Creating Demilune curve

[alexh1]

Hi, I saw a used demilune cabinet listed on a website that had already been sold but the shape was the most pleasing I have ever seen. I cannot take measurements and I do not have a perfect vertical picture. 

Originally I thought it was 2 simple radii but seems more likely its an ellipse and simple radius on the side. The side does not terminate at a right angle relative to the back, it continues to curve inward a bit as shown on the crude drawing and this is why I assume the side is a simple radius.

Not sure if these types of design elements were or are formalized in furniture design books. 
In any case I suppose best approach is to experiment with a full size drawing, just wondering if my assumptions are reasonable.

[jteneyck]

It might be a super ellipse.  Look it up.  You'll see that there's a formula that defines a super ellipse.  You can change the input parameters to adjust the shape, as needed.  Much of the modern Danish modern tables were done using a super ellipse formula.  I used it for a glass topped coffee table I made several years ago so it would better fill the space where I wanted to put it.