title: Simplified (or smooth) polygons that contain the original detailed polygon
body: <p>I have a detailed 2D polygon (representing a geographic area) that is defined by a very large set of vertices. I'm looking for an algorithm that will simplify and smooth the polygon, (reducing the number of vertices) with the constraint that the <em>area</em> of the resulting polygon must contain all the vertices of the detailed polygon.</p>
  
  <p>For context, here's an example of the edge of one complex polygon:</p>
  
  <p><img src="https://i.stack.imgur.com/gU9ok.png" alt="enter image description here"></p>
  
  <p>My research:</p>
  
  <ul>
  <li><p>I found the Ramer–Douglas–Peucker algorithm which will reduce the number of vertices - but the resulting polygon will not contain all of the original polygon's vertices. See this article <a href="http://en.wikipedia.org/wiki/Ramer-Douglas-Peucker_algorithm" rel="noreferrer" title="Ramer-Douglas-Peucker algorithm">Ramer-Douglas-Peucker on Wikipedia</a></p></li>
  <li><p>I considered expanding the polygon (I believe this is also known as outward polygon offsetting). I found these questions: <a href="https://stackoverflow.com/questions/3749678/expand-fill-of-convex-polygon" title="Expanding a polygon">Expanding a polygon (convex only)</a> and <a href="https://stackoverflow.com/questions/1109536/an-algorithm-for-inflating-deflating-offsetting-buffering-polygons" title="Inflating a polygon">Inflating a polygon</a>. But I don't think this will substantially reduce the detail of my polygon.</p></li>
  </ul>
  
  <p>Thanks for any advice you can give me!</p>