Animation with Sage (Hopf fibration)

[Niles]

Hello Sage marketers!

I've just finished a long-term side project related to visualizing the
Hopf fibration; the result is an HD animation on YouTube which I think
turned out really well [1]. I produced the animation frames entirely
with Sage, and so I thought some people on this list might be
interested. In particular, I made use of the following:

* plotting parametric functions (to draw the fibers)
* numerical integration and find_root to parametrize curves by arc
length (to move points along curves on the two-sphere with constant
speed)
* interface to Tachyon (for the ray-tracing)
* parallel processing support (for rendering a large number of frames
-- see ticket 11461)
* python as the basic language (for writing code to generate and
organize the basic animation data)

The source code is a .sage file on my website [2], in case you're
interested.

best,
Niles

[1] www.youtube.com/watch?v=AKotMPGFJYk
[2] www.nilesjohnson.net/hopf-production.html

[Jason Grout]

On 8/26/11 9:54 AM, Niles wrote:
> Hello Sage marketers!
>
> I've just finished a long-term side project related to visualizing the
> Hopf fibration; the result is an HD animation on YouTube which I think
> turned out really well [1]. I produced the animation frames entirely
> with Sage, and so I thought some people on this list might be
> interested. In particular, I made use of the following:
>
> * plotting parametric functions (to draw the fibers)
> * numerical integration and find_root to parametrize curves by arc
> length (to move points along curves on the two-sphere with constant
> speed)
> * interface to Tachyon (for the ray-tracing)
> * parallel processing support (for rendering a large number of frames
> -- see ticket 11461)
> * python as the basic language (for writing code to generate and
> organize the basic animation data)

Cool! Maybe it could be added to the wikipedia article on Hopf
fibration? There are some other animations referenced at the bottom of
that article.

Thanks,

Jason

[kcrisman]

Niles, you rock! I just was showing my classes the Moebius
transformation video, and I'll be sure to pass this on as a video they
can comment on for a wee bit of extra credit :)