Nicely done. I'd like to see the results for the surface method too. I think you and I would have a lot of fun at a GTG, but everyone else would be looking at us like we're from Mars or something. Consider a section view of a toroid. At its center place a circle with its bottom tangent coincident with the toroid's center, having diameter equal to the outer ring diameter of the torus. The area of the circle will overlie part of the torus' cross section, but there's an arc area extending from the toroid center outward to the torus' perimeter, beneath the arc of the circle, which will be uncovered. My question is, can this uncovered area be modeled as the area lying between a hyperbola and its asymptote? If you could "denature" the arced area onto a flat axis, would it result in what I'm hoping for? I've been tossing this around for a couple months and can't convince myself it would represent a hyperbolic arc. Whaddaya think??