We present a new technique for reconstructing a single shape and its non-rigid motion from 3D scanning data. Our algorithm takes a set of time-varying unstructured sample points that show partial views of a deforming object as input and reconstructs a single shape and a deformation field that fit the data. This representation yields dense correspondences for the whole sequence, as well as a completed 3D shape in every frame. In addition, the algorithm automatically removes spatial and temporal noise artifacts and outliers from the raw input data. Unlike previous methods, the algorithm does not require any shape template but computes a fitting shape automatically from the input data. Our reconstruction technique is based upon a novel topology aware adaptive sub-space deformation technique that allows handling long sequences with high resolution geometry efficiently. The algorithm accesses data in multiple sequential passes, so that long sequences can be streamed from hard disk, not being limited by main memory. We apply the technique to several benchmark data sets, increasing the complexity of the data that can be handled significantly in comparison to previous work, while at the same time improving the reconstruction quality.