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-MFra-21-Topaz II
21-Topaz II
February 27, 2021
Solved

How do I draw a surface, expressed in polar coordinates?

  • February 27, 2021
  • 2 replies
  • 4339 views

Hello,
I have a circular symmetry system. A physical quantity defined in the circular section of such a system is defined by a function of the two polar variables r and φ. How to have the graph of this surface using CreateMesh () and pol2xy ()? I find some difficulties, maybe trying and trying again I succeed. But I would like your suggestion so as not to waste time. The function, in polar coordinates, is for example F (r, φ) = Jn (1,0.383r) cos (φ).

Best answer by -MFra-

I'm sorry. Problem solved.

2 replies

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-MFra-21-Topaz IIAuthorAnswer
21-Topaz II
February 27, 2021

I'm sorry. Problem solved.

ttokoro
ttokoro21-Topaz I
21-Topaz I
February 27, 2021

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t.t.
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-MFra-21-Topaz IIAuthor
21-Topaz II
February 27, 2021

Modes.jpg

W
Werner_E25-Diamond I
25-Diamond I
February 27, 2021

Some remarks:

  1. You can get rid of the if-function in the definition of F.z because Mathcad#s 3D plot won't accept NaN's anyway and would throw an error
  2. Using atan(y/x) gives you wrong results (wrong sign) for x<0 and an error if x=0 (try Bound:=101)
    You should use atan2(x,y) instead
  3. To avoid an error if your mesh includes x=y=0 you should create an error trapping Atan2 function which returns 0 if x=y=0.

Werner_E_0-1614451805978.png

 

W
Werner_E25-Diamond I
25-Diamond I
February 27, 2021

One additional remark because you asked how to use CreateMesh with a mapping function like pol2xy.

You can't use pol2xy as this mapping function only works in 2D.

You are dealing with cylinder coordinates and so you will have to use the predefined cyl2xyz() -> see F2
Of course you always can define your own mapping function, too -> see F3

Werner_E_0-1614453693474.png

Of course the 3D plots with F2 and F2 are limited to a circular base area in the xy-plane as they are dealing directly with the original polar coordinates in xy, while F1 has a rectangular base in the xy-plane.

But in your initial question you wrote "A physical quantity defined in the circular section" and so I was irritated that your solution used a rectangular/square section instead.

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