Locally Injective Mappings

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 loca...

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Bibliographic Details
Published in:Computer graphics forum Vol. 32; no. 5; pp. 125 - 135
Main Authors: Schüller, Christian, Kavan, Ladislav, Panozzo, Daniele, Sorkine-Hornung, Olga
Format: Journal Article
Language:English
Published: Oxford, UK Blackwell Publishing Ltd 01.08.2013
Subjects:
Algorithms
Animation
Barriers
Computer graphics
Computer science
Deformation
Interactive
Mapping
Parametrization
Studies
United States > US
ISSN:0167-7055, 1467-8659
Online Access:Get full text
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Summary: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.
Bibliography:ArticleID:CGF12179
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ISSN:0167-7055
1467-8659
DOI:10.1111/cgf.12179