (DSP) that is introduced here. With temporal DSP the spatial resolution of the shape measurement is improved considerably compared with previously reported results with projected random patterns. A calibration procedure is described that uses a sequence of independent random patterns to calibrate measurement volume. As a result, independent space coordinates for each subimage are obtained. The accuracy is of the order of 1/1000 of the field of view where a subimage size of 8 pixels seems to be a good compromise between reliability and spatial resolution. The technique is illustrated with a measurement of an electrical plug and a 9-V battery.