## Fast Planar Projection Onto An Ellipsoid

In a previous post I talk about fast planar projections onto spheres. After I put that out I wondered if it were possible to do the same thing with other shapes. If you haven't read that original post, I would recommend it because in this post I am only going to cover the part that is unique to the ellipsoids. The formula that defines an ellipsoid is: It isn't necessary to understand how this formula is derived but if you are interested then here is an explanation of the for

## Planar Projection Onto A Sphere (Improved Eyelid Deformations)

A common eyelid rigging technique is to create a curve, create a locator on the curve for each span of the eyelid, and then aim a joint from the center of the eye to that curve. This is essentially a spherical projection of the locators onto the curve. The issue with a spherical projection, is that a translation of the curve cv's in a single axis can correspond to a translation in all three axis of the joint. This unwanted translation can mess up movement of the spans. If we

## Workaround for IntersectCurve cycle error

NOTE: In the video I say that you can drive the crease with a second set of joints on the brow curve that move up and down, depending on your character you may be able to do that directly, but you may need to aim a joint from the center of the eye to the point on the curve or project the point on the curve onto a nurbs sphere centered on the eye (I have used the projection technique).