Strict minimizers for geometric optimization

Zohar Levi, Denis Zorin

Research output: Contribution to journalArticlepeer-review


We introduce the idea of strict minimizers for geometric distortion measures used in shape interpolation, deformation, parametrization, and other applications involving geometric mappings. The L-norm ensures the tightest possible control on the worst-case distortion. Unfortunately, it does not yield a unique solution and does not distinguish between solutions with high or low distortion below the maximum. The strict minimizer is a minimal L-norm solution, which always prioritizes higher distortion reduction. We propose practical algorithms for computing strict minimizers. We also offer an efficient algorithm for L optimization based on the ARAP energy. This algorithm can be used on its own or as a building block for an ARAP strict minimizer. We demonstrate that these algorithms lead to significant improvements in quality.

Original languageEnglish (US)
JournalACM Transactions on Graphics
Issue number6
StatePublished - Nov 19 2014


  • Deformation
  • Geometric modeling
  • Parametrization
  • Shape interpolation

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design


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