Adding a separate factor for NFP to calculate umbilic configurations

[rahulgaur104]

An umbilic torus is a 3D shape with a continuous sharp edge that goes around three times toroidally before meeting itself. This shape can be thought of as a stellarator with a rational field period because the cross-section is only exactly identical (each sharp point completes a full poloidal rotation) after three toroidal turns.

Practically, these configurations are useful for resonant divertor design and simplifies divertor placement.

The objective of this PR is to add an additional factor that adds an integer NFP_umbilic_factor so that NFP -> NFP/NFP_umbilic_factor and make sure that the code runs without any issues.

To create an umbilic edge, we take the boundary of the stellarator and a 3D umbilic curve on the boundary and vary both the curve and the surface to obtain a stellarator that resembles an umbilic-torus-like shape.

[github-actions]

Remaining comments which cannot be posted as a review comment to avoid GitHub Rate Limit

flake8

desc/geometry/core.py|120 col 89| line too long (107 > 88 characters)
desc/geometry/core.py|367 col 89| line too long (107 > 88 characters)
desc/geometry/core.py|416 col 89| line too long (109 > 88 characters)

[unalmis]

When you construct the grid, it's fine to give nodes $\zeta \in [0, 2\pi / \text{NFP})$ or with the duplicate endpoint $\zeta \in [0, 2\pi / \text{NFP}]$. This change you have made is correct to ensure that still works with $\text{NFP} = \text{rational NFP}$. However, don't expect this logic to be sufficient to give correct behavior if you construct a grid with nodes $\zeta \in [0, 2\pi]$ when $\text{NFP} \neq 1$.

[unalmis]

I liked the earlier description more

[codecov]

Codecov Report

Attention: Patch coverage is 51.72414% with 98 lines in your changes missing coverage. Please review.

Project coverage is 95.01%. Comparing base (b1900b3) to head (90f0cf8).

Files	Patch %	Lines
desc/objectives/_geometry.py	13.51%	96 Missing ⚠️
desc/geometry/curve.py	93.75%	1 Missing ⚠️
desc/objectives/normalization.py	75.00%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #819      +/-   ##
==========================================
- Coverage   95.42%   95.01%   -0.41%     
==========================================
  Files          89       89              
  Lines       22434    22578     +144     
==========================================
+ Hits        21407    21453      +46     
- Misses       1027     1125      +98     

Files	Coverage Δ
desc/basis.py	98.20% <100.00%> (+0.01%)	⬆️
desc/coils.py	97.26% <100.00%> (+<0.01%)	⬆️
desc/compat.py	83.96% <100.00%> (ø)
desc/equilibrium/equilibrium.py	95.71% <100.00%> (ø)
desc/examples/__init__.py	100.00% <100.00%> (ø)
desc/geometry/core.py	91.82% <100.00%> (+0.16%)	⬆️
desc/geometry/surface.py	96.85% <100.00%> (+<0.01%)	⬆️
desc/grid.py	92.98% <100.00%> (+0.08%)	⬆️
desc/io/hdf5_io.py	81.96% <ø> (ø)
desc/io/optimizable_io.py	86.30% <ø> (ø)
... and 9 more