Week 3: Vector and Raster Representations

PPOL 6805 / DSAN 6750: GIS for Spatial Data Science
Fall 2026

Class Sessions

Author

Affiliation

Jeff Jacobs

jj1088@georgetown.edu

Published

Wednesday, September 9, 2026

Open slides in new tab →

Logistical Table-Setting

HW1 Public Tests will be updated ASAP
TA Intros!
Coding Workshops!

TA Intros

(In alphabetical order by surname wohoo)

Jackson Howes (DSAN)
jh2787@georgetown.edu

BS in Government AND Mathematics (Honors), St. Lawrence, Canton, NY
Survived fire and flames of this class 🤯

Hermine Wilhelmsen (McCourt)
hw623@georgetown.edu

Recent MSc in Sustainability and Social Innovation, HEC Paris 🥳🧑‍🎓
Ombuds-person, UNFCCC alum

Relevant Word of the Day: 山 (Shān) = Mountain

Where We Left Off: Let’s Make Some Dang Maps!

Our First Map: Polygons!

From OpenData DC… Last week .shp, this week .geojson!

Code

library(tidyverse)

── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
✔ dplyr     1.2.1     ✔ readr     2.2.0
✔ forcats   1.0.1     ✔ stringr   1.6.0
✔ lubridate 1.9.5     ✔ tibble    3.3.1
✔ purrr     1.2.1     ✔ tidyr     1.3.2
── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
✖ dplyr::filter() masks stats::filter()
✖ dplyr::lag()    masks stats::lag()
ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors

Code

library(rmarkdown)
library(sf)

Linking to GEOS 3.13.0, GDAL 3.8.5, PROJ 9.5.1; sf_use_s2() is TRUE

Code

# Load DC tracts data
dc_sf_fpath <- "data/Census_Tracts_-_2020.geojson"
dc_sf <- st_read(dc_sf_fpath);

Reading layer `Census_Tracts_-_2020' from data source 
  `/Users/jpj/gtown-local/ppol6805/w03/data/Census_Tracts_-_2020.geojson' 
  using driver `GeoJSON'
Simple feature collection with 206 features and 315 fields
Geometry type: POLYGON
Dimension:     XY
Bounding box:  xmin: -77.11976 ymin: 38.79165 xmax: -76.9094 ymax: 38.99585
Geodetic CRS:  WGS 84

Code

cols_to_keep <- c(
  "OBJECTID", "TRACT", "GEOID", "ALAND", "AWATER",
  "STUSAB", "SUMLEV", "GEOCODE", "STATE", "NAME",
  "POP100", "HU100", "geometry"
)
dc_sf <- dc_sf |> select(cols_to_keep)

Warning: Using an external vector in selections was deprecated in tidyselect 1.1.0.
ℹ Please use `all_of()` or `any_of()` instead.
  # Was:
  data %>% select(cols_to_keep)

  # Now:
  data %>% select(all_of(cols_to_keep))

See <https://tidyselect.r-lib.org/reference/faq-external-vector.html>.

`sf` Objects

dc_sf is an R object of type sf (short for “simple features”), which extends data.frame by adding a special column named geometry (containing POLYGONs)

Code

class(dc_sf)

[1] "sf"         "data.frame"

Code

dim(dc_sf)

[1] 206  13

Code

rmarkdown::paged_table(dc_sf, options=list(rows.print=6))

