[SciPy-User] Orthogonal polynomials on the unit circle

[David Warde-Farley]

On Sat, Oct 27, 2012 at 11:38 AM,  <josef.pktd at gmail.com> wrote:
> On Sat, Oct 27, 2012 at 3:19 AM, David Warde-Farley
> <wardefar at iro.umontreal.ca> wrote:
>> On Fri, Oct 26, 2012 at 9:40 PM,  <josef.pktd at gmail.com> wrote:
>>> http://en.wikipedia.org/wiki/Orthogonal_polynomials_on_the_unit_circle
>>> with link to handbook
>>>
>>> application: goodness of fit for circular data
>>> http://onlinelibrary.wiley.com/doi/10.1111/j.1467-842X.2009.00558.x/abstract
>>>
>>> Are those available anywhere in python land?
>>>
>>> What's the difference between orthogonal polynomials on the unit
>>> circle and periodic polynomials like Fourier series?
>>>
>>> Josef
>>> circular statistics - what's that?
>>> It's like TDD, you go in circles
>>
>> I have some code somewhere for Zernike polynomials if you're
>> interested. I was using them for rotation-invariant feature
>> extraction.
>
> Thanks David. For now I'm looking at the circle, and from what I have
> seen Zernike polynomials are for disks or similar shapes.

Ah, yes. I misunderstood, you're right, Zernike polynomials are
defined on x^2 + y^2 <= 1, rather than x^2 + y^2 == 1.