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We propose an efficient algorithm for computing large-scale bounded distortion maps of triangular and tetrahedral meshes. Specifically, given an initial map, we compute a similar map whose differentials are orientation preserving and have bounded condition number. Inspired by alternating optimization and Gauss-Newton approaches, we devise a first order method which combines the advantages of both. On the one hand, its iterations are as computationally efficient as those of alternatingdoi:10.1145/2816795.2818098 fatcat:2ufht2xberci5jg3flt6x7v7by