Week 2: How Do Maps Work?
PPOL 6805 / DSAN 6750: GIS for Spatial Data Science
Fall 2026
Wednesday, September 2, 2026
ArcGIS…
- For info on Georgetown’s provision of ArcGIS (Online, Pro, and Desktop), see the Library Guide
Then… Why Can’t We Just Use ArcGIS?
Analogy from non-geospatial data science:
| Text Drawn Map |
→ | Speadsheet Digital Map |
→ | Equations Maps w/ArcGIS |
→ | Code This Class |
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Start writing
info.txt |
Start entering info in rows
|
Start using equations
|
Write code 
Profit 💲💰🤑💰💲 |
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R and/or Python and/or JS
- My Geometry vs. Algebra Rant… Euclid’s Elements, Book VI, Proposition 28.
- The problem: Divide a given straight line so that the rectangle contained by its segments may be equal to a given area, not exceeding the square of half the line.
Geometers solved w/geometry (300 BC)…
…Algebraists solved w/algebra (2000 BC)…
\[ \begin{align*} &ax^2 + bx + c = 0 \\ \Rightarrow \; & x_+ = \frac{-b + \sqrt{b^2 - 4ac}}{2a} \end{align*} \]
…From 1637 onwards, whichever is easier! 🤯🤯🤯 (Isomorphism)
He’s Literally Extremely Correct!
And… Actually Displaying the Map!
And with ggplot!
Spatial Randomness
Code
library(tidyverse)
library(spatstat)
set.seed(6805)
N <- 60
r_core <- 0.05
obs_window <- square(1)
# Regularity via Inhibition
#reg_sims <- rMaternI(N, r=r_core, win=obs_window)
cond_reg_sims <- rSSI(r=r_core, N)
# CSR data
#csr_sims <- rpoispp(N, win=obs_window)
cond_sr_sims <- rpoint(N, win=obs_window)
### Clustered data
#clust_sims <- rMatClust(kappa=6, r=2.5*r_core, mu=10, win=obs_window)
#clust_sims <- rMatClust(mu=5, kappa=1, scale=0.1, win=obs_window, n.cond=N, w.cond=obs_window)
#clust_sims <- rclusterBKBC(clusters="MatClust", kappa=10, mu=10, scale=0.05, verbose=FALSE)
# Each cluster consist of 10 points in a disc of radius 0.2
nclust <- function(x0, y0, radius, n) {
#print(n)
return(runifdisc(10, radius, centre=c(x0, y0)))
}
cond_clust_sims <- rNeymanScott(kappa=5, expand=0.0, rclust=nclust, radius=2*r_core, n=10)
# And PLOT
plot_w <- 400
plot_h <- 400
plot_scale <- 2.25
cond_reg_plot <- cond_reg_sims |> sf::st_as_sf() |>
ggplot() +
geom_sf() +
dsan_theme() +
transparent_bg()
ggsave("images/cond_reg.png", cond_reg_plot, width=plot_w, height=plot_h, units="px", scale=plot_scale)
cond_sr_plot <- cond_sr_sims |> sf::st_as_sf() |>
ggplot() +
geom_sf() +
dsan_theme() +
transparent_bg()
ggsave("images/cond_sr.png", cond_sr_plot, width=plot_w, height=plot_h, units="px", scale=plot_scale)
cond_clust_plot <- cond_clust_sims |> sf::st_as_sf() |>
ggplot() +
geom_sf() +
dsan_theme() +
transparent_bg()
ggsave("images/cond_clust.png", cond_clust_plot, width=plot_w, height=plot_h, units="px", scale=plot_scale)| Autocorrelation | \(I = -1\) | ← | \(I = 0\) | → | \(I = 1\) |
|---|---|---|---|---|---|
| Description | Negative Autocorr | No Autocorr | Positive Autocorr | ||
| Event at \(\mathbf{s} = (x,y)\) Implies | Less likely to find another point nearby | No information about nearby points | More likely to find another point nearby | ||
| Resulting Pattern | Regularity | Reg/Clustered Mix | Clustering | ||
