Locally injective mappings

Christian Schüller, Ladislav Kavan, Daniele Panozzo, Olga Sorkine-Hornung

Research output: Contribution to journalArticle

Abstract

Mappings and deformations are ubiquitous in geometry processing, shape modeling, and animation. Numerous deformation energies have been proposed to tackle problems like mesh parameterization and volumetric deformations. We present an algorithm that modifies any deformation energy to guarantee a locally injective mapping, i.e., without inverted elements. Our formulation can be used to compute continuous planar or volumetric piecewise-linear maps and it uses a barrier term to prevent inverted elements. Differently from previous methods, we carefully design both the barrier term and the associated numerical techniques to be able to provide immediate feedback to the user, enabling interactive manipulation of inversion-free mappings. Stress tests show that our method robustly handles extreme deformations where previous techniques converge very slowly or even fail. We demonstrate that enforcing local injectivity increases fidelity of the results in applications such as shape deformation and parameterization.

Original languageEnglish (US)
Pages (from-to)125-135
Number of pages11
JournalComputer Graphics Forum
Volume32
Issue number5
DOIs
StatePublished - Aug 2013

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design

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    Schüller, C., Kavan, L., Panozzo, D., & Sorkine-Hornung, O. (2013). Locally injective mappings. Computer Graphics Forum, 32(5), 125-135. https://doi.org/10.1111/cgf.12179