OBJECTID	TRACT	GEOID	ALAND	AWATER	STUSAB	SUMLEV	GEOCODE	STATE	NAME	POP100	HU100	geometry
1	002002	11001002002	849376	0	DC	140	11001002002	11	Census Tract 20.02	4072	1532	POLYGON ((-77.03642 38.9497…
2	002101	11001002101	600992	0	DC	140	11001002101	11	Census Tract 21.01	5687	2335	POLYGON ((-77.02824 38.9581…
3	002102	11001002102	725975	0	DC	140	11001002102	11	Census Tract 21.02	5099	2221	POLYGON ((-77.01997 38.9581…
4	002201	11001002201	415173	0	DC	140	11001002201	11	Census Tract 22.01	3485	1229	POLYGON ((-77.02743 38.9518…
5	002202	11001002202	698895	566	DC	140	11001002202	11	Census Tract 22.02	3339	1454	POLYGON ((-77.01968 38.9520…
6	000101	11001000101	199776	5261	DC	140	11001000101	11	Census Tract 1.01	1406	999	POLYGON ((-77.05714 38.9105…
7	000102	11001000102	1706484	516665	DC	140	11001000102	11	Census Tract 1.02	3417	2053	POLYGON ((-77.06927 38.9005…
8	000201	11001000201	505004	0	DC	140	11001000201	11	Census Tract 2.01	4108	11	POLYGON ((-77.07927 38.9126…
9	000202	11001000202	776435	439661	DC	140	11001000202	11	Census Tract 2.02	4672	2169	POLYGON ((-77.07991 38.9050…
10	000300	11001000300	1042157	2305	DC	140	11001000300	11	Census Tract 3	6161	2845	POLYGON ((-77.08263 38.9212…
11	000400	11001000400	1541239	69	DC	140	11001000400	11	Census Tract 4	1643	998	POLYGON ((-77.07319 38.9276…
12	000501	11001000501	940249	29503	DC	140	11001000501	11	Census Tract 5.01	3829	2489	POLYGON ((-77.05899 38.9183…
13	000502	11001000502	581507	0	DC	140	11001000502	11	Census Tract 5.02	3418	1881	POLYGON ((-77.0664 38.93097…
14	000600	11001000600	1441865	71	DC	140	11001000600	11	Census Tract 6	4676	2435	POLYGON ((-77.07651 38.9422…
15	000702	11001000702	308967	0	DC	140	11001000702	11	Census Tract 7.02	3452	2472	POLYGON ((-77.08252 38.9217…
16	000703	11001000703	232137	0	DC	140	11001000703	11	Census Tract 7.03	3022	2136	POLYGON ((-77.08165 38.9262…
17	000704	11001000704	332346	0	DC	140	11001000704	11	Census Tract 7.04	2753	1724	POLYGON ((-77.07973 38.9334…
18	000802	11001000802	1688582	669985	DC	140	11001000802	11	Census Tract 8.02	3327	1541	POLYGON ((-77.10086 38.9112…
19	000803	11001000803	308153	0	DC	140	11001000803	11	Census Tract 8.03	3174	1692	POLYGON ((-77.08773 38.9357…
20	000804	11001000804	2566768	167978	DC	140	11001000804	11	Census Tract 8.04	3832	1347	POLYGON ((-77.10517 38.9172…
21	000902	11001000902	1867106	307257	DC	140	11001000902	11	Census Tract 9.02	2317	894	POLYGON ((-77.11975 38.9343…
22	000903	11001000903	928101	0	DC	140	11001000903	11	Census Tract 9.03	4202	484	POLYGON ((-77.10104 38.9351…
23	000904	11001000904	2024710	75151	DC	140	11001000904	11	Census Tract 9.04	3148	1216	POLYGON ((-77.11258 38.9402…
24	001002	11001001002	889722	0	DC	140	11001001002	11	Census Tract 10.02	3643	2544	POLYGON ((-77.08564 38.9382…
25	001003	11001001003	982460	0	DC	140	11001001003	11	Census Tract 10.03	3111	1129	POLYGON ((-77.10063 38.9491…
