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Current alignment algorithms for registering range data captured from a 3D scanner assume that the range data depicts identical geometry taken from different views. However, in the presence of scanner calibration errors, the data will be slightly warped. These warps often cause current alignment algorithms to converge slowly, find the wrong alignment, or even diverge. We present a method for aligning warped range data represented by polygon meshes. Our strategy can be characterized as a coarse-to-fine hierarchical approach, where we assume that since the warp is global, we can compensate for it by treating each mesh as a collection of smaller piecewise rigid sections, which can translate and rotate with respect to each other. We split the meshes subject to several constraints, in order to ensure that the resulting sections converge reliably.