title: Maximize Rectangle in an Area on the X, Y plane with a list of points representing the area
body: <p>Okay, I need help maximizing the area of a rectangle in the sliver object that can be many different shapes. I've already done most of the work.</p>
  
  <p>I'm working in C# with a kinect and the depth pixels.</p>
  
  <p>This image is just the best representation of what I'm talking about that I could find.</p>
  
  <p><img src="https://i.stack.imgur.com/9qOuX.png" alt="enter image description here"></p>
  
  <p>I need to produce a rectangle in this area on the x, y plane that maximizes the area while having every edge be solid.</p>
  
  <p>I already have the solid shape represented as a list of points on the x, y plane. So I have the shape on the 2D plane. Kind of like this:</p>
  
  <p><img src="https://i.stack.imgur.com/LkkNW.png" alt="enter image description here"></p>
  
  <p>To simplify the problem, I'm just going to produce a rectangle with edges that are parallel to the x and y lines.
  I'm not looking for code. I just need some direction or an algorithm that I can read up on and attempt to implement.</p>
  
  <p>If any clarification is needed, please let me know.</p>