26	001004	11001001004	1471925	0	DC	140	11001001004	11	Census Tract 10.04	4480	1810	POLYGON ((-77.09292 38.9431…
27	001100	11001001100	1676650	0	DC	140	11001001100	11	Census Tract 11	5300	2414	POLYGON ((-77.08573 38.9607…
28	001200	11001001200	1219204	0	DC	140	11001001200	11	Census Tract 12	5371	2672	POLYGON ((-77.07883 38.9465…
29	001301	11001001301	2855501	26550	DC	140	11001001301	11	Census Tract 13.01	4160	2187	POLYGON ((-77.06943 38.9543…
30	001303	11001001303	889581	5274	DC	140	11001001303	11	Census Tract 13.03	3763	2532	POLYGON ((-77.06568 38.9479…
31	001304	11001001304	707155	9432	DC	140	11001001304	11	Census Tract 13.04	4018	3087	POLYGON ((-77.06157 38.9409…
32	001401	11001001401	788095	0	DC	140	11001001401	11	Census Tract 14.01	3258	1477	POLYGON ((-77.07743 38.9673…
33	001402	11001001402	895209	0	DC	140	11001001402	11	Census Tract 14.02	3514	1791	POLYGON ((-77.07331 38.9610…
34	001500	11001001500	4684714	39895	DC	140	11001001500	11	Census Tract 15	6156	2282	POLYGON ((-77.07165 38.9717…
35	001600	11001001600	2667590	7820	DC	140	11001001600	11	Census Tract 16	4471	1720	POLYGON ((-77.05163 38.9871…
36	001702	11001001702	939295	0	DC	140	11001001702	11	Census Tract 17.02	3356	1737	POLYGON ((-77.02532 38.9700…
37	001803	11001001803	1136289	31909	DC	140	11001001803	11	Census Tract 18.03	4102	1640	POLYGON ((-77.04763 38.9647…
38	001804	11001001804	601755	0	DC	140	11001001804	11	Census Tract 18.04	5500	2225	POLYGON ((-77.03342 38.9622…
39	001901	11001001901	769304	0	DC	140	11001001901	11	Census Tract 19.01	4206	1644	POLYGON ((-77.02803 38.9610…
40	001902	11001001902	877346	0	DC	140	11001001902	11	Census Tract 19.02	2117	883	POLYGON ((-77.0199 38.95938…
41	002001	11001002001	632724	1132	DC	140	11001002001	11	Census Tract 20.01	2926	1130	POLYGON ((-77.04338 38.9614…
42	002301	11001002301	407679	0	DC	140	11001002301	11	Census Tract 23.01	3266	1254	POLYGON ((-77.01996 38.9431…
43	002302	11001002302	2010924	5298	DC	140	11001002302	11	Census Tract 23.02	1762	686	POLYGON ((-77.01923 38.9368…
44	002400	11001002400	556408	0	DC	140	11001002400	11	Census Tract 24	4095	1724	POLYGON ((-77.0266 38.94613…
45	002501	11001002501	543460	0	DC	140	11001002501	11	Census Tract 25.01	2688	1099	POLYGON ((-77.03643 38.9429…
46	002503	11001002503	292105	0	DC	140	11001002503	11	Census Tract 25.03	3031	1523	POLYGON ((-77.02971 38.9368…
47	002504	11001002504	311721	0	DC	140	11001002504	11	Census Tract 25.04	3349	1375	POLYGON ((-77.03645 38.9377…
48	002600	11001002600	2106150	60195	DC	140	11001002600	11	Census Tract 26	2592	1013	POLYGON ((-77.05212 38.938,…
49	002702	11001002702	479022	7175	DC	140	11001002702	11	Census Tract 27.02	5825	2806	POLYGON ((-77.05078 38.9330…
50	002703	11001002703	163863	0	DC	140	11001002703	11	Census Tract 27.03	2614	1289	POLYGON ((-77.04419 38.9330…
