How to rotate a function about the y-axis

I wonder if anyone can help.

I have a Bessel function defined from x=0:20. I am trying to rotate it about the y-axis, so I can get a plot which resembles an Airy function.

I am struggling to write a for loop which will do this. Does anyone have a suggestion or pointers?

Thank you

[Wayne King]

Hi Katy, please post the relevant MATLAB code so somebody can try to help you.

[Jan]

Do you want to plot dots or a surface? For the later you can take a look into the source of SPHERE: Rotating around the Y-Axis is like drawing a deformed hemisphere.

[Katy Pointer]

Hi Wayne; all I have at the moment is

x=[0.1:0.1:20];

J=besselj(1,x);

y=(J./x);

I don't even know how to get started trying to rotate it!

I want to end up with a matrix of values of height above the xy plane, so I can perform an fft on the result.

Thank you

[Jan]

At first you asked for a method to plot the values. Now you want the results as a matrix. This is a different job.

[Katy Pointer]

Isn't that the same thing? Then I can do mesh(matrix) to get the plot.

[Jan]

You can plot a matrix. But rotating the Bessel function leads to a circular shape, not to a rectangular matrix.

Answer 1

[Teja Muppirala]

Something like this maybe?

[X,Y]=meshgrid(-20:0.1:20);
R = sqrt(X.^2 + Y.^2);

J=besselj(1,R); 
Z=(J./R);
Z(isnan(Z)) = 0.5; %Fix the divide by zero problem

surf(X,Y,Z);
shading flat;
camlight;

[Katy Pointer]

That's amazing! Thank you. I had tried something similar, but didn't quite get the radius bit right. Thanks so much :)

Answer 2

[Patrick Kalita]

You might have a look at this similar question:

http://www.mathworks.com/matlabcentral/answers/9377-changing-reference-axis-for-plot-rotating-a-set-of-points-by-an-angle

Answer 3

[Jan]

What about using AIRY?

v = -20:0.1:20;
m = bsxfun(@plus, v, i*v');
Z = airy(m);