| Process(es) Which Could Produce Pattern | 1st Order: Random within even-spaced grid 2nd Order: Competition |
1st Order: i.i.d. points 2nd Order: i.i.d. distances |
1st Order: Tasty food at clust centers 2nd Order: Cooperation |
||
| Fixed \(N\) | 60 | 60 | 60 | ||
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 |
Complete Spatial Randomness (CSR)
Code
library(tidyverse)
library(spatstat)
set.seed(6807)
lambda <- 60
r_core <- 0.05
obs_window <- square(1)
# Regularity via Inhibition
# Regularity via Inhibition
reg_sims <- rMaternI(lambda, r=r_core, win=obs_window)
# CSR data
csr_sims <- rpoispp(N, win=obs_window)
### Clustered data
clust_mu <- 10
clust_sims <- rMatClust(kappa=lambda / clust_mu, scale=2*r_core, mu=10, win=obs_window)
# And PLOT
plot_w <- 400
plot_h <- 400
plot_scale <- 2.25
reg_plot <- reg_sims |> sf::st_as_sf() |>
ggplot() +
geom_sf() +
labs(title=paste0("N = ",reg_sims$n)) +
dsan_theme() +
transparent_bg()
ggsave("images/reg.png", reg_plot, width=plot_w, height=plot_h, units="px", scale=plot_scale)
csr_plot <- csr_sims |> sf::st_as_sf() |>
ggplot() +
geom_sf() +
labs(title=paste0("N = ",csr_sims$n)) +
dsan_theme() +
transparent_bg()
ggsave("images/csr.png", csr_plot, width=plot_w, height=plot_h, units="px", scale=plot_scale)
clust_plot <- clust_sims |> sf::st_as_sf() |>
ggplot() +
geom_sf() +
labs(title=paste0("N = ",clust_sims$n)) +
dsan_theme() +
transparent_bg()
ggsave("images/clust.png", clust_plot, width=plot_w, height=plot_h, units="px", scale=plot_scale)| Autocorrelation | \(I = -1\) | ← | \(I = 0\) | → | \(I = 1\) |
|---|---|---|---|---|---|
| Description | Negative Autocorr | No Autocorr | Positive Autocorr | ||
| Event at \(\mathbf{s} = (x,y)\) Implies | Less likely to find another point nearby | No information about nearby points | More likely to find another point nearby | ||
| Resulting Pattern | Regularity | Reg/Clustered Mix | Clustering | ||
| Process(es) Which Could Produce Pattern | 1st Order: Random within even-spaced grid 2nd Order: Competition |
1st Order: i.i.d. points 2nd Order: i.i.d. distances |
1st Order: Tasty food at clust centers 2nd Order: Cooperation |
||
| Fixed Intensity \(\lambda\) | 60 | 60 | 60 | ||
| Random \(N\) |  |
 |
 |
R and/or Python and/or JS
- My Geometry vs. Algebra Rant… Euclid’s Elements, Book VI, Proposition 28.
- The problem: Divide a given straight line so that the rectangle contained by its segments may be equal to a given area, not exceeding the square of half the line.
Geometers solved w/geometry (300 BC)…
…Algebraists solved w/algebra (2000 BC)…
\[ \begin{align*} &ax^2 + bx + c = 0 \\ \Rightarrow \; & x_+ = \frac{-b + \sqrt{b^2 - 4ac}}{2a} \end{align*} \]
…From 1637 onwards, whichever is easier! 🤯🤯🤯 (Isomorphism)
He’s Literally Extremely Correct!
Step 1: Union of All Tracts
Step 2: Rasterize (terra)
Code
[1] 29 23 1
Rasters From Scratch
Welcome to Gridtown!
- Raster indices vs. values: The above plot displays indices for each cell: since a raster is a regular grid, can achieve memory-efficient representation with a single index (rather than, e.g., \((x, y)\) coords). But what we really care about are…
Raster Layer Values
Figure 6: Gridtown Values