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Mathematical Progress in Expressive Image Synthesis IIITetrisation of Triangular Meshes and Its Application in Shape Blending

Mathematical Progress in Expressive Image Synthesis III: Tetrisation of Triangular Meshes and Its... [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.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Mathematical Progress in Expressive Image Synthesis IIITetrisation of Triangular Meshes and Its Application in Shape Blending

Part of the Mathematics for Industry Book Series (volume 24)
Editors: Dobashi, Yoshinori; Ochiai, Hiroyuki
Kaji, Shizuo
Mathematical Progress in Expressive Image Synthesis III — May 22, 2016
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12 pages

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Publisher
Springer Singapore
Copyright
© Springer Science+Business Media Singapore 2016
ISBN
978-981-10-1075-0
Pages
7 –19
DOI
10.1007/978-981-10-1076-7_2
Publisher site
See Chapter on Publisher Site

Abstract

[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.]

Published: May 22, 2016

Keywords: Shape blending; Tetrahedral mesh; As-rigid-as-possible deformation

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