feat(api): inner well geometry unit tests

[caila-marashaj]

Overview

This pr resolves the geometry calculations pertaining to liquid tracking. It updates a lot of the inner well geometry definitions according to the hardware team's measurements, and includes some math and logic fixes.

Frustum Whoopsie

One notable math fix is that the first time height_to_volume_circular or volume_to_height_circular are called for a given well, we'll now generate a table in shared-data containing the volume calculated at every height within the well at a 0.005 mm interval. We did this because the inverse function of the polynomial relationship (only for circular frusta) we came up with was shown to have an exponential increase in error with respect to height that peaked at the middle of each well segment.

To clarify, finding the volume from the height within a conical frustum works reliably well. This is because the relationship between height and volume takes the following shape:
Volume = a * target_height^3 + b * target_height^2 + c * target_height, where a, b, and c are found from the heights and radii of the top and bottom faces.

This makes finding the volume only a matter of addition and multiplication, but finding the height from some arbitrary volume to require an estimation of the roots of a third-degree polynomial. So, the solution here is just to avoid using that estimation and rely on a set number of the more reliable volume calculations that are done all at once.

For whatever reason, this was only a problem when calculating heights in circular, and not rectangular, frusta, so we left the rectangular math as is.

Changelog

• aforementioned restructuring of the circular height and volume calculations
• add unit tests that compare our calculations with the measured values from the hardware team laid out in this doc
• updates to inner well geometry definitions according to hardware's measurements

[codecov]

Codecov Report

Attention: Patch coverage is 23.52941% with 13 lines in your changes missing coverage. Please review.

Project coverage is 73.82%. Comparing base (906d841) to head (a255168).
Report is 89 commits behind head on edge.

Files with missing lines	Patch %	Lines
...pentrons_shared_data/labware/labware_definition.py	23.52%	13 Missing ⚠️

Additional details and impacted files

@@             Coverage Diff             @@
##             edge   #17082       +/-   ##
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- Coverage   92.43%   73.82%   -18.62%     
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  Files          77       43       -34     
  Lines        1283     3301     +2018     
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+ Hits         1186     2437     +1251     
- Misses         97      864      +767     

Flag	Coverage Δ
g-code-testing	?
shared-data	73.82% <23.52%> (?)

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Files with missing lines	Coverage Δ
...pentrons_shared_data/labware/labware_definition.py	78.00% <23.52%> (ø)

... and 119 files with indirect coverage changes