Mickeal Verschoor

PhD Thesis, Eindhoven University of Technology

**Summary:** An animation is an illusion of motion that is created by showing a sequence of still images. This illusion is obtained when consecutive images have a minimal difference and are displayed at a sufficient high rate. Using this principle, an animator is able to bring the objects and characters in these images to life. Formerly, these images were mainly drawn by hand, nowadays computers are important tools for creating such animations. Thanks to animation software, animators are able to animate complex objects and scenes. However, when it comes to realistic animations of complex objects, or complex scenes containing many objects, some physical principles should be obeyed. These are for example gravity, deformation and contact between the surfaces of the involved objects. Each can depend on the shape, material and other properties of the involved objects. Creating realistic animations of such systems manually can be very challenging and time consuming. Therefore, one approach to improve the animation process for this kind of animations is by using computer simulations.

Using computer simulations, the motion and deformation of an object can be computed given the external and internal forces working on the body. Additionally, a simulation can compute this for many objects while computing the contact and friction forces between the objects. However, this kind of simulations often require a large amount of computational resources. The direct and indirect influence of each object onto their motions makes this a difficult problem to solve, especially when objects can deform. Computer simulations can also be applied in interactive animation applications, like VR and gaming. For those applications it is important that the simulation runs fast and stable.

In this dissertation the following research question is addressed:

*How can we accurately and efficiently simulate rigid and deformable solids that can collide, in a fast and stable way for computer animation applications?*

In particular, this dissertation presents methods that can improve the simulation process of elastically deformable objects, applied to (interactive) computer animations, while taking the accuracy into account. We address how to efficiently use graphics processors (GPUs) for assembling and solving the numerical problems related to such simulations. These numerical problems can be in general described by linear systems having large sparse matrices. These matrices have to be processed efficiently by a GPU, while solving the linear system. Apart from simulating the internal physics of deformable models, this dissertation presents methods for solving contact and friction between the surfaces of the simulated objects. By solving the coupled problem containing contact, friction, motion and deformation, one can obtain accurate results faster. Here the accurate detection of collisions, while taking possible deformations into account, is an important aspect.