Orientation-preserving rod elements for real-time thin-shell simulation

Nan Zhang, Huamin Qu, Robert Sweet

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


We propose a new computation model for simulating elastic thin shells at interactive rates. Existing graphical simulation methods are mostly based on dihedral angle energy functions, which need to compute the first order and second order partial derivatives with respect to current vertex positions as bending forces and stiffness matrices. The symbolic derivatives are complicated in nonisometric element deformations. To simplify computing the derivatives, instead of directly constructing the dihedral angle energy, we use the orientation change energy of mesh edges. A continuum-mechanics-based orientation-preserving rod element model is developed to provide the bending forces. The advantage of our method is simple bending force and stiffness matrix computation, since in the rod model, we apply a novel incremental construction of the deformation gradient tensor to linearize both tensile and orientation deformations. Consequently, our model is efficient, easy to implement, and supports both quadrilateral and triangle meshes. It also treats shells and plates uniformly.

Original languageEnglish (US)
Article number5487516
Pages (from-to)822-835
Number of pages14
JournalIEEE Transactions on Visualization and Computer Graphics
Issue number6
StatePublished - 2011

Bibliographical note

Funding Information:
The authors thank the anonymous reviewers for their invaluable comments and suggestions in improving the quality of this paper. The authors are grateful with Professor Desong Sha for his inspiration in the rod-based ARC deformation gradient, Dr. Xiangmin Zhou and Dr. Yunhe Shen for constant discussions throughout the research, and Dan Burk for providing geometric models of the organs and animation rendering. The authors additionally thank Dr. Ying Du for proofreading an early draft of this paper. Huamin Qu is partially supported by grant HK RGC GRF 619309.


  • Physically based modeling
  • bending energy
  • orientation preserving
  • rod element
  • thin-shell simulation

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