Scalable locally injective mappings

Michael Rabinovich, Roi Poranne, Daniele Panozzo, Olga Sorkine-Hornung

Research output: Contribution to journalArticlepeer-review


We present a scalable approach for the optimization of flip-preventing energies in the general context of simplicial mappings and specifically for mesh parameterization. Our iterative minimization is based on the observation that many distortion energies can be optimized indirectly by minimizing a family of simpler proxy energies. Minimization of these proxies is a natural extension of the local/global minimization of the ARAP energy. Our algorithm is simple to implement and scales to datasets with millions of faces. We demonstrate our approach for the computation of maps that minimize a conformal or isometric distortion energy, both in two and three dimensions. In addition to mesh parameterization, we show that our algorithm can be applied to mesh deformation and mesh quality improvement.

Original languageEnglish (US)
Article number16
JournalACM Transactions on Graphics
Issue number2
StatePublished - Apr 2017


  • Bijectivity
  • I.3.5 [computer graphics]: computational geometry and object modeling - geometric algorithms, languages, and systems
  • Mesh parameterization
  • Optimization
  • Parameterization
  • Scalability

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design


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