feat: Persistent homology example

[jiriminarcik]

Description

This PR adds new example illustrating Persistent homology.

Implementation strategy and design decisions

The example was added to the registry.

Examples with steps to reproduce them

Run npx roger watch persistent-homology.sub persistent-homology.sty persistent-homology.dsl from/packages/examples/src/persistent-homology. Or npx roger watch persistent-homology.sub persistent-homology.sty persistent-homology-basic.dsl for a simplified version without labels.

Checklist

• I have commented my code, particularly in hard-to-understand areas
• My changes generate no new ESLint warnings
• I have reviewed any generated changes to the diagrams/ folder

Open questions

• The .sub file can be simplified after Allow Boolean logic in where clause of Style selectors #775 is resolved - we are unable to use negator in selector within the .sty file now.
• The complexity of this example was constrained by Cannot use two different images in the same diagram #1008.

[codecov]

Codecov Report

Merging #1007 (ce10bb9) into main (15053e3) will not change coverage.
The diff coverage is n/a.

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  Hits         4964     4964           
  Misses       2723     2723           
  Partials      114      114           

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[samestep]

This is super cool!

[joshsunshine]

@jiriminarcik can you explain exactly how you would use not in this example?

[minarj]

@jiriminarcik can you explain exactly how you would use not in this example?

In this example I need to make sure that two circles overlap iff the respective points satisfy e.g. the ConnectedOnFrame1 predicate, otherwise they must be disjoint. It is straightforward to enforce the positive condition, but not the negative one.

The current work-around involves defining the NotConnectedOnFrame1 predicate and explicitly writing down all combinations of points for which ConnectedOnFrame1 does not hold in .sub file.

With not, we could just use ConnectedOnFrame1 and write (in .sty):

forall Point p1; Point p2 
where not ConnectedOnFrame1(p1, p2) {
  ensure disjoint(p1.circle1, p2.circle1, 10)
}

instead of the current work-around:

forall Point p1; Point p2 
where NotConnectedOnFrame1(p1, p2) {
  ensure disjoint(p1.circle1, p2.circle1, 10)
}

This would eliminate most of the lines in packages/examples/src/persistent-homology/persistent-homology.sub (see comment on line 43).