Bounded distortion parametrization in the space of metrics

Edward Chien, Zohar Levi, Ofir Weber

Research output: Contribution to journalArticlepeer-review

30 Scopus citations


We present a framework for global parametrization that utilizes the edge lengths (squared) of the mesh as variables. Given a mesh with arbitrary topology and prescribed cone singularities, we flatten the original metric of the surface under strict bounds on the metric distortion (various types of conformal and isometric measures are supported). Our key observation is that the space of bounded distortion metrics (given any particular bounds) is convex, and a broad range of useful and well-known distortion energies are convex as well. With the addition of nonlinear Gaussian curvature constraints, the parametrization problem is formulated as a constrained optimization problem, and a solution gives a locally injective map. Our method is easy to implement. Sequential convex programming (SCP) is utilized to solve this problem effectively. We demonstrate the flexibility of the method and its uncompromised robustness and compare it to state-of-the-art methods.

Original languageEnglish
Article number215
JournalACM Transactions on Graphics
Issue number6
StatePublished - Nov 2016

Bibliographical note

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© 2016 Copyright held by the owner/author(s). Publication rights licensed to ACM.


  • Bounded distortion
  • Injective maps
  • Mesh parametrization


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