By reconstructing time-varying geometry one frame at a time, one ignores the continuity of natural motion, wasting useful information about the underlying video-image formation process and taking into account temporally discontinuous reconstruction results. In 4D spacetime, the surface of a dynamic object describes a continuous 3D hyper-surface. This hyper-surface can be implicitly defined as the minimum of an energy functional designed to optimize photo-consistency. Based on an Euler-Lagrange reformulation of the problem, we find this hyper-surface from a handful of synchronized video recordings. The resulting object geometry varies smoothly over time, and intermittently invisible object regions are correctly interpolated from previously and/or future frames.