Stretch-Minimizing Volumetric Parameterization
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Journal: Journal of Computer Science and Technology
© 2015, Springer Science+Business Media New York. Not many methods for parameterization guarantee bijectivity or local injectivity, which is essential for foldoverfree mappings. Stretch-minimizing parameterization which is widely used for surface parameterization, provides foldover-free mappings and is capable of trading off between angle and area distortions. We extend its usage to volumetric parameterization in this paper by deriving a 3D version of stretch-distortion energy and incorporating fixed boundary conditions. Our energy definition includes a natural barrier term which effectively prevents elements from collapsing and folding over. It saves the effort in other methods of formulating additional energy or constrains to ensure the local injectivity. We propose to minimize the overall energy integrated over the whole mesh with a relaxation-enhanced solver and optimize the energy globally. This is different from the conventional approach of surface parameterization where mesh nodes are optimized individually. Compared with other volumetric parameterizations, our approach bears the advantages of stretch-minimizing method, being foldover-free and offering a good trade-off between angle and volume distortions.