The Visual Computer

, Volume 34, Issue 6–8, pp 937–947 | Cite as

Deformation simulation based on model reduction with rigidity-guided sampling

  • Shuo-Ting Chien
  • Chen-Hui HuEmail author
  • Cheng-Yang Huang
  • Yu-Ting Tsai
  • Wen-Chieh Lin
Original Article


The deformation results of previous model reduction methods with external forces applied show noticeable differences from full-scale finite element method (FEM) simulation. We found that data-driven approaches, specifically proper orthogonal decomposition, can be a solution to this nonlinear deformation simulation problem in the subspace. Nevertheless, off-line FEM simulation with an infinite number of possible input forces at different locations makes it infeasible if no prior information is given. We propose rigidity-guided sampling to efficiently select the points of application of forces (force sample points) to construct more effective and compact subspace bases, thereby improving the simulation accuracy of reduced deformable models with applied external forces and still retaining fast run-time performance. The key idea of our approach is that distinct deformations of an object at different force sample points can be estimated prior to FEM simulation. By selecting the force sample points with distinct deformations, the computational cost of off-line FEM simulation can be reduced significantly. Our run-time deformation results are much closer to the full-scale FEM simulation with external forces applied, compared to the results of using only the modal derivative bases while the speedup over full-scale simulation is still substantial.


Deformation Model reduction Rigidity fields Finite element method Harmonic fields 



We thank Prof. Jernej Barbič for providing help about Vega FEM [6] in the early stage of this study. We also thank Yan-Ting Liu for making the accompanying video. This work was supported in part by the Ministry of Science and Technology of Taiwan under Grant Nos. 104-2628-E-009-001-MY3 and 105-2221-E-009-095-MY3.

Funding This study was funded in part by the Ministry of Science and Technology of Taiwan under Grant Nos. 104-2628-E-009-001-MY3 and 105-2221-E-009-095-MY3.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Supplementary material

Supplementary material 1 (mp4 39808 KB)

371_2018_1533_MOESM2_ESM.pdf (1.9 mb)
Supplementary material 2 (pdf 1931 KB)


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Computer Science, College of Computer ScienceNational Chiao Tung UniversityHsinchuTaiwan
  2. 2.Department of Computer Science and EngineeringYuan Ze UniversityTaoyuanTaiwan

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