Update constant_angle_in_spherical_domain_issue.md

[ljhwang]

Edits for clarity.

Please feel free to edit.

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Comparison is base (2d07a63) 92.54% compared to head (2dfcc38) 92.58%.
Report is 30 commits behind head on main.

Additional details and impacted files

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+ Coverage   92.54%   92.58%   +0.04%     
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  Files          92       92              
  Lines        6369     6368       -1     
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+ Hits         5894     5896       +2     
+ Misses        475      472       -3     

see 2 files with indirect coverage changes

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[gassmoeller]

two small typos left

[gassmoeller]

Suggested change

When defining a line with a certain angle to the surface in a sphere, you can look at this in one of two ways. The first option is to define a constant angle at its starting point. This works mostly fine except for large distances where it will burst through the surface of the planet out into space. This can be see in the left figure below. The other option is to define a constatnt angle with respect to the surface above. This results in a logarithmic spiral as seen in the right figure below.

When defining a line with a certain angle to the surface in a sphere, you can look at this in one of two ways. The first option is to define a constant angle at its starting point. This works mostly fine except for large distances where it will burst through the surface of the planet out into space. This can be seen in the left figure below. The other option is to define a constant angle with respect to the surface above. This results in a logarithmic spiral as seen in the right figure below.

[github-actions]

Benchmark	Main	Feature	Difference (99.9% CI)
Slab interpolation simple none	1.020 ± 0.005 (s=458)	1.016 ± 0.003 (s=429)	-0.5% .. -0.4%
Slab interpolation curved simple none	1.016 ± 0.004 (s=445)	1.013 ± 0.004 (s=445)	-0.4% .. -0.3%
Spherical slab interpolation simple none	1.162 ± 0.007 (s=395)	1.164 ± 0.008 (s=381)	+0.0% .. +0.3%
Slab interpolation simple curved CMS	1.058 ± 0.004 (s=395)	1.054 ± 0.004 (s=460)	-0.5% .. -0.3%
Spherical slab interpolation simple CMS	1.545 ± 0.009 (s=286)	1.544 ± 0.008 (s=299)	-0.2% .. +0.1%
Spherical fault interpolation simple none	1.169 ± 0.008 (s=362)	1.171 ± 0.005 (s=410)	-0.0% .. +0.2%
Cartesian min max surface	2.298 ± 0.019 (s=190)	2.301 ± 0.028 (s=204)	-0.2% .. +0.5%
Spherical min max surface	7.182 ± 0.044 (s=66)	7.188 ± 0.046 (s=62)	-0.3% .. +0.5%