1 field — just the hospital’s name. Nothing here says which municipio each one is in.

1 field each — NAME_2. This is the attribute we want to hand to the points.

Two hospitals sit in Mérida, one in Progreso. Your eye does the join instantly; st_join is how you say it to R.

2 fields, and both Mérida hospitals got the same value. The polygon hands its attribute to every point inside it — still three rows, none added, none lost.

DENUE already carries a municipio column, so you can check this answer. Later today we do exactly that at scale — and find where the two disagree.

A spatial join matches rows from two layers by a geometric relationship. Everything today is a variation on this — the difference is that with 6,460 points you cannot check by eye.

Every panel on the last slide was a constructor — geometry in, new geometry out.

A join is a predicate plus bookkeeping: st_join(x, y, join = st_within) runs the predicate, then attaches columns. That is why the predicate is an argument.

This session walks the three families in order: A joins, B measures, C constructors.

Read the legend: every point now carries a municipio name it arrived without. That is what st_join bought you — you can now count, filter and group these 6,460 rows by municipio, using nothing but their coordinates.

Same data, same join. On the linear scale Mérida’s 4,218 swamps everything; on the log scale you can finally see the other 105 municipios differ from one another.

The inset shows where we are — central Yucatán, east of Mérida. Seven municipios, the black dots are the establishments, and the number on each is exactly how many fell inside it. Tinum 22, Yaxcabá 12, Chankom 5, Kaua 3 — darker means more, and the label proves it.

Seven establishments DENUE labels Kanasín have coordinates inside Mérida; one labelled Mérida falls in Umán. Every one sits on the metropolitan boundary — where an address and a GPS reading are most likely to part company.

The last is a coastal clinic in San Felipe, sitting 34 m outside GADM’s simplified shoreline. The clinic is real; the coastline is approximate.

Eight disagree, one lands nowhere. Neither answer is simply “right”: the label is the administrative address a registry recorded; the geometry is where a GPS reading fell, judged against a boundary file that is itself simplified.

Identical — 6,460 rows, 1 unmatched, either way.

Tizimín 3,847 km² against Sanahcat 26 km² — a 148-fold spread. Municipios are nothing like equal-sized, which is why a count per municipio told you so little.

0.025 square degrees against 292,689,496 square metres. The first is a bare number; the second knows what it is.

The same map twice. The two columns correlate at 1.00 — nothing about the picture tells you one of them is measured in a unit that means different things at different latitudes.

The geometric centre of mass — the same operation as the top-left panel of the toolkit, on real municipios.

Still Chikindzonot — but 46.4 km instead of 44.2, and the top five change order.

Without the union, overlapping buffers would double-count the area they share.

intersection is “in both”, difference is “in the first but not the second”, union is “in either”. Those three cover most overlay work.

Only 29.9% of Yucatán is within 10 km of a hospital — and that is straight-line distance, so the real figure is worse.

Together they come to 7.6 km². Casting them off changes the state’s area by 0.02% — but it changes the number of features from one to six, and that is what breaks a loop.

Those five islands are 0.02% of the area but 43.8 km of coastline — 3.6% of the total. Casting them off is an analytical decision, not housekeeping.

Next session: rasters — continuous surfaces, and extracting them to your polygons.