Locally Injective Mappings
Article first published online: 19 AUG 2013
© 2013 The Author(s) Computer Graphics Forum © 2013 The Eurographics Association and John Wiley & Sons Ltd.
Computer Graphics Forum
Volume 32, Issue 5, pages 125–135, August 2013
How to Cite
Schüller, C., Kavan, L., Panozzo, D. and Sorkine-Hornung, O. (2013), Locally Injective Mappings. Computer Graphics Forum, 32: 125–135. doi: 10.1111/cgf.12179
- Issue published online: 19 AUG 2013
- Article first published online: 19 AUG 2013
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.