51	002704	11001002704	295339	2427	DC	140	11001002704	11	Census Tract 27.04	2993	1689	POLYGON ((-77.05045 38.9332…
52	002801	11001002801	171910	0	DC	140	11001002801	11	Census Tract 28.01	4398	1999	POLYGON ((-77.03646 38.9341…
53	002802	11001002802	229696	0	DC	140	11001002802	11	Census Tract 28.02	4685	2430	POLYGON ((-77.03671 38.9271…
54	002900	11001002900	300632	0	DC	140	11001002900	11	Census Tract 29	4443	1944	POLYGON ((-77.03274 38.9319…
55	003000	11001003000	210636	0	DC	140	11001003000	11	Census Tract 30	3561	1748	POLYGON ((-77.03267 38.9301…
56	003100	11001003100	296819	0	DC	140	11001003100	11	Census Tract 31	3873	1818	POLYGON ((-77.02826 38.9318…
57	003200	11001003200	447929	0	DC	140	11001003200	11	Census Tract 32	5099	2174	POLYGON ((-77.02429 38.9363…
58	003301	11001003301	442120	0	DC	140	11001003301	11	Census Tract 33.01	3824	1847	POLYGON ((-77.01494 38.9206…
59	003302	11001003302	204237	0	DC	140	11001003302	11	Census Tract 33.02	2434	1216	POLYGON ((-77.01428 38.9150…
60	003400	11001003400	911458	159593	DC	140	11001003400	11	Census Tract 34	5120	1572	POLYGON ((-77.02297 38.9272…
61	003500	11001003500	382021	0	DC	140	11001003500	11	Census Tract 35	4801	2587	POLYGON ((-77.02705 38.9267…
62	003600	11001003600	305616	0	DC	140	11001003600	11	Census Tract 36	4775	2609	POLYGON ((-77.03241 38.9265…
63	003701	11001003701	172840	0	DC	140	11001003701	11	Census Tract 37.01	2916	1628	POLYGON ((-77.0365 38.91929…
64	003702	11001003702	119532	0	DC	140	11001003702	11	Census Tract 37.02	2906	1612	POLYGON ((-77.03649 38.9234…
65	003801	11001003801	148928	0	DC	140	11001003801	11	Census Tract 38.01	1800	1211	POLYGON ((-77.04171 38.9196…
66	003802	11001003802	207186	0	DC	140	11001003802	11	Census Tract 38.02	3911	2378	POLYGON ((-77.04269 38.9226…
67	003901	11001003901	120715	0	DC	140	11001003901	11	Census Tract 39.01	2598	1769	POLYGON ((-77.04355 38.9235…
68	003902	11001003902	266513	11205	DC	140	11001003902	11	Census Tract 39.02	2022	1379	POLYGON ((-77.04981 38.9278…
69	004001	11001004001	271037	2414	DC	140	11001004001	11	Census Tract 40.01	3941	2494	POLYGON ((-77.05018 38.9212…
70	004002	11001004002	194755	0	DC	140	11001004002	11	Census Tract 40.02	3291	2251	POLYGON ((-77.0463 38.91632…
71	004100	11001004100	788701	7303	DC	140	11001004100	11	Census Tract 41	2836	1757	POLYGON ((-77.05881 38.9158…
72	004201	11001004201	204529	0	DC	140	11001004201	11	Census Tract 42.01	3548	2367	POLYGON ((-77.04166 38.9141…
73	004202	11001004202	207646	0	DC	140	11001004202	11	Census Tract 42.02	2850	2060	POLYGON ((-77.04599 38.9145…
74	004300	11001004300	236694	0	DC	140	11001004300	11	Census Tract 43	4436	3030	POLYGON ((-77.03651 38.9142…
75	004401	11001004401	246895	0	DC	140	11001004401	11	Census Tract 44.01	3430	2302	POLYGON ((-77.03195 38.9199…
76	004402	11001004402	274746	0	DC	140	11001004402	11	Census Tract 44.02	2755	1629	POLYGON ((-77.03196 38.9155…
