Loading

Nomials on the Complex Unit Circle

by colah, published

Nomials on the Complex Unit Circle by colah Jul 15, 2011

Description

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...

Recent Comments

view all

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...

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.

Liked By

view all

Give a Shout Out

If you print this Thing and display it in public proudly give attribution by printing and displaying this tag. Print Thing Tag

Comments

You must be logged in to post a comment.

WilliamAAdams on Jul 17, 2011 said:

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.

Anonymous on Jul 17, 2011 said:

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...

Top