  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.
