Efficient mesh deformation using tetrahedron control mesh

It is a challenging problem to interactively deform densely sampled complex objects. This paper proposed an easy but efficient approach to it by using coarse control meshes to embed the target objects. The control mesh can be efficiently deformed by various existing methods, and then the target object can be accordingly deformed by interpolation. One of the most simplest interpolation methods is to use the barycentric coordinates, which however generates apparent first-order discontinuity artifacts across the boundary due to its piecewise linear property. To avoid such artifacts, this paper introduced a modified barycentric interpolation (modified-BI) technique. The central idea is to add a local transformation at each control vertex for interpolation, so that we can minimize the first-order discontinuity by optimizing the local transformations. We also minimize the second order derivatives of the interpolation function to avoid undesired vibrations. While focus on deforming 3D objects embed in tetrahedron meshes, the proposed method is applicable to 2D image objects embed in planar triangular meshes. The experimental results in both 2D and 3D demonstrated the success and advantages of the proposed method.