ag/cross section fix

[andrewgiuliani]

I have used the Surface.cross_section algorithm on the entire QUASR database, and notice that very infrequently, the algorithm fails, see below

I rewrote the algorithm, making it simpler, to fix the bug. Rerunning the new algorithm on the entire dataset, I can't find any incorrect cross sections anymore.

Note that the jagged cross section where varphi=0 is because it uniformly samples the cross section in the Boozer theta angle, which may be insufficient as you can see.

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Codecov Report

Attention: Patch coverage is 97.56098% with 1 line in your changes missing coverage. Please review.

Project coverage is 92.36%. Comparing base (f0f0ec4) to head (d13538d). Report is 89 commits behind head on master.

Files with missing lines	Patch %	Lines
src/simsopt/geo/surfacexyztensorfourier.py	50.00%	1 Missing :warning:

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #428      +/-   ##
==========================================
+ Coverage   92.25%   92.36%   +0.10%     
==========================================
  Files          82       82              
  Lines       16015    16235     +220     
==========================================
+ Hits        14775    14995     +220     
  Misses       1240     1240              

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unittests	92.36% <97.56%> (+0.10%)	:arrow_up:

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[andrewgiuliani]

@mishapadidar for future reference, I'm including the figure illustrating what the algorithm is doing (all angles are normalized by 2*pi for consistency with Surface objects in simsopt).

The first graph shows the cylindrical angle as calculated by atan2(y(varphi, theta),x(varphi, theta))/(2*pi). The problem is that this has a discontinuity when the surface crosses +/- 0.5. So we shift by atan2(y(0, theta),x(0, theta))/(2*pi) in the second graph. Any part of the shifted curve that is less than 0 has crossed +/- 0.5, so we shift negative function values up by 1 to obtain the function in the third graph. The resulting function is continuous provided that the surface crosses +/- 0.5 only once.

[mishapadidar]

its looking good. just address the couple comments about documentation and we can get this thing landed.