\documentclass{usiinfbachelorproject} \usepackage[]{caption} \usepackage[]{url} \usepackage[]{subcaption} \usepackage[]{float} \usepackage[]{multicol} \usepackage{tikz} \usepackage{tkz-euclide} \usetikzlibrary{external,shapes,through} \tikzexternalize[prefix=figures/] \tikzstyle{none}=[] \input{./tikzs/styles.tikzstyles} \pgfdeclarelayer{nodelayer} \pgfdeclarelayer{edgelayer} \pgfsetlayers{edgelayer,nodelayer,main} \graphicspath{{../figures/}{./figures/}} \newcommand*{\vv}[1]{\overrightarrow{#1}} \newcommand*{\figref}[1]{\figurename~\ref{#1}} \captionsetup{labelfont={bf}} \newcommand{\diff}{\mathop{}\!\mathrm{d}} \author{Arnaud Fauconnet} \title{From Flying Balls to Colliding Polygons} \subtitle{2D Physics Engine: Rigid Body Simulation} \versiondate{\today} \begin{committee} \advisor[Universit\`a della Svizzera Italiana, Switzerland]{Prof.}{Antonio}{Carzaniga} \end{committee} \newcommand{\inputtikz}[2][1]{ \resizebox{#1 \textwidth}{!}{ \tikzsetnextfilename{#2} \input{../tikzs/#2.tikz} } } \abstract { Physics engines are a fun and interesting way to learn about a lot of different subjects. First the theoretical concepts, such as the equations that dictate the motion of the objects, together with their components, need to be thoroughly understood. Then there is the necessity of finding a way to represent all of those concepts in a given programming language and to make them as efficient as possible so that the simulation runs fluidly. The task to be completed here was to extend an already existing physics engine that only made circles bounce off each other. The extension was focused on having the ability to generate some arbitrary polygons and make them bounce off each other in a physically accurate way. The main issues that rose up during the development of the extension: determining the inertia of a arbitrary polygon, which is important for realistic impacts; having an accurate collision detection system, which allows the engine to know when to make two polygons bounce off each other. Once those aspects were worked on and polished, the rest of the implementation went smoothly. } \counterwithin{figure}{section} \counterwithin{equation}{section} \usepackage{subfiles} % Best loaded last in the preamble \begin{document} \maketitle \tableofcontents \newpage \subfile{./sections/intro.tex} \newpage \subfile{./sections/tech_background.tex} \newpage \subfile{./sections/theoretical_background.tex} \newpage \subfile{./sections/solution.tex} \newpage \subfile{./sections/conclusion.tex} \newpage %%%%% \bibliographystyle{unsrt} \bibliography{references} \newpage \subfile{./sections/appendix.tex} \end{document}