title: Volume of irregular piece of pie
body: <p>Imagine that we cut a piece of pie with known fixed height (H). We cut it in such a way that the upper arc has angle A1 and the bottom arc has angle A2. However, we also know that the upper arc has two radii (R1 and R2) and the bottom arc has two different radii (R3 and R4). These four radii are not connected anyhow to each other (might be elliptic axis, but might be total random).
  <a href="https://i.stack.imgur.com/A6VZ8.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/A6VZ8.png" alt="enter image description here"></a>
  Technically, if not thinking about pies, we have two polygons (with the same number of points), with mass centers a bit different from each other. Taking two points from the upper polygon, we assume they form a local elliptic arc with two radii and angle A1. (The other arc from the same polygon will most likely have different radii values and angle).
  We can take two points from the lower polygon which will correspond to the two points of the upper polygon (typically, using index values) and form the lower local elliptic arc with another angle and radii values.</p>
  
  <p>Thus the question is how to calculate the volume of this piece? Again, two upper radii (R1 and R2), two bottom radii (R3 and R4), fixed height (H) and two angles (A1 and A2). Note: the centers of the upper and bottom parts (essentially, polygons) might be different.</p>
  
  <p>Thanks in advance for help</p>