Polygons from First Principles

ILGISA 2026 · Peoria

How χGRIDs extend the UN's 2025 settlement methodology to neighborhood-scale geographies. Everything from the talk, and one question for you.

The slides, in your browser — arrow keys to move, n for sources
The slides (PDF) — 27 slides, one per page
What Is Chicago? — the UN rule, replayed step by step on Chicago's 1 km grid
Parallel Peorias — to the UN, Peoria is a town; the same rule finds its twins worldwide
χGRIDs on GitHub — polygons (GeoJSON, Shapefile, GeoPackage), generators, MIT; interactive explorer
Comparables for every Illinois settlement — a one-page PDF for your settlement and a statewide spreadsheet, by email
Penlight — Chicago measures by ward, neighborhood and chi

The recipe: the UN's 2025 rule in six steps, in ArcGIS Pro or QGIS

Data: GHS-WUP-POP E2025 and GHS-LAND, 1 km cells in the Mollweide projection (ESRI:54009), free from the JRC Global Human Settlement Layer. Check your result against the published GHS-WUP-DEGURBA class-30 cells. These tool chains are close equivalents of the replay shown in the talk, which matched the UN's Chicago boundary cell for cell.

Step	Rule	ArcGIS Pro	QGIS
1. Start from the grid	Download GHS-WUP-POP E2025 (1 km, Mollweide ESRI:54009) and GHS-LAND from https://jeodpp.jrc.ec.europa.eu/ftp/jrc-opendata/GHSL/, and keep the grid in its own projection.	add both rasters as-is; set the processing extent to your window and the cell size and snap raster to the population grid.	Same: load both, align to the population grid.
2. Keep the dense squares	People per km² of land = population / (GHS-LAND m² / 1,000,000); a cell is dense at 1,500 or more.	Raster Calculator: Con("pop" / ("land" / 1000000) >= 1500, 1).	Raster Calculator with the same expression.
3. Connect edge to edge	Dense cells that share an edge form one cluster; corners do not count.	Region Group with number_neighbors FOUR.	r.clump without the -d (diagonal) flag.
4. Require 50,000 people	Keep clusters of 50,000 people or more.	Zonal Statistics (SUM of population by region), then Con(sum >= 50000).	r.stats.zonal method=sum, then the Raster Calculator.
5. Fill small holes	Fill enclosed gaps smaller than 15 km² inside each surviving cluster.	Region Group on the non-cluster cells (FOUR); fill groups under 15 cells that do not touch the outside.	r.clump on the gaps, r.stats to count cells, then the Raster Calculator.
6. Smooth by majority vote	3×3 majority vote among land cells, the centre included; ties join; cells are only added; repeat until nothing changes.	Focal Statistics (3×3 rectangle, SUM) on the cluster mask and on the land mask; add cells where cluster sum ≥ half the land sum; iterate.	r.neighbors size=3 method=sum on both masks, same rule, iterate.