BPM: Blended Piecewise Möbius Maps

Shir Rorberg, Amir Vaxman, Mirela Ben-Chen

Research output: Contribution to journalArticlepeer-review


We propose a novel Möbius interpolator that takes as an input a discrete map between the vertices of two planar triangle meshes, and outputs a continuous map on the input domain. The output map interpolates the discrete map, is continuous between triangles, and has low quasi-conformal distortion when the input map is discrete conformal. Our map leads to considerably smoother texture transfer compared to the alternatives, even on very coarse triangulations. Furthermore, our approach has a closed-form expression, is local, applicable to any discrete map, and leads to smooth results even for extreme deformations. Finally, by working with local intrinsic coordinates, our approach is easily generalizable to discrete maps between a surface triangle mesh and a planar mesh, i.e., a planar parameterization. We compare our method with existing approaches, and demonstrate better texture transfer results, and lower quasi-conformal errors.

Original languageEnglish
Article numbere14914
JournalComputer Graphics Forum
Issue number5
StatePublished - Aug 2023

All Science Journal Classification (ASJC) codes

  • Computer Graphics and Computer-Aided Design


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