Because of no answering in the issues, I post it in stack overflow, too, as a bounty question, which didn’t get any answer, too. I would be very grateful if the developers or the experts of this library who know any solution or … would guide me and answer in one of these two links. I am pinging based on contribution in similar posts, @ianthomas23 , @jklymak , @timhoffm , @dstansby
Please accept my apologies for any inconvenience caused due to my inexperience in GitHub issues.

The contouring algorithm doesn't know that it is acting on a polar plot, so when the contours are drawn in polar space the polygons are approximated. It's really hard to imagine doing much more for this, and your approaches of interpolating the data seem fine.

Now that contouring is in a separate repo in contourpy, @ianthomas23 may be able to provide more projection-specific contouring?

Now that contouring is in a separate repo in contourpy, @ianthomas23 may be able to provide more projection-specific contouring?

I have mentioned him in my last comment. I produce more points among the arrays and interpolate with method linear using RBF SciPy, It seems this way can be helpful in this regard, which result is smoother than linear method used in griddata SciPy (way 2). I will recheck my work, hope others could get a better solution.

@alisheikholeslam Both contour and tricontour produce lines and/or polygons that are piecewise linear, so sequences of (x, y) points that are connected with straight lines. Here you are contouring in polar space, the points are transformed to cartesian (i.e. screen) space and they are connected with straight lines. A line at constant radius, like all lines, is drawn straight but you would like it to be drawn as a circular segment. The more points you have, the shorter the lines are and the closer this looks to a circular segment.

If this bothered me I wouldn't draw the outer black circle, or I would draw it wider so no gaps are visibie.

This isn't actually a contouring issue, it is an issue of whether a straight line in one coordinate system should be transformed to a straight or non-straight line in another coordinate system. It applies equally to any polygon (e.g. just a simple triangle) specified in, for example, polar coordinates, and rendered in cartesian (screen) coordinates. Currently all such lines are drawn straight, with the exception of polar bar charts (there might be more exceptions, I haven't checked).

It would be possible, in general, to have a path transform function to convert straight-lines-in-polar-coordinates to curved-lines-in-cartesian-coordinates be approximating the curves using quadratic bezier curves, which would almost but not quite double the length of the points buffer. It would also need to deal with paths that are already bezier curves of course. The work required for this is (1) the maths, (2) the implementation, and (3) the API. I would expect that cartopy maintainers would have already done something along these lines (pun intended) as they deal with much more complicated transforms that just cartesian and polar.

@ianthomas23 is there a configuration setting to increase the polygon point density? Going up a factor of 2-3 would likely be a practical workaround to fix the present case.

@ianthomas23 is there a configuration setting to increase the polygon point density? Going up a factor of 2-3 would likely be a practical workaround to fix the present case.

No there isn't.

Contouring is always an approximation. You will need to come up with a practical solution to this problem, rather than expect the algorithm to change.

In the above, if I do ax.set_ylim(0, 89) the gaps disappear. If you really want the ring to go to exactly 90, then fill in a dummy row of data at deviation=100 and do ax.set_ylim(0, 90).

@jklymak , I think this solution or something like thickening (or using thicker) the boundary are not good solutions and depending on the input data; I saw several examples that not-filled area is not small, unlike the example in this post, and using this solution for curing will miss a big area. @ianthomas23 thanks for the explanation and the possible solution. I am not very familiar with cartopy library, but will try to communicate with its experts if have problem in my future plots. As I said earlier, as a workaround, I tried to produce some data and interpolation, which solves the white voids issue near the boundaries and produce almost acceptable results in the SO link. By the way, I am seeking for any better solution than mine and not sure about closing this issue and leave it to you. Thank you all for participating in this issue.

I think for the explanations given in comments above it's worth closing this as expected behaviour that we can't fix. Thanks for opening the issue though, and sorry there isn't a fix we can implement for it.