Tetrisation of Triangular Meshes and Its Application in Shape Blending

  • Shizuo Kaji
Conference paper
Part of the Mathematics for Industry book series (MFI, volume 24)


The As-Rigid-As-Possible (ARAP) shape deformation framework is a versatile technique for morphing, surface modelling, and mesh editing. We discuss an improvement of the ARAP framework in a few aspects: 1. Given a triangular mesh in 3D space, we introduce a method to associate a tetrahedral structure, which encodes the geometry of the original mesh. 2. We use a Lie algebra based method to interpolate local transformation, which provides better handling of rotation with large angle. 3. We propose a new error function to compile local transformations into a global piecewise linear map, which is rotation invariant and easy to minimise. We implemented a shape blender based on our algorithm and its MIT licensed source code is available online.


Shape blending Tetrahedral mesh As-rigid-as-possible deformation 



This work was partially supported by the Core Research for Evolutional Science and Technology (CREST) Program titled “Mathematics for Computer Graphics” of the Japan Science and Technology Agency (JST), by KAKENHI Grant-in-Aid for Young Scientists (B) 26800043, and by JSPS Postdoctoral Fellowships for Research Abroad.


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Copyright information

© Springer Science+Business Media Singapore 2016

Authors and Affiliations

  1. 1.Yamaguchi University/JST CRESTYamaguchiJapan

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