what is a good way to mesh the desired domain

Given the mesh below (I can find the mesh and I plotted over the mesh two vertical lines), I would like to know a good way to find a proper rectangular mesh to divide the domain on the two regions. What I actually have is a domain with inner and outer radius ri and ro and angles thetai and thetao, which is pretty simple to mesh:

R = ri:dr:ro;
Theta = 0:dtheta:theta0;
[theta,r] = meshgrid(Theta,R);
mesh(r.*cos(theta),-r.*sin(theta),0*r); view(-90,90);

The code snippet above gives the mesh plotted on the figure. I'm working with finite volumes, that is why I'm using a rectangular mesh.

Now, I want to divide my region on two distinct regions. The vertical lines do not need to be vertical, they must be parallel to each other (they will be vertical if the starting angle is 0°). I have a function to define the height of each volume:

f = @(theta) h(theta);

On the original mesh, this function is simply defined. However, when I want to divide my mesh in two portions, to make the outlet paralell to the inlet, I'm having trouble to find a proper mesh or how to divide the mesh I already have.