77	004600	11001004600	437422	0	DC	140	11001004600	11	Census Tract 46	3543	1844	POLYGON ((-77.01811 38.9146…
78	004702	11001004702	326418	0	DC	140	11001004702	11	Census Tract 47.02	3934	2762	POLYGON ((-77.02192 38.9025…
79	004703	11001004703	124124	0	DC	140	11001004703	11	Census Tract 47.03	3331	2356	POLYGON ((-77.02192 38.9029…
80	004704	11001004704	198509	0	DC	140	11001004704	11	Census Tract 47.04	1945	881	POLYGON ((-77.01482 38.9054…
81	004801	11001004801	317222	0	DC	140	11001004801	11	Census Tract 48.01	2820	1636	POLYGON ((-77.02192 38.9115…
82	004802	11001004802	288793	0	DC	140	11001004802	11	Census Tract 48.02	3634	2070	POLYGON ((-77.02192 38.9031…
83	004901	11001004901	271866	0	DC	140	11001004901	11	Census Tract 49.01	3380	2031	POLYGON ((-77.02704 38.9106…
84	004902	11001004902	263879	0	DC	140	11001004902	11	Census Tract 49.02	3449	2070	POLYGON ((-77.02705 38.9041…
85	005001	11001005001	200969	0	DC	140	11001005001	11	Census Tract 50.01	2012	1273	POLYGON ((-77.03195 38.9108…
86	005003	11001005003	94136	0	DC	140	11001005003	11	Census Tract 50.03	2143	1381	POLYGON ((-77.03195 38.9072…
87	005004	11001005004	143156	0	DC	140	11001005004	11	Census Tract 50.04	3861	2524	POLYGON ((-77.03033 38.9096…
88	005202	11001005202	246292	0	DC	140	11001005202	11	Census Tract 52.02	3408	2309	POLYGON ((-77.03653 38.9083…
89	005203	11001005203	93419	0	DC	140	11001005203	11	Census Tract 52.03	2979	2450	POLYGON ((-77.03457 38.9072…
90	005302	11001005302	117635	0	DC	140	11001005302	11	Census Tract 53.02	2518	1832	POLYGON ((-77.04167 38.9115…
91	005303	11001005303	168769	0	DC	140	11001005303	11	Census Tract 53.03	3215	2484	POLYGON ((-77.04298 38.9101…
92	005501	11001005501	164749	0	DC	140	11001005501	11	Census Tract 55.01	2303	1776	POLYGON ((-77.05142 38.9031…
93	005502	11001005502	251302	0	DC	140	11001005502	11	Census Tract 55.02	2968	2016	POLYGON ((-77.0488 38.90776…
94	005503	11001005503	213338	4682	DC	140	11001005503	11	Census Tract 55.03	2492	1799	POLYGON ((-77.05596 38.9045…
95	005601	11001005601	185309	1275	DC	140	11001005601	11	Census Tract 56.01	2900	2437	POLYGON ((-77.05762 38.9026…
96	005602	11001005602	273491	6261	DC	140	11001005602	11	Census Tract 56.02	4100	2355	POLYGON ((-77.0586 38.90134…
97	005801	11001005801	232951	0	DC	140	11001005801	11	Census Tract 58.01	1672	1312	POLYGON ((-77.02192 38.8935…
98	005802	11001005802	682488	0	DC	140	11001005802	11	Census Tract 58.02	2145	1616	POLYGON ((-77.03365 38.8973…
99	005900	11001005900	641993	0	DC	140	11001005900	11	Census Tract 59	2617	1705	POLYGON ((-77.01993 38.8936…
100	006400	11001006400	691410	243648	DC	140	11001006400	11	Census Tract 64	2481	1956	POLYGON ((-77.01535 38.8621…
101	006500	11001006500	509297	0	DC	140	11001006500	11	Census Tract 65	2609	1630	POLYGON ((-77.00912 38.8819…
102	006600	11001006600	285156	0	DC	140	11001006600	11	Census Tract 66	2164	1297	POLYGON ((-77.00352 38.8897…
