Physically based mesh-free deformation framework and techniques for computer graphics
In this thesis, we introduce a mesh-free deformation framework. Four different applications are presented based on it. Among them, a technique of mesh-free deformations and a technique ofreusable deformations are to model the deformations in two different ways, while the hyper-twist and the force mapping are applied to other graphic purposes related to deformations.Existing physicanv-based deformation techniques, such as the finite element method and the massspring systems, require the deformed object to be properly meshed. The proposed mesh-free deformations are constructed with unconnected points and no mesh is required in the computation.This process strict~1' follows the principles of classic mechanics and a deformation is defined as a combination of fundamental solutions. Because no mesh is involved, deforming a complex shape is as straightforw'ard as deforming a simple one and the trade-off between efficiency and accuracy is easy to achieve by redistributing the points concerned. Experiments show that this method is fast and offers similar accuracy to the finite element methods.Reducing both computational cost and amount of unnecessary human intervention remains a pressing issue in the animation production. To provide a faster and more user-friendly tool, we extend the above mesh-free deformations technique and develop another technique. A key feature is thereusability of deformations. Existing deformations can be simply extracted and reapplied physicallyusing the 'copy' and 'paste' operations. it relieves the modelling efforts. In this way, the visual realism is combined with the modelling efficiency and the user-friendliness for animators.The mesh-free deformation framework is capable to describe the deformations in an infinite body which is in line with the distortion of a 3D space. The twist of an infinite body, hyper-twist, is investigated to show how a 3D space and the object embedded can be radically deformed. Abstract shapes with aesthetic effects can be created in this process as well as their animations. Following the idea of mesh-free computation, we apply forces on a surface to create the fine details of the surface. A force map records the applied forces and their distributions. We call this technique force mapping, which can be used for surface modeling, compression, reconstruction and editing. As an alternative to displacement mapping, force mapping benefits from the fact that the physical property, force, is integrated into a geometric surface explicitly.