Issue No. 06 - June (2011 vol. 17)
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TVCG.2010.92
Nan Zhang , University of Minnesota at Twin Cities, Minneapolis
Huamin Qu , Hong Kong University of Science and Technology, Hong Kong
Robert Sweet , University of Minnesota at Twin Cities, Minneapolis
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.
Physically based modeling, rod element, bending energy, thin-shell simulation, orientation preserving.
R. Sweet, N. Zhang and H. Qu, "Orientation-Preserving Rod Elements for Real-Time Thin-Shell Simulation," in IEEE Transactions on Visualization & Computer Graphics, vol. 17, no. , pp. 822-835, 2010.