Imagine an object such as a paper sheet being waved in front of some sensor. Reconstructing the time-varying 3D shape of the object finds direct applications in computer animation. The goal of this paper is to provide such a deformation capture system for surfaces. It uses temporal range data obtained by sensors such as those based on structured light or stereo. So as to deal with many different kinds of material, we do not make the usual assumption that the object surface has textural information. This rules out those techniques based on detecting and matching keypoints or directly minimizing 1