How to make a polar grid with variable number of angular points?

Greetings...

I am making a grid to discretize a circular disk area for an integration process:

1. we have the radial variable ρ and the angle ϕ.
2. Making it using "meshgrid" (even with nonuniform ticks) yields a unnecessary large density of ϕ at small ρ and a poor density of ϕ at large ρ. This affects the convergence of the integral, and capturing the variaion on the disk will require to take inefficient very large grids.

Requirements:

1. Making the grid on varying density basis. That is, as the value of ρ increases, the number of ϕ samples increase.
2. The grid should be integrable in MATLAB. I mean, can we use trapz or any built in numerical integration function? Or do it using "sum" in a straight foreward manner?

Thanks in advance for any help.

Answer 1

[Matt J]

I would use integral2() which, for one thing, does not require you to provide a meshgrid of samples. However, remember that with 2D integrals in polar coordinates, you have to multiply the integrand by ρ.

[Mohamed Abd El Raheem]

I don't have a formula to integrate. As I know, integral2 should take a formula through an input function handle.

I have numerical data. The data are generated on the disc area through some calculations, and then need to be integrated numerically.

[Matt J]

I don't have a formula to integrate. As I know, integral2 should take a formula through an input function handle.

You need a function handle, but that doesn't mean you need a formula. You can supply a handle to a function that interpolates the data.