103	006700	11001006700	428358	0	DC	140	11001006700	11	Census Tract 67	3927	2062	POLYGON ((-76.99497 38.8861…
104	006801	11001006801	244750	0	DC	140	11001006801	11	Census Tract 68.01	2238	1173	POLYGON ((-76.98365 38.8871…
105	006802	11001006802	280108	0	DC	140	11001006802	11	Census Tract 68.02	2580	1206	POLYGON ((-76.98366 38.8797…
106	006804	11001006804	1542277	477741	DC	140	11001006804	11	Census Tract 68.04	2429	17	POLYGON ((-76.98153 38.8789…
107	006900	11001006900	398513	0	DC	140	11001006900	11	Census Tract 69	2799	1793	POLYGON ((-76.99377 38.8845…
108	007000	11001007000	439473	0	DC	140	11001007000	11	Census Tract 70	2697	1346	POLYGON ((-77.00205 38.8806…
109	007100	11001007100	602223	149901	DC	140	11001007100	11	Census Tract 71	3218	1939	POLYGON ((-76.99154 38.8772…
110	007201	11001007201	781457	312419	DC	140	11001007201	11	Census Tract 72.01	2985	2672	POLYGON ((-77.0091 38.87564…
111	007202	11001007202	183977	0	DC	140	11001007202	11	Census Tract 72.02	4303	3563	POLYGON ((-77.00915 38.8798…
112	007203	11001007203	384178	0	DC	140	11001007203	11	Census Tract 72.03	3748	2246	POLYGON ((-77.00574 38.8808…
113	007301	11001007301	4684643	5139082	DC	140	11001007301	11	Census Tract 73.01	3841	1272	POLYGON ((-77.04801 38.8412…
114	007304	11001007304	1232841	8983	DC	140	11001007304	11	Census Tract 73.04	4410	1765	POLYGON ((-76.99423 38.8437…
115	007401	11001007401	1209113	200980	DC	140	11001007401	11	Census Tract 74.01	1259	644	POLYGON ((-77.0054 38.8688,…
116	007403	11001007403	330904	0	DC	140	11001007403	11	Census Tract 74.03	2613	1056	POLYGON ((-76.98128 38.8466…
117	007404	11001007404	826388	0	DC	140	11001007404	11	Census Tract 74.04	3637	1453	POLYGON ((-76.99228 38.8534…
118	007406	11001007406	360152	0	DC	140	11001007406	11	Census Tract 74.06	3528	1286	POLYGON ((-76.99365 38.8567…
119	007407	11001007407	608700	0	DC	140	11001007407	11	Census Tract 74.07	3491	1570	POLYGON ((-76.99424 38.8608…
120	007408	11001007408	372349	0	DC	140	11001007408	11	Census Tract 74.08	2867	1205	POLYGON ((-76.9759 38.85364…
121	007409	11001007409	404873	5767	DC	140	11001007409	11	Census Tract 74.09	3835	1613	POLYGON ((-76.98059 38.8454…
122	007502	11001007502	648317	0	DC	140	11001007502	11	Census Tract 75.02	4687	1997	POLYGON ((-76.97491 38.8617…
123	007503	11001007503	515179	0	DC	140	11001007503	11	Census Tract 75.03	2528	1152	POLYGON ((-76.99259 38.8649…
124	007504	11001007504	764081	0	DC	140	11001007504	11	Census Tract 75.04	2730	1321	POLYGON ((-76.98798 38.8602…
125	007601	11001007601	1115359	141529	DC	140	11001007601	11	Census Tract 76.01	4693	2350	POLYGON ((-76.98973 38.8716…
126	007603	11001007603	1226616	0	DC	140	11001007603	11	Census Tract 76.03	4185	2374	POLYGON ((-76.9682 38.85891…
127	007604	11001007604	1369580	0	DC	140	11001007604	11	Census Tract 76.04	3803	2056	POLYGON ((-76.97134 38.8739…
