3D Deformation Using Geometry Methods

Shape deformation and editing are important for animation and game design. Based on as-rigid-as-possible (ARAP) surface modeling, an efficient approach is proposed to approximately preserve the volume of an object with large-scale deformations. The classical ARAP surface modeling uses two-stage iterations to recover rotations and preserve edge lengths. However, there is no volume preserving constraint, which may cause undesired artifacts. We show that the volume can be roughly kept by leveraging the skeleton information. First a skeleton is selected, and points are evenly generated on the skeleton. Then each point is correlated with several vertices on the surface of the object. The connectivity between the skeleton and the surface is defined as skeleton edges, which can be easily added into the linear system of the ARAP method as additional rows without breaking the manifoldness or sacrificing speed. Since this linear system is able to preserve the lengths of both the surface and skeleton edges, the area of cross sections and the volume between cross sections can be approximately preserved. In our experiments, we show that the rotations are natural and volumes are roughly kept. The system achieves real time performance for surface meshes with 5k vertices.


  • Shaoting Zhang, Junzhou Huang and Dimitris Metaxas: Robust Mesh Editing Using Laplacian Coordinates, in Graphical Models, volume 73, issue 1, pp.10-19, January, 2011.
  • Shaoting Zhang, Andrew Nealen and Dimitris Metaxas: Skeleton Based As-Rigid-As-Possible Volume Modeling, in Proc. of Eurographics 2010 , Norrkoping, Sweden, May 3-7, 2010.
  • Peter Borosan, Reid Howard, Shaoting Zhang and Andrew Nealen: Hybrid Mesh Editing, in Proc. of Eurographics 2010 , Norrkoping, Sweden, May 3-7, 2010.