Add writeup

Writeup.tex

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+\documentclass{article}
+\date{2022-09-29}
+
+%\usepackage{amsmath}
+%\usepackage{amssymb}
+\usepackage{fancyhdr}
+
+\usepackage[hmargin=1in,vmargin=1in]{geometry}
+\pagestyle{fancy}
+\lhead{Emi Simpson}
+\chead{Introduction to AI - Lab 1 - Summer Orienteering}
+\rhead{\thepage}
+\fancyfoot{}
+
+\newcommand{\f}[1]{\textnormal{#1}}
+\newcommand{\st}{\textnormal{ s.t. }}
+\newcommand{\bb}[1]{\mathbb{#1}}
+\newcommand{\var}[1]{\textnormal{#1}}
+\newcommand{\bld}[1]{\textbf{#1}}
+\newcommand{\flr}[1]{\left\lfloor#1\right\rfloor}
+\newcommand{\paren}[1]{\left(#1\right)}
+\newcommand{\sqb}[1]{\left[#1\right]}
+\newcommand{\ben}{\begin{enumerate}}
+\newcommand{\een}{\end{enumerate}}
+
+\begin{document}
+	\section{Writeup}
+
+	My code is divided into a fed discrete modules, each of which detailed below.
+
+	\subsection{\texttt{read\_in} and \texttt{write\_out}}
+
+	These two modules are dedicated to transforming data to and from the specified format.
+	For improving testability, as many functions as possible work on data itself.  Other
+	than that, it's pretty mundane.
+
+	Of note, I've chosen to represent distances and elevations as integer values rather
+	than floating point.  To ensure that no significant data is lost, we measure distances
+	in millimeters and speeds is seconds per kilometer (or equivalently microseconds per
+	meter).  This was mostly done out of my strong distaste for floating point numbers,
+	but seems to have benefitted performance slightly.
+
+	\subsection{\texttt{a\_star}}
+
+	This is where the actual routing algorithm lies, although not the heuristic nor the
+	neighbor finding algorithm.  The A* algorithm I've implement is pretty generic and
+	works on any search space for which a neighbor function and a heuristic can be
+	defined.
+
+	It may be interesting to you that I've combined the cost and neighbor function.  This
+	mostly to make the code a little simpler.  However, the core mechanics of the
+	algorithm work nonetheless.
+
+	I've also written the function \texttt{pathfind\_multi}, which is able to find a path
+	which passes through several different checkpoints.  This is the function which is
+	ultimately called to perform pathfinding.
+
+	This function simply repeatedly calls the normal \texttt{pathfind} function for each
+	pair of adjacent goals.
+
+	\subsection{\texttt{world}}
+
+	Perhaps the most interesting part of the code, this module is what defines the search
+	space, heuristic function, and neighbor function.  Each node is simply represented by
+	a tuple containing an X and a Y coordinate.  When the \texttt{neighbor} function is
+	called, these coordinates are looked up.  Each adjacent node is evaluated, and a cost
+	(in seconds) is produced for moving to any valid node, and the results are returned.
+	More details about the specifics can be found in the detailed doccomment written for
+	the \texttt{neighbor} function.
+
+	This section also contains a heuristic function, which is considerably simpler.  By
+	looking only at the coordinates of the function, we can compute the minimum distance
+	needed to be travelled between the two points.  On a flat surface, this computation is
+	exact.  For performance, we leave out height from the computation.  However, by
+	assuming that all terrain is flat, we have not affected the admissibility of the
+	heuristic.  Real conditions will be equivalent or worse than the predicted measure.
+
+	The last step in computing the heuristic is simply to convert between distance (in
+	millimeters) and time (in microseconds).  To do this, we just use the fastest speed
+	possible, as to keep admissibility.  In our implementation, this happens to be 500
+	microseconds per millimeter, the speed we have selected for \texttt{ROAD} terrain, and
+	also a reasonable human jogging speed.
+
+	\subsection{Conclusion}
+
+	If this writeup has left you with any unanswered questions, I encourage you to look
+	into the docstrings I've left in my code.  Almost all functions defined for this
+	project should be documented, and most have examples that you can run using
+	doctesting.
+
+\end{document}