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\usepackage{listings} % For listing code

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    \lhead{\textbf{Group 66}}

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    \chead{\textbf{Kishna Glista - liero clone}}

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    \rhead{\textsl{AS-0.1102}}

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% Title information

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\title{Kishna Glista - Liero Clone}

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\author{\normalsize{\begin{tabular}{lll}

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Atle Kivelä & 79171V & atle.kivela@tkk.fi \\

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Eric Malmi & 80351A & eric.malmi@tkk.fi \\

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Tero Marttila & & \\

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Marko Rasa & & \\

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\end{tabular}}}

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% The document begins

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\begin{document}

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\maketitle

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\section{Instructions for compiling and use}

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You can compile the program by going trough the following procedure:

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\begin{itemize}

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\item \textsl{cd build}

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\item \textsl{./mkcmake.sh}

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\item \textsl{make install}

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\end{itemize}

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\subsection{Basic usage}

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Starting. Default Keys. Starting the server. Connecting. etc.

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Controls are currently liero default controls.

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\begin{center}

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\begin{tabular}{l|l}

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\textbf{Action} & \textbf{Default key(s)} \\

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\hline

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Move left & Arrow left \\

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Move right & Arrow right \\

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Aim up & Arrow up \\

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Aim down & Arror down \\

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Shoot & Right CTRL \\

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Jump & Right shift \\

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Change weapon & Enter \\

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Shoot rope & Change weapon + jump \\

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Change rope length & Change weapon + aim up/down \\

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\end{tabular}

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\end{center}

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\subsubsection*{Starting the game}

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Somekind of intstuctions on starting the server, connecting etc...

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\subsection{Configuration}

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How to make configuration changes.

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\section{Program architecture}

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TODO: A nice image here would probably do the job.

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A brief description of the program architecture.

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\begin{itemize}

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\item Network

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\item Graphics

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\item Input etc.

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\item Physics

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\end{itemize}

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\section{Data structures and algorithms}

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\subsection{Basic data structures}

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\begin{itemize}

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\item Vector

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\item List

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\end{itemize}

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\subsection{World and Objects}

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% COMMENT: I think these should be in a very basic level and they

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% shouldn't discuss too much about the game itself. The idea is just

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% to explain different kinds of structures and algorithms.

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% Terrain

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The terrain is an important part of our game. We represent our terrain

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as a large array. Each shell of the array has a type that tells what

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is in that position. Currently, possible terrain types are EMPTY, DIRT

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and ROCK. 

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% Usually, in side view 2D-games, the terrain is representated as a

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% polygon. This allows us to implement collision detection and

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% bouncing rather easily, and it is also a very compact way of storing

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% the map. In our opinion Liero, however, is fundamentally a pixel

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% based game and therefore we represent the terrain as a large array

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% of pixels. These pixels are, however, abstract pixels, i.e. they are

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% not necessarily in the same scale than the physical resolution. In

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% other words, the server has an abstract resolution, which is the

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% same for all clients, and the clients can visualize this abstract

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% array of pixels in any resolution they wish.

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% Objects

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In our physics simulation the shapes of the different elements in the

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game are represented as polygons. A polygon is a vector of points that

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define the edges of the shape.

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% On top of the terrain, the world also includes a list of all objects

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% in it (players, projectiles and ropes). The objects have a polygon

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% shape which is used in the collision detection between the objects

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% and the terrain and the objects with each other.

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\subsection{Collision Detection}

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\begin{itemize}

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\item Polygon collision detection

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\item Pixel collision detection

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\end{itemize}

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Collision detection algorithms check if objects in the physics

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simulation are colliding with eachother. Because our terrain is

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represented as an array and objects are represented as polygons we

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have two different kinds collision detection algorithms.

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The pixel based collision detection used to check collisions with the

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terrain is quite simple. It ``draws'' a line between two points A and

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B. The algorithm iterates over the line from point A to B and on each

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iteration it checks if theres a collision (i.e. the type of the

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current point is ROCK or DIRT).

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In order to implement bouncing from the terrain we have to have a way

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of calculating a normal for the slope of the terrain in the collision

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point. We came up with the following algorithm for calculating the

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approximation for the normal. Take the collision point and the point

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before the collision and consider a 3x3 array of pixels which has the

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collision point in the middle of it. Then, do sort of an bredth-first

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search from the previous point to get all the empty pixels. Take the

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vectors from the collision point to the empty point and sum these

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vectors. The resulting vector will point approximately along the

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normal. % Picture would explain this a lot. 

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\subsection{Physics}

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The fourth-order Runge-Kutta method is a numerical method for

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approximating the solution of an ordinary differential equation. In

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our game the Runge-Kutta method is used to calculate positions and

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velocities of physics objects when we apply forces to them.

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The mathematical formulation of the Runge-Kutta method:

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If we have an initial value problem of the form

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y' = f(t, y), \quad y(t_0) = y_0.

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The we can describe the RK4 method for this problem by equations

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y_{n+1} &= y_n + \tfrac{1}{6}h\left(k_1 + 2k_2 + 2k_3 + k_4 \right) \\

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t_{n+1} &= t_n + h \\

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where $y_{n+1}$ is the RK4 approximation of $y(t_{n+1})$, and

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k_1 &= f(t_n, y_n) \\

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k_2 &= f(t_n + \tfrac{1}{2}h, y_n + \tfrac{1}{2}h k_1) \\

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k_3 &= f(t_n + \tfrac{1}{2}h, y_n + \tfrac{1}{2}h k_2) \\

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k_4 &= f(t_n + h, y_n + h k_3) \\

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The next value $(y_n+1)$ is determined by the present value $(y_n)$,

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the product of the interval $(h)$ and an estimated slope that is

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defined as $\frac{1}{6}h\left(k_1+2k_2+2k_3+k_4\right)$.

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\section{Known bugs}

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A lots of them (or maybe not).

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\section{Tasks sharing and schedule}

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Hectic ass hell. Communication worked pretty well but we weren't as systematic

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as we should have been.

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\section{Differences to the original plan}

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The plan was loose enough to let us make decisions during development. 

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% References

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\begin{thebibliography}{99}

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\bibitem{gaffer} Gaffer on games. Game

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  Physics. 2006. http://gafferongames.wordpress.com/game-physics/

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  (read: 2008-12-08)

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\bibitem{fractal} Terrain texture generation.  http://www.gameprogrammer.com/fractal.html

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\end{thebibliography}

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\end{document}