Research On Physcally Based Simulation Of Elastic Deformation

Simulation of elastic deformation has extensive application and research on it has been an important area in Computer Graphics. There are two categories of techniques for this problem: non-physical methods and physically based simulation. With the overgrowth of the computer hardware and the improvement of the application, increasingly importance has been attached to physically based simulation. In fact, physically based simulation has at least three outstanding advantages. Firstly, plausible result can be obtained because physically based method is in compliance with objective movement laws. Secondly, the complex deformation can be simply and rationally controlled. Finally, the simulation results are more easily applied by the visual-aid analysis of the engineering area.Three problems are studied in this thesis: finite element simulation of elastic deformation driven by skeleton, meshless simulation of elastic deformation driven by skeleton and the treatment of changing of geometry topology in elastic deformation.In the finite element simulation of elastic deformation driven by skeleton, a novel method is proposed which estimates finite elements rotation by diffusing from sampling points in attached skeleton structure and using an empirical formula of rotation quaternion. In calculating deformation based on the static equation, our method can greatly accelerate computing of deformation without fussy sub-step calculation, while it can make the whole solution more stable in kinetics calculation. Moreover, our method can reduce the user interaction and obtain rational results.A meshless simulation system is presented for elastic deformation driven by skeleton in chapter 5. In this system, Galerkin meshless method based moving least square approximation is applied in space coordinate domain. In addition, a new method for calculating node rotation is proposed while applying a similar technique with stiffness warping to tackle the nonlinear large deformation. In our method, all node rotations are evaluated from sampling points in attached skeleton by constructing and solving the diffusion partial differential equation. The experiments indicated that the method can enhance the stability of the dynamics and avoid fussy sub-step calculation in static deformation edition.As for the problem of the changing of geometry topology, that is cutting and fracturing of model, a finite element simulation framework without remeshing is presented. The kernel is adding a discontinuous function for the standard approximation to account for the crack. A feasible technique is adopted for dealing with multiple cracks and intersecting cracks. Several involved problems including extended freedoms of finite element nodes and mass matrix calculation etc are discussed. The technique is easy to simulate changing geometric topology. Moreover, previous methods developed in standard finite element framework, such as stiffness warping method, can be extended and utilized.