Here is my challenge to you:

I have a cylinder with its axis of rotation on the x axis and of radius r. I cut the cylinder with two planes both perpenticular to the y-x plane and passing through the origin: one at 45 degree from the x axis and one at 135 degree. I understand that I will get two elipses on the surfaces of the cut cylinder but my question if I "peel" the cut cylinder (only one piece) as if it was made of fabric and flatten it, how can I draw this piece?

How could I get the distance between a and b as a function of x? or just the equations of the two curves?

any idea would be aprecieated.

Uploaded with ImageShack.us

Uploaded with ImageShack.us