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Paul Fricker

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29 Oct 2014 Screenshot getNearestNeighborDistances.m Compute nearest-neighbor distances for the regions in a Boolean image. Author: Paul Fricker distance, regionpropsimage anal... 10 0
04 Jun 2012 Screenshot Hermite polynomials Hermite polynomials of order N. Author: Paul Fricker mathematics, physics, chemistry, statistics 15 0
14 May 2012 Screenshot SPHERESURF Display a matrix of surface data overlaid on a sphere. Author: Paul Fricker communications, earth science, wireless 11 0
29 Feb 2012 Screenshot Zernike polynomials Zernike polynomials and functions (orthogonal basis on the unit circle). Author: Paul Fricker chemistry, physics, zernike, optics, orthogonal basis, circular domain 111 20
  • 4.70588
4.7 | 17 ratings
29 Feb 2012 Screenshot Modified Zernike Decomposition Computes Zernike modal coefficients and orientation axes for data on the unit disk. Author: Paul Fricker biotech, mathematics, physics 14 0
  • 5.0
5.0 | 1 rating
Comments and Ratings on Paul Fricker's Files View all
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09 Apr 2014 Zernike polynomials Zernike polynomials and functions (orthogonal basis on the unit circle). Author: Paul Fricker Anael

Well documented!

01 Apr 2014 Modified Zernike Decomposition Computes Zernike modal coefficients and orientation axes for data on the unit disk. Author: Paul Fricker Karthik Velakur

07 Jan 2014 Zernike polynomials Zernike polynomials and functions (orthogonal basis on the unit circle). Author: Paul Fricker Mathieu

Hi,

Thanks for providing these files to the comunity !
However, did you check the othogonality of the functions created?
It seems to me that something's wrong there.
I generated 2 polynoms like it is shown in the doc :

z(idx) = zernfun(3,1,r(idx),theta(idx));
z2(idx) = zernfun(4,0,r(idx),theta(idx));

When I check the orthogonality by simply doing :

sum(sum(z(idx).*z2(idx)))

the result is not 0.

Am I doing someting wrong or is there a pb here?

Thanks in adavnce

26 Mar 2013 Zernike polynomials Zernike polynomials and functions (orthogonal basis on the unit circle). Author: Paul Fricker Konstantin

12 Jun 2012 @JUAN CARDENAS
n = floor((-1+sqrt(1+8*p))/2);
m=-(n-2*p+n.*(n+1));

Very good solution for using any p but
I think you were missing a '-'sign for your definition of m. (can be seen when plotting the Zernike-Polynomials)

12 Jun 2012 Zernike polynomials Zernike polynomials and functions (orthogonal basis on the unit circle). Author: Paul Fricker JUAN CARDENAS

Thank you Paul.
An update for enabling any P order, in zernfun2, instead of:

n = ceil((-3+sqrt(9+8*p))/2);
m = 2*p - n.*(n+2);

change it by:

n = floor((-1+sqrt(1+8*p))/2);
m=n-2*p+n.*(n+1);

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