Need some geometry help

[Roxy]

I must protest, there is nothing fake going on, no mirroring, no special treatment of quadrants. But there is a modified definition of pow() which preserves the sign ... which is in effect achieving the quadrant mappings.

Yes... This threw us for a loop. The equations specified at:

http://paulbourke.net/geometry/torus/supertoroid3.gif show these as the equations to generate the toriods:

supertoroid_equations.gifPerhaps 'fake' is the wrong word. I was trying to say 'not real'. Let's use the word 'imaginary'. I'm pretty confident that most math types would say these equations produce 'imaginary' numbers over part of the range when n1 & n2 are fractional powers.

So to my point, these equations did *NOT* generate the toriods shown at: http://paulbourke.net/geometry/torus/. You can not pick a fractional number for n1 & n2 and plot the points generated in real space as theta and phi vary from 0 to 2*pi.

In order to plot these functions in real space it required a redefinition of the pow() function to be something outside of what is commonly accepted as 'correct'.

I didn't get a chance to post this bit of Dr Bourke's reply to my emails:

I don't think the code I gave can be translated to OpenScad, it is after
all just an implementation of the equations. Openscad does things very
differently, my code is creating a surface whereas Openscad is wanting
to work on solids.

The attached file handles most of the values for n1 & n2 and is written in OpenScad. Rather than modify the pow() function, this code generates the shape in the first quadrant where the equation's values are real and mirrors that to form the rest of the toroid.

Welcome to our community Dr Bourke.
OME

Agreed....