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....

[Mjolinor]

Originally Posted by old man emu
Welcome to our community Dr Bourke.
OME

Bit formal isn't it.

Welcome Peter.

[old man emu]

Bit formal isn't it.

Welcome Peter.

Had to do that to show all you Northern Hemisphere types that under the Southern Cross we respect the accomplishments of a man. Having done so, the correct appellation is now "G'day, Pete. Ow ya goin'?"

And Roxy,


OME

[Mjolinor]

Had to do that to show all you Northern Hemisphere types that under the Southern Cross we respect the accomplishments of a man. Having done so, the correct appellation is now "G'day, Pete. Ow ya goin'?"

OME

Except one doesn't join a forum like this to be reminded of how one is addressed when in those boring meetings with suits on.

[Roxy]

Are you really going to make square doughnuts?

[old man emu]

Are you really going to make square doughnuts?

Square doughnuts + square pizza = square meal. Nutritional Nirvana!

[old man emu]

Except one doesn't join a forum like this to be reminded of how one is addressed when in those boring meetings with suits on.

In an egalitarian society such as we have in Australia, clothes do not maketh the man. Using an appellation that recognizes skill and experience is like tipping one's hat in respect. Any demand for such behaviour after the first encounter is rejected because here, Jack is as good as his Master.

OME

[Mjolinor]

In an egalitarian society such as we have in Australia, clothes do not maketh the man. Using an appellation that recognizes skill and experience is like tipping one's hat in respect. Any demand for such behaviour after the first encounter is rejected because here, Jack is as good as his Master.

OME

It would be good if it were indeed like that but suits or no, Australians are the same as the rest of the world when it comes to business meetings and the use of titles on business cards and the like.

A Phd means you are part of the way to knowing more and more about less and less until ultimately you know everything about nothing.

[Geoff]

Are you really going to make square doughnuts?

I wish I had something tangible to add to this conversation, but all I can come up with is Bacon and Egg Tacos.

[old man emu]

I wish I had something tangible to add to this conversation, but all I can come up with is Bacon and Egg Tacos.

You could try a Four'n'Twenty or a Big Ben. Let your imagination go. Don't put a damper on it. How bout some underground mutton? And finish up with a lamington and slice of pav.

Could we haul this topic back from Hell's Kitchen to Dunkin' Donuts?

OME