Two of the methods common in video game fluid simulation are SmoothedParticle Hydrodynamics (SPH), and Position Based Dynamics (PBD). They are both Lagrangian methods of fluid simulation. SPH has been used for many years in offline simulations and has truthful visuals, but is not as stable as the newer method PBD when using larger timesteps. SPH also tends to become unstable during compression. In this report both methods have been tested on different scenarios as the methods’ performance and visual depend on the scenario used. Additionally, the size of the particle radius was varied when comparing Compressible SPH (CSPH), Weak Compressible SPH (WCSPH), and PBD. From these tests, the conclusion could be drawn that CSPH performed slightly better than PBD regarding frames per second (FPS) in all cases except one. However, WCSPH and sometimes CSPH had stability issues. The stability of PBD and its possibility for larger timesteps with only minor FPS difference lead to the conclusion that PBD is overall the more suitable method for fluid simulation in video games. / Två av metoderna som är vanliga vid vätskesimulering i videospel är SmoothedParticle Hydrodynamics (SPH) och Position Based Dynamics (PBD). De är båda Lagrangiska metoder för vätskesimulering. SPH har använts i många år i offline-simuleringar och har realistiskt utseende, men är inte lika stabil som den nyare metoden PBD vid användning av större tidssteg. SPH tenderar också att bli instabil under kompression. Båda metoderna blev testade i olika scenarion eftersom deras prestanda och utseende beror på det använda scenariot. Storleken av partikelradien har också varierat när Compressible SPH (CSPH), Weak Compressible SPH (WCSPH) och PBD jämfördes. Från dessa tester kunde man se att CSPH presterade lite bättre än PBD gällande bilder per sekund (FPS) i alla fall utom ett. Däremot hade WCSPH och ibland CSPH stabilitetsproblem. Stabiliteten av PBD och dess möjlighet att ta större tidssteg med endast minimala FPS skillnader ledde till slutsatsen att PBD är överlag den mer lämpliga metoden för vätskesimulering i videospel.

Today, soft body simulations are essential for a wide range of applications. They are for instance used for medical training in virtual reality and in video games to simulate clothes and hair. These kinds of interactive applications rely on real-time simulations, which entails very strict requirements. The simulation has to be fast enough and must never break, regardless of what deformation might occur. Two methods that perform well with regard to these requirements are the position-based dynamics (PBD) method and the shape matching method. Even though these methods have been used for years, it is still unclear when you should use either method. This thesis has compared the two methods with regard to the mentioned requirements. More specifically, the thesis has evaluated the performance of the simulation loop as well as the simulated objects’ ability to restore their shape after deformation. The performance results clearly show that the PBD method is the fastest. But the results of the simulated objects’ ability to restore their shape were not as conclusive. Overall, the PBD method seemed to perform the best again, but there were cases the method could not handle. Although the shape matching method performed slightly worse, it did manage to restore the shape of every deformed object. In conclusion, for most applications, the PBD method is likely the better option, but if the application relies on the fact that simulated objects can restore their shape, then the shape matching method may be preferable. / Idag är simulering av mjuka kroppar viktiga för en mängd olika tillämpningar. De används exempelvis för medicinsk träning i virtuell verklighet och i datorspel för att simulera kläder och hår. Dessa typer av interaktiva applikationer förlitar sig på realtidssimuleringar, vilket medför många stränga krav. Simuleringen måste vara tillräckligt snabb och får aldrig gå sönder, oavsett vad för slags deformation som kan uppstå. Två metoder som presterar bra med avseende på dessa krav är position-based dynamics (PBD) och shape matching. Trots att dessa metoder har använts i många år, så är det fortfarande oklart när vilken metod är mest lämplig. Denna avhandling har jämfört de två metoderna med hänsyn till de nämnda kraven. Mer specifikt har avhandlingen utvärderat metodernas prestanda samt de simulerade objektens förmåga att återställa sin form efter deformation. Resultaten för prestanda visar tydligt att PBD-metoden är snabbast. Men resultaten av de simulerade objektens förmåga att återställa sin form var inte lika enhälliga. Sammantaget verkade PBD-metoden prestera bäst igen, däremot fanns det fall som metoden inte kunde hantera. Fastän shape matching metoden presterade något sämre, så lyckades den återställa formen för varje deformerat objekt. Sammanfattningsvis, för de flesta applikationer är PBD-metoden troligen det bättre alternativet, men om applikationen förlitar sig på att de simulerade objekten kan återställa sina former, så kan shape matching metoden vara att föredra.

Context. Fluid simulations are an important part for enhancing the visualization of games, movies and other graphical applications. Fluid simulations can be achieved in different type of context ranging between slow, high-quality simulations which is mainly used for movies, to fast lower-quality simulations which is primarily used for real-time applications such as games. Objectives. The goal was to compare the visual appearance of a Lagrangian method and a semiLagrangian method when it came to realistic appearance.  Methods. Identical scenes of water being rendered are made for both the Lagrangian and the semiLagrangian algorithm. This is later measured by using a user study which will provide the result of which method that provides a more realistic appearance Results. The result of the tests showed that the visual realism between the semi-Lagrangian and Lagrangian were different depending on the scene environment.  Conclusions. The conclusion of the data presented in the result yields that the Lagrangian and semiLagrangian looks very much alike and there is no real realistic difference between the methods, some scene yields a vast majority of votes in the favor of one method.

Using an explicit integration method in physically based animations has many advantages including conceptual and computational simplicity, however, it re- quires small time steps to ensure low numerical instability. Simulations with large numbers of individually interacting components such as cloth, hair, and fluid models, are limited by the sections of particles most susceptible to error. This results in the need for smaller time steps than required for the majority of the system. These sections can be diverse and dynamic, quickly changing in size and location based on forces in the system. Identifying and handling these trou- blesome sections could allow for a larger time step to be selected, while preventing a breakdown in the simulation. This thesis presents Smarticles (smart particles), a method of individually de- tecting particles exhibiting signs of instability and stabilizing them with minimal adverse effects to visual accuracy. As a result, higher levels of error introduced from large time steps can be tolerated with minimal overhead. Two separate approaches to Smarticles were implemented. They attempt to find oscillating particles by analyzing a particle’s (1) past behavior and (2) behavior with re- spect to its neighbors along a strand. Both versions of Smarticles attempt to correct unstable particles using velocity dampening. Smarticles was applied to a two dimensional hair simulation modeled as a continuum using smooth particle hydrodynamic. Hair strands are formed by linking particles together using one of two methods: position based dynamics or mass-spring forces. Both versions of Smarticles, as well as a control of normal particles, were directly compared and evaluated based on stability and visual fluidity. Hair particles were exposed to various forms of external forces under increasing time step lengths. Testing showed that both versions of Smarticles working together allowed an average increase of 18.62% in the time step length for hair linked with position based dynamics. In addition, Smarticles was able to significantly reduce visible instability at even larger time steps. While these results suggest Smarticles is successful, the method used to correct particle instability may jeopardize other important aspects of the simulation. A more accurate correction method would likely need to be developed to make Smarticles an advantageous method.