128	007605	11001007605	453794	0	DC	140	11001007605	11	Census Tract 76.05	3663	1834	POLYGON ((-76.98435 38.8666…
129	007703	11001007703	1017741	1059	DC	140	11001007703	11	Census Tract 77.03	5227	2418	POLYGON ((-76.95737 38.8838…
130	007707	11001007707	842851	0	DC	140	11001007707	11	Census Tract 77.07	3927	1757	POLYGON ((-76.94487 38.8791…
131	007708	11001007708	745809	129100	DC	140	11001007708	11	Census Tract 77.08	2574	1275	POLYGON ((-76.97146 38.8806…
132	007709	11001007709	828872	82685	DC	140	11001007709	11	Census Tract 77.09	2072	1096	POLYGON ((-76.97803 38.8768…
133	007803	11001007803	986677	3755	DC	140	11001007803	11	Census Tract 78.03	4590	2301	POLYGON ((-76.94941 38.8968…
134	007804	11001007804	838428	5705	DC	140	11001007804	11	Census Tract 78.04	3499	1421	POLYGON ((-76.93919 38.8994…
135	007806	11001007806	671434	0	DC	140	11001007806	11	Census Tract 78.06	3457	1122	POLYGON ((-76.94286 38.9020…
136	007807	11001007807	522749	0	DC	140	11001007807	11	Census Tract 78.07	2114	926	POLYGON ((-76.92627 38.8966…
137	007808	11001007808	936852	7722	DC	140	11001007808	11	Census Tract 78.08	3792	1703	POLYGON ((-76.92797 38.8899…
138	007809	11001007809	535254	0	DC	140	11001007809	11	Census Tract 78.09	3155	1369	POLYGON ((-76.94249 38.9020…
139	007901	11001007901	402041	0	DC	140	11001007901	11	Census Tract 79.01	4148	1895	POLYGON ((-76.98366 38.8977…
140	007903	11001007903	247945	0	DC	140	11001007903	11	Census Tract 79.03	1865	917	POLYGON ((-76.97726 38.8941…
141	008001	11001008001	322795	0	DC	140	11001008001	11	Census Tract 80.01	3103	1448	POLYGON ((-76.99025 38.8973…
142	008002	11001008002	578961	0	DC	140	11001008002	11	Census Tract 80.02	3366	1708	POLYGON ((-76.99154 38.8898…
143	008100	11001008100	290284	0	DC	140	11001008100	11	Census Tract 81	3153	1645	POLYGON ((-76.99497 38.8909…
144	008200	11001008200	338424	0	DC	140	11001008200	11	Census Tract 82	2695	1664	POLYGON ((-77.00593 38.8918…
145	008301	11001008301	303973	0	DC	140	11001008301	11	Census Tract 83.01	3220	1761	POLYGON ((-77.00357 38.9002…
146	008302	11001008302	260891	0	DC	140	11001008302	11	Census Tract 83.02	3026	1560	POLYGON ((-76.99846 38.8941…
147	008402	11001008402	274180	0	DC	140	11001008402	11	Census Tract 84.02	2447	1804	POLYGON ((-76.99497 38.8974…
148	008410	11001008410	219939	0	DC	140	11001008410	11	Census Tract 84.10	1843	898	POLYGON ((-76.99496 38.9013…
149	008701	11001008701	382686	0	DC	140	11001008701	11	Census Tract 87.01	2814	1498	POLYGON ((-77.00903 38.9111…
150	008702	11001008702	486411	0	DC	140	11001008702	11	Census Tract 87.02	3574	2073	POLYGON ((-77.00528 38.9093…
151	008802	11001008802	468578	0	DC	140	11001008802	11	Census Tract 88.02	4360	2240	POLYGON ((-76.99314 38.9040…
152	008803	11001008803	1168294	0	DC	140	11001008803	11	Census Tract 88.03	4036	2026	POLYGON ((-77.00243 38.9083…
