Optimization of Physics Simulations in 3D Graphics: The Influence of Collision Approximations on Computational Intensity and Simulation Accuracy

This bachelor’s thesis examines the correlation between computational costs of a physics simulation and its physical accuracy, depending on chosen collision approximation. The main motivation for this thesis is to formulate specific recommendations on choosing the right collision shapes for similar physics simulations in the future. The theoretical part first explains the processes behind simulations, from the basics of computer animation to the principles of physics engines, focusing on the Bullet physics engine. It then pays special attention to simulation loops, distinct phases of collision detection (broadphase and narrowphase) and their corresponding mathematical algorithms, such as Gilbert-Johnson-Keerthi (GJK) and Expanding Polytope Algorithm (EPA). In addition, the theoretical section provides sufficient background on the differences between various collision approximations, ranging from primitives to complex triangle meshes. The practical part presents a controlled quantitative experiment made in Blender. This experiment consists of a Jenga tower being toppled by a projectile impact. The use of a custom Python script eliminates any potential human interference. Furthermore, it automates the application of all physical parameters on the Jenga blocks and enables the measuring of key data metrics. A few of the metrics to mention are the time needed to finish each simulation, the amount of excess jittering or the scatter distance of all the Jenga blocks from the center. The results of the quantitative analysis show that the Convex Hull approximation offers higher levels of realism (a 7 % increase in the distance travelled by each block and a 10 % larger scatter distance from the center). On the other hand, the Convex Hull approximation tends to be 119 % more computationally excessive than the Box approximation. What is more surprising is the Box collision shape proves to be the more stable alternative due to its 19% lower amount of excess jittering. The Mesh collision shape being examined as the third shape turned out to be completely unsuitable for dynamic objects because of its instability.