title: Calculating Fitness function for Polygonal Map Generation
body: <p>I'm currently working on a thesis regarding procedural map generation and using fitness functions to calculate the capability of the algorithms used and their resultant procedural maps.</p>
  
  <p>I'm basing my work off of Amitp's <a href="http://www-cs-students.stanford.edu/~amitp/game-programming/polygon-map-generation/" rel="nofollow noreferrer">Polygonal Map Generation</a>, found a Unity version I could use from his sources, updated it to a recent version, corrected some missing sections and stripped away some eye candy which goes beyond the scope of my thesis.  The problem now is to run fitness functions on it.</p>
  
  <p><a href="https://i.stack.imgur.com/0PJGg.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/0PJGg.png" alt="enter image description here"></a></p>
  
  <p>Some notes on the map:</p>
  
  <ul>
  <li>The map isn't intended to have any practical resources or bases (which is one of my major problems in regards to calculating fitness functions, since the ones I found assume the presences of such elements)</li>
  <li>The focus is to evaluate at least a couple of algorithms (perlin is one of them, second one I'm not sure yet - could be the radial process included, however I have yet to find a paper discussing this algorithm to validate its use) for how "fit and healthy" the maps that result from these algorithms are.</li>
  </ul>
  
  <p>As for the fitness functions, sourced from the following paper: <a href="https://www.itu.dk/~yannakakis/a8-Togelius.pdf" rel="nofollow noreferrer">Toward multiobjective procedural map generation</a> (Julian Togelius).  These focus around fairness, interestingness and playability - not necessarily the most applicable components for my line of work, but it's the only metric evaluation I've been able to locate thus far.</p>
  
  <ul>
  <li>Base Distance (Average weighted distance between bases).  Considering a map without any bases (or discrete resources for that matter), this is a tough one to use.</li>
  <li>Base on Ground (Average elevation per base from ground).  Same as above.</li>
  <li>Map Asymmetry (Average elevation difference between strategically chosen cells and their counterparts opposite on x and y axis).  This is weird to use due to the nature of Polygonals' map generation by Amitp - elevation increases inland, and the map is polygonal, therefore there are no direct opposites on x, y or any other midway axis.</li>
  <li>Resource Distance (1- [max dist - min dist]).  As above, no discrete resources to speak of.  The entire map could be considered a wide variety of resources in this case.</li>
  <li>Resource Clustering (How abundant / scarce resources are) as per above.</li>
  </ul>
  
  <p>So i'm really just <strong>stuck</strong> at this point... I am attempting to evaluate somehow, the potential fitness and health of a map, but the only functions I could find clearly do not relate to the kind of polygonal map generation present that I'm able to work with, and my attempts at transferring this approach to a gridded system, while not fruitless were nowhere near the expected outcome.</p>
  
  <p><strong>My Question</strong></p>
  
  <p>How can I adapt these above fitness functions to fit a polygonal map, shown below, or alternatively locate some alternative fitness functions (which are scholarly valid) to utilize instead for calculating such results.</p>
  
  <p>Coming up with my own functions <strong>may</strong> not be valid, if there is no background study somehow validating the use of such metrics, even though I can't entirely rule out the possibility as a backup.</p>