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In this paper, we propose a novel mesh morphing approach based on polycubic cross-parameterization. We compose parameterizations over the surfaces of the polycubes whose shape is similar to that of the given meshes. Because the polycubes capture the large-scale features, we can easily preserve the shape of the models, mapping legs to legs, head to head, and so on. For the finer features that are not reflected by the shape of the polycubes, we split the polycubes into matching patches and optimize them to get a low-distortion bijection that satisfies user-prescribed constraints. Our approach works well for meshes with arbitrary genus as long as the polycubes capture this feature and transfers texture seamlessly. We can also build maps with singularities between models with different genus. Copyright © 2005 John Wiley & Sons, Ltd.