Existing approaches to nonrigid structure from motion assume that the instantaneous 3D shape of a deforming object is a linear combination of basis shapes, which have to be estimated anew for each video sequence. In contrast, we propose that the evolving 3D structure be described by a linear combination of basis trajectories. The principal advantage of this lateral approach is that we do not need to estimate any basis vectors during computation. Instead, we show that generic bases over trajectories, such as the Discrete Cosine Transform (DCT) bases, can be used to effectively describe most real motions. This results in a significant reduction in unknowns, and corresponding stability, in estimation. We report empirical performance, quantitatively using motion capture data and qualitatively on several video sequences exhibiting nonrigid motions including piece-wise rigid motion, articulated motion, partially nonrigid motion (such as a facial expression), and highly nonrigid motion (such as a person dancing).