@DK: I'm sorry if the tutorial is a little hard or if it goes so straight to the concepts. Perhaps it needs a better introduction about the 3D cartesian stuff. Let m try to explain some concepts again.

1) We are using this technique to mainly rotate the solid by the Y axis. The X rotation a little special.

2) Imagine that you have a potatoe and cross it by a wire like if it were the Y axis. The other axis is an imaginary axis and represent the X axis.

3) Consider that the wire (axis Y) is now parallel to the projection plane (perpendicular to your view direction) and you rotate the potatoe by its Y axis. ANY point in the potatoe will describe a 3D circle. But, in projection, the considered point is projecting a straight line (an oscilation). The rotation radious is the perpendicular length between the point in consideration and the Y axis. For any position place the rotation radious is as long as the green line in the tutorial.

4) Imagine now that you rotate the potatoe by its imaginary axis X, Then the Y axis will rotate also as well as the wire is pricking the potatoe. Now rotate again the potate by its Y axis using the wire. NOW the considered point of the potatoe will produce an ellipse in the projection plane (and not a straigt line). The horizontal axis of the ellipse is the same as the horizontal oscilation before. It stills always the same. But the vertical axis of the ellipse is bigger as big is the X rotation.

5) If you rotate the potatoe by its X axis until the wire (the Y axis) is pointing to your eyes, then if you rotate the potatoe by its Y axis (the wire) the considered point of the potatoe wil produce a perfect circle in the projection plane (in fact a circle is an special kind of ellipse). Really ALL the points of the potatoe are producing circles in the projection plane.

6) So the rotation technique is a little special. The X axis rotation is invariable and always is at the same position. It always produce straight lines in projection. On the other hand the Y axis

rotates with the X axis rotation so the projection ellipses are different for every rotation by the X axis.

Al the things that I have done are to simulate those elliptical rotation using a combination of springy bones.

@heyvern: I knew that you should understand it without this tutorial. Anyway it is good that the technique is explained without "complex math" (asin, atan, sqrt and so on)

There are two main (well three) drawbacks.

1) You need to reorder the shapes to perform the rotation realistic. It is not so difficult because you can create the bones inside a switch layer and switch to the proper shapes ordered layer when you need it manually. For partial parts of the solid (the ears, nose or eyes) you can make them in individual switch layers and use Flipbybones bones by Rasheed to order the layers. To rotate all the switch layers at the same time you can use the script layer from heyvern (I thinks it is form him) that allows to rotate any bone for a layer with the rotation of othe bone in other layer (I don't remember its name now). ((please heyvern refresh my mind with the link...)

2) For some shapes and ppositions there is a problem with the curvature of the point. A projected curve have different curvature than its non projected curve. So you need to fix it manually for evey frame. It is not a problem as well as you are saving animation time using bones to realistically rotate the solid.

The last drawback is the big amount of bones that you need...

Enjoy!

Genete