Graphical Simulation of Deformable Models

In this chapter, we introduce the objectives of dynamics simulation of deformable objects. We conduct an in-depth survey on the relevant research topics, especially the simulation of deformable models with anisotropic materials, which is less exploited in existing research. We are motivated to improve the physical realism of simulation, since many real-world objects have complex mechanical rather than isotropic properties. Both physically-based and geometrically-based approaches are studied, and our contributions are made in modeling and control of anisotropic dynamics deformations. Deformable models have been studied for nearly three decades in computer graphics since the late 1980s. In this chapter, we introduce some influential works that have fueled the development of modeling and simulation of deformable objects in the graphics community. Our research focus is on efficiency, stability, controllability and accuracy of dynamics simulation. First, we introduce the geometrically-based deformable models, which formulate a mathematical model of deformable objects from a geometric perspective rather than rigorous physics. Some deformation approaches in geometry processing are introduced. A group of position-based methods for dynamics simulation are discussed. Although being geometrically motivated, these models are related to physical models to some extent, with constraints based on physical principles. Secondly, we briefly review a simple physical model of mass spring system and its extension to particle systems. Thirdly, we give a comprehensive introduction to the physically-based deformable models based on continuum mechanics, from which we initiated our research. Continuum-based models in combination with finite element discretization can produce physically-realistic results. However, in graphics applications, they encounter challenges related to high computational complexity, numerical instability and controllability. Various approaches have been proposed to solve these problems, and we analyze them from different perspectives. © Springer International Publishing Switzerland 2016 J. Cai et al., Graphical Simulation of Deformable Models, DOI 10.1007/978-3-319-51031-6_1 1 Fourthly, we introduce some hybrid models developed in recent years, which attempt to reconcile geometrical methods with physical models and bridge the gap between these two groups, leading to new research potentials. And finally, we broadly introduce the deformation control methods, which provide users with control over material properties or complex deformation behaviors. 1.1 Geometrically-Based Methods