Yes, that's the difficulty that I'm having. How can I possibly explain what I'm talking about? Thanks for your patience.

The object represents a function that exists between two angles, each of which is formed between two planes. It's a novel approach. Nothing like it exists in any literature that's out there.

If I can walk you through exactly how the object is created, then we might be able to move on to discuss what makes the object new and unique, and why I think it would resist all attempts at transformation.

The first angle that we are concerned with is the elevation angle E. It is formed when we intersect a sphere with two planes, like this:

__https://youtu.be/ho8XCHIT-Oo__
The second angle is more complicated. It is formed between a plane of longitude and a "tangent" plane which lies in a conical orbit. The construction of the longitude plane is not too complicated, but its orientation is very specific. The orientation of the longitude plane is such that it intersects a point on a small circle which is constructed on the surface of the sphere at a 45 degree angle, like this:

__https://youtu.be/xwjIeHC3Nb0__
The "tangent" plane lies along the surface of a cone formed by the sphere center and the 45 degree small circle. As the elevation angle E is varied, the position of this tangent plane changes such that it remains coincident with the intersecting point on the circumference of the small circle, like this:

https://youtu.be/6OnSZki9yp0[/U]

If we call the angle that is made between the longitude plane and the tangent plane the angle \(\displaystyle \alpha \), then the object is defined by the function:

\(\displaystyle \cot( \alpha) = \dfrac{1-\sin(E)}{\sin(E)} \)

At least I think it is. My algebra is pathetic.