<p>This study describes a fast approach using GPU to process self-collision in cloth animation without significant compromise in physical accuracy. The proposed fast approach is built and works effectively on a modification of Mass Spring Model which is seen in a variety of cloth simulation study. Instead of using hierarchical data structure which needs to be updated each frame, this fast approach adopts a spatial hashing technique which virtually partitions the space where the cloth object locates into small cubes and stores the information of the particles being held in the cells with an integer array. With the data of the particles and the cells holding information of the particles, self-collision detection can be processed in a very limited cost in each thread launched in GPU regardless of the increase in the amount of particles. This method is capable of visualizing self-collision detection and response in real time with limited cost in accessing memory on the GPU. </p> <p>The idea of the proposed fast approach is extremely straightforward, however, the amount of memory which is needed to be consumed by this method is its weakness. Also, this method sacrifices physical accuracy in exchange for the performance.</p>

Simulating realistic human behavior on a virtual avatar presents a difficult task. Because the simulated environment does not adhere to the same scientific principles that we do in the existent world, the avatar becomes capable of achieving infeasible postures. In an attempt to obtain realistic human simulation, real world constraints are imposed onto the non-sentient being. One such constraint, and the topic of this thesis, is self-collision avoidance. For the purposes of this topic, a posture will be defined solely as a collection of angles formed by each joint on the avatar. The goal of self-collision avoidance is to eliminate the formation of any posture where multiple body parts are attempting to occupy the exact same space. My work necessitates an extension of this definition to also include collision avoidance with objects attached to the body, such as a backpack or armor. In order to prevent these collisions from occurring, I have implemented an effort-based approach for correcting afflicted postures. This technique specifically pertains to postures that are sequenced together with the objective of animating the avatar. As such, the animation's coherence and defining characteristics must be preserved. My approach to this problem is unique in that it strategically blends the concept of keyframe interpolation with an optimization-based strategy for posture prediction. Although there has been considerable work done with methods for keyframe interpolation, there has been minimal progress towards integrating a realistic collision response strategy. Additionally, I will test this optimization-based approach through the use of a complex kinematic human model and investigate the use of the results as input to an existing dynamic motion prediction system.

Title: Billiard time machine Author: Jindřich Dolanský Department: Institute of Theoretical Physics Supervisor: doc. RNDr. Jiří Langer, CSc. Supervisor's e-mail address: Jiri.Langer@mff.cuni.cz Abstract: In this work we investigate a simple interacting system of an elastic particle in the non-relativistic spacetime with a nontrivial causal structure realized by a worm- hole with a time shift. We require that standard local physical laws hold, and search for their globally consistent solutions, i.e, we assume the validity of the principle of self-consistency. If there were nontrivial set of initial conditions which would violate this principle, the system would be logically inconsistent. We show that the investigated system is not inconsistent in this sense, i.e., that all standard initial conditions have a globally consistent evolution. Even for the so called dangerous initial conditions which threaten to result into the paradoxical situation a consistent solution exists. In this case, the paradoxical collision-free trajectory is superseded by a special consistent self-colliding trajectory. Moreover, we demonstrate that more than one globally consistent evolution exists for a wide class of initial conditions. Thus, the evolution of the described system is not unique due to the nontrivial causal structure...

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