Globally Injective Flattening via a Reduced Harmonic Subspace

Guy Fargion, Ofir Weber

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


We present a highly efficient-and-robust method for free-boundary flattening of disk-like triangle meshes in a globally injective manner. We show that by restricting the solution to a low-dimensional subspace of harmonic maps, we can dramatically accelerate the process while obtaining a low-distortion result. The algorithm consists of two main steps. A linear subspace construction, and a nonlinear nonconvex optimization for finding a low-distortion globally injective map within that subspace. The complexity of the first step dominates the algorithm's runtime and is merely that of solving a linear system. We combine recent results for computing locally-and-globally injective maps with that of harmonic maps into a conceptually simple algorithm that guarantees global injectivity. We demonstrate the great efficiency of our method over a dataset of 100 large scale models with more than 2M triangles each. Our algorithm is 10 times faster on average compared to the state-of-the-art Efficient Bijective Parameterizations (EBP) method [Su et al. 2020], on these high-resolution meshes, and more than 20 times faster on challenging examples (Figures 1,11). The speedup over [Jiang et al. 2017; Smith and Schaefer 2015] is even more dramatic.

Original languageEnglish
Article number253
JournalACM Transactions on Graphics
Issue number6
StatePublished - 30 Nov 2022

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  • harmonic maps
  • injective maps
  • newton method
  • parameterization


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