ACCEPTED SOLUTION
Accepted Solutions
Some remarks:
- 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
- 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 - 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.
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
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.
Here's another way doing it without using a mapping function in CreateMesh by defining the base function not as R^2 -> R but rather R^2-> R^3.
Of course this just means to manually apply the mapping function when defining f(r,phi). So the most convenient way is letting CreateMesh do the job using the built-in cyl2xyz mapping function (as shown above, F2). Personally I'd prefer F4 as it dispplays more clearly what's going on under the hood.
Maybe a sketch is worth a thousand words ....
In fact something is missing .... I will complete tomorrow ...
