Visual simulation of deformable models

Computer animations are an essential part of today’s visual production pipeline, for feature animated films and video games. By moving from static to dynamic scenes, immersion in virtual environments is greatly enhanced. Most of these animations however are concerning rigid or articulated bodies, and are generated manually by an artist or off-line. The interactive animation of deformable objects still is a challenging task, requiring high computational resources. Moreover, interactive environments for dressing up with virtual clothing or training surgeons on unaccustomed procedures pose higher requirements on fidelity as simple plausibility, which we denote by visual simulation. This thesis presents a framework for the visual simulation of deformable objects, which is fast enough to be integrated into virtual environments. The modelling of these objects is based on continuum mechanics, yielding a better accuracy than the techniques commonly used in graphics. An important aspect of modelling are material laws. Measurements have shown viscoelasticity to be a distinctive characteristic of biological soft tissue, the hysteresis of cloth is a well known observation in standard Kawabata experiments. We introduce the modelling of viscoelasticity to graphics, which integrates smoothly into the continuum dynamical setting, and present the first interactive implementation of a viscoelastic model. Chapter 2 introduces the basic concepts of this approach, which results in a partial differential equation; the following chapter discusses the numerical methods we employ for its solution. We use the method of lines to solve this equation. Hence, as a first step the equation is discretised in space using finite elements on a tetrahedral mesh of the object. This reduces the problem to the solution of an ordinary differential equation. The efficient time integration of this equation is vital for the performance of the application. The implicit methods we introduce for this task are well suited for two-dimensional structures such as cloth as well as for three-dimensional soft objects. Implicit integration requires the solution of large systems of equations. Hence, the efficiency of these schemes again critically depends on the linear solver; we propose to use several methods new to the field. Two applications are presented in chapter 4 and 5 respectively, a core for cloth simulation using a simpler space discretization method, and a soft object simulator, assembling all the techniques we described in a set of flexible building blocks. The latter application allows the real-time simulation of soft objects composed of up to several thousand tetrahedral elements; the blocks can be configured to trade execution speed for approximation accuracy and hence to match the requirements of the actual area of usage.