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<!DOCTYPE HTML>
<html>
<head>
<title>Order Types</title>
<meta name="description" content="website description"/>
<meta name="keywords" content="website keywords, website keywords"/>
<meta http-equiv="content-type" content="text/html; charset=UTF-8"/>
<link rel="stylesheet" type="text/css" href="style/style.css" title="style"/>
<script src="https://code.jquery.com/jquery-3.5.1.min.js"
integrity="sha256-9/aliU8dGd2tb6OSsuzixeV4y/faTqgFtohetphbbj0=" crossorigin="anonymous"></script>
</head>
<body>
<div id="main">
<div id="header">
<div id="menubar">
<ul id="menu">
<li class="selected"><a href="index.html">Home</a></li>
<li><a href="tutorial.html">Tutorial</a></li>
<li><a href="glossary.html">Glossary</a></li>
<li><a href="demo.html">Interactive Demo</a></li>
<li><a href="implementation.html">Implementation details</a></li>
</ul>
</div>
</div>
<div id="site_content">
<div id="content" style="height: 100%;">
<h1 class="bold_title">Welcome to this website about Order Types of point sets</h1>
<p>Here, you will find several resources to help you learn about Order Types.</p>
<br>
<h2>Introduction</h2>
<p>
You can follow a step-by-step tutorial, giving you an intuition for what they are and what they can
be used for. If, during the reading, some word or concept is unclear, you can always search through
the glossary. <br><br> For a more hands-on and visual approach the interactive demo will allow you to
play around and compare the properties of point sets and their order type. The demo also allows for
the search of the exhaustive database of Order Types compiled by [Aichholtzer et al. (2001)].
Finally, the last page goes through the implementation details of some key algorithms making the
demo possible.</p>
<br>
<h2>Goals</h2>
<p>
The goals of this project were to create a website for the familiarisation with the concept of Order
Types of point sets and the exploration of the exhaustive database of Order Types and their
properties. With this in mind, a theoretical introduction to the topic is provided in form of a
tutorial and a glossary, as well as a more hands-on approach consisting of a demo application the users
can play with. </p>
<br>
<h2>Shortcomings and possible improvements</h2>
<p>
The major shortcoming of the demo is an error in the search of an equivalent point set to the set drawn
by the user, which in certain cases fails. This error is caused by fact that the logic computing the
λ-matrix is built under the assumption of general position. In certain cases, three points drawn
by the user might be co-liniar. In this situation the ordering of the points giving the minimum λ-matrix
needs to be computed in a different way, otherwise its columns might be permuted, leading to a
non-minimal value. A temporary fix to avoid the situation where the search for an equivalent order type
does not return the desired result would be to make sure the drawing does not contain any triplets of
co-liniar points. This can be easily done by analysing the complete graph of the drawing using the
provided option to show the complete graph.
</p>
<p>
The web version of the demo only handles a maximum of 9 points due to large file sizes for 10 points and
above, files which need to be transferred to the client in order to be processed.
</p>
<br>
<h2>
Credits
</h2>
<p>
This project was realised for the course INFO-F420 - Computational Geometry - 2020-2021, given by prof.
S.
Langerman, by Olivier De Cannière and Mădălin Ionescu.
</p>
<h2>
Distribution of work
</h2>
<p>
Disclaimer: even if initially some part were developed individually, they were almost always modified
multiple times by both parties through an iterative approach.
</p>
<ul>
<li>
Hosting the website: Olivier
</li>
<li>
Base design of the website: Olivier
</li>
<li>
Base design of the demo: Madalin
</li>
<li>
Update to the design and UI fixes: Madalin & Olivier
</li>
<li>
Server side in node.js: Olivier
</li>
<li>
Demo: Madalin, with small updates from Olivier
</li>
<li>
Natural λ-matrix algorithm & binary search: Olivier, with small improvements from Madalin
</li>
<li>
General algorithmic improvements and debugging: Madalin & Olivier
</li>
<li>
Tutorial & glossary: Olivier
</li>
<li>
Implementation details page: Madalin & Olivier
</li>
</ul>
</div>
</div>
</div>
</body>