Nomials on the Complex Unit Circle

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Published on July 15, 2011

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The real and imaginary components of the first few nomials on the complex unit circle. That is: Re(z⁰), Re(z¹), Re(z²), Re(z³)... Im(z¹)... Because of Taylor's theorem, these are deeply fundamental functions.

This is an example for surfcad, a surface oriented python cad library. The python code generates all the STLs. Only the real ones have been uploaded since you can just rotate them and get the complex ones where necessary.

A blog post on surfcad can be found at christopherolah.wordpress.com/2011/07/16/surface-oriented-cad-math-telescopes/ . surfcad itself can be found at github.com/colah/surfcad but is just in its infancy and subject to substantial API changes. Thus, it has also been attached...

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I think surfcad is a great idea. As I progress in my designs, I find that I'm outgrowing the simplicity of standard CSG, and having to provide more surface based things anyway. It would be great to integrate the two.

Thanks!

It would definitely be nice to be able to use both approaches (there's a lot of things CSG does better), though every way I've thought of to do it would be complicated and ugly.

Firstly, the software doesn't know whether a surface is closed or not. There would have to be some function that the us
er would use on a surface that would 'promise' that the surface is closed.

Then CSG could be done to those surfaces... Except I can't think of anyway to do that without rendering them into a trinagle mesh and passing them to some library, so post CSG objects will be fundamentally different, a bunch
of triangles instead of functions describing surfaces...

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