Need some geometry help

[Roxy]

OK. Let's put this on hold for the weekend. I've sent an email to Dr Bourke asking for his help.

OME

I changed the wording up above... I had an error. Specifically, it would be useful to ask Dr. Bourke how he generated that table with fractional values. Because (and here is the updated wording):

So we need to restrict theta to values of 0 to pi/2. You can not restrict phi to that range because you wont get the complete shape of the toroid. Phi needs to still vary from 0 to pi. What this means is there may still be some limitations on n2 being stuck at positive numbers because you can't be raising cos(phi) (with a negative value) to a fractional power. However, I think n1 is free to be both positive and negative with this technique.

I think you can fake many cases and replicate the data from other parts of the toroid where you can generate valid results. But I'm checking right now, and those fractional values for n1 & n2 seem to be imaginary. Here is the only part of the surface that can be generated for the n1=.2 & n2=.2 case. Notice both theta and phi are sweeping 0 to 360 degrees. And you only get the outside shell of the first quadrant. He faked the data (and entry) in that table:

partial_toriod.jpg

Here are the square toriod's using the mirror() fake out method


:Square_Toriod.jpg