Conformal Mesh Deformations with Möbius Transformations

Amir Vaxman, Christian Müller, O. Weber

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


We establish a framework to design triangular and circular polygonal meshes by using face-based compatible Möbius transformations. Embracing the viewpoint of surfaces from circles, we characterize discrete conformality for such meshes, in which the invariants are circles, cross-ratios, and mutual intersection angles. Such transformations are important in practice for editing meshes without distortions or loss of details. In addition, they are of substantial theoretical interest in discrete differential geometry. Our framework allows for handle-based deformations, and interpolation between given meshes with controlled conformal error.
Original languageAmerican English
Title of host publicationSIGGRAPH
PublisherACM Transactions on Graphics
StatePublished - 2015

Bibliographical note

Place of conference:Los Angeles, U.S.A


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