Dissolve
It exists already.
Dissolve (Data Management tools)
So why another one?
Simple. You need an attribute to dissolve on.
You are doing your aggregation of shapes based on a common attribute, so it is grouping things based on commonalities.
The work around, is to fill a column with a common attribute, then away you go.
As part of my work on the Geo array that I use for my Free Tools project, I began to explore how dissolve actually works. Sadly, it isn't as simple as I thought and reading the academic papers or tearing apart code left me feeling a bit lost. I admit, reading my code after a few days away leaves me feeling the same.
In short:
- find common segments in your polygons
- which means find the adjacent polygons, then
- for each one find the common segment(s)
- remembering that the edges of common segments will go in the opposite direction
- and you have the floating point comparison thing
- (I know I have forgot something... check my code 😐)
- remove the common segments and rejoin the remaining segments
- don't get me started... there are no examples of this in useful pseudo-code and
- yeah, yeah, the plane sweep thingy, why does it take multiple classes to define one it is all just an array
- don't forget the case where a polygon can join other polygons at multiple points
- don't forget to keep those around that aren't done yet
- are you keeping inner rings? (aka, holes)
- what about multipart shapes? split them? keep them if they are disjoint?
- what about meeting at a point?
- I know, I know, two points sharing the same coordinates form a degenerate line, but there is no through access... my suggestion, dump'em until they learn to be more open.
So some examples:
Laughing person ... before and after dissolve


Note the shapes aren't in order which makes it a challenge. You can do a lexicographic sort of the left-most coordinate to speed up the identification of adjoining shapes.
Bird on Dog ... before and after dissolve


This example shows two groupings of geometry. I chose the dump the holes option.
The Dissolve Boundaries tool

References
numpy geometry
arcpro_npg ... npg ... (n)um(p)y (g)eometry the code
Github version
Dissolve ... in geonumeracy
GitHub Pages
Dissolve ... GitHub pages
geonumeracy... a compendium of geometry learnings
geonumeracy... on GitHub Pages
Try taking down a few boundaries yourself... either in life or geometry 😁 .