This concept is demonstrated clearly in my quilled sunset project.
I have glued the curved shapes to follow the contour of the oval so it appears rounded in contrast to the right side where I have glued the marqee straight lengthwise not following the curved contour thus making it appear flat and 2dimensional.
Here is another PIC which shows how you can achieve different depth and effect using the same shape just by changing the direction they are glued in.
The object to the left looks more rounded and smoother bringing out a softer look just based on the direction and shape ofwase quilled basic shape .
This is what I am talking about when I say use the quilled shapes to bring out 3rd dimension , which is depth, same as in painting.
Hence, when quilling birds and animals or any other object, you can acheive a more realistic appearance if you use the quilled shapes to follow the shape or curves of the object being quilled.
I hope this tutorial was helpful and clears up whatever confusion that some of you may have had.