153	008804	11001008804	778052	0	DC	140	11001008804	11	Census Tract 88.04	2417	1551	POLYGON ((-76.98883 38.9077…
154	008903	11001008903	305651	0	DC	140	11001008903	11	Census Tract 89.03	3062	1661	POLYGON ((-76.98296 38.9008…
155	008904	11001008904	449343	0	DC	140	11001008904	11	Census Tract 89.04	3137	1806	POLYGON ((-76.98327 38.9003…
156	009000	11001009000	1427114	31550	DC	140	11001009000	11	Census Tract 90	4676	2548	POLYGON ((-76.96516 38.9252…
157	009102	11001009102	1816287	0	DC	140	11001009102	11	Census Tract 91.02	4608	2173	POLYGON ((-77.0015 38.91045…
158	009201	11001009201	629781	0	DC	140	11001009201	11	Census Tract 92.01	3103	1549	POLYGON ((-77.00627 38.9270…
159	009203	11001009203	581087	0	DC	140	11001009203	11	Census Tract 92.03	2775	1352	POLYGON ((-77.009 38.91811,…
160	009204	11001009204	308465	0	DC	140	11001009204	11	Census Tract 92.04	2889	1414	POLYGON ((-77.00337 38.9240…
161	009301	11001009301	1109091	0	DC	140	11001009301	11	Census Tract 93.01	3853	1385	POLYGON ((-76.99484 38.9337…
162	009302	11001009302	391905	0	DC	140	11001009302	11	Census Tract 93.02	1750	878	POLYGON ((-76.99604 38.9213…
163	009400	11001009400	1582882	0	DC	140	11001009400	11	Census Tract 94	4424	1800	POLYGON ((-76.9804 38.94309…
164	009503	11001009503	1423609	0	DC	140	11001009503	11	Census Tract 95.03	3106	1282	POLYGON ((-76.98953 38.9502…
165	009504	11001009504	1033168	0	DC	140	11001009504	11	Census Tract 95.04	3208	1442	POLYGON ((-76.99912 38.9462…
166	009505	11001009505	1033208	0	DC	140	11001009505	11	Census Tract 95.05	3796	1674	POLYGON ((-77.01072 38.9623…
167	009507	11001009507	295290	0	DC	140	11001009507	11	Census Tract 95.07	1525	623	POLYGON ((-77.00224 38.9568…
168	009508	11001009508	962212	0	DC	140	11001009508	11	Census Tract 95.08	4243	2068	POLYGON ((-77.00905 38.9533…
169	009509	11001009509	648848	0	DC	140	11001009509	11	Census Tract 95.09	3194	1377	POLYGON ((-77.00201 38.9510…
170	009510	11001009510	841510	0	DC	140	11001009510	11	Census Tract 95.10	4525	1939	POLYGON ((-77.01086 38.9446…
171	009511	11001009511	719468	0	DC	140	11001009511	11	Census Tract 95.11	2066	10	POLYGON ((-77.00836 38.9413…
172	009601	11001009601	1905262	189666	DC	140	11001009601	11	Census Tract 96.01	2086	819	POLYGON ((-76.95789 38.9062…
173	009602	11001009602	1306709	67073	DC	140	11001009602	11	Census Tract 96.02	4481	2046	POLYGON ((-76.96222 38.8995…
174	009603	11001009603	607400	0	DC	140	11001009603	11	Census Tract 96.03	3971	1892	POLYGON ((-76.95637 38.8902…
175	009604	11001009604	503381	65762	DC	140	11001009604	11	Census Tract 96.04	1996	1005	POLYGON ((-76.96327 38.8903…
176	009700	11001009700	403051	3427	DC	140	11001009700	11	Census Tract 97	3188	1355	POLYGON ((-76.99486 38.8292…
177	009801	11001009801	431384	7884	DC	140	11001009801	11	Census Tract 98.01	1848	898	POLYGON ((-77.00386 38.8309…
178	009802	11001009802	200745	0	DC	140	11001009802	11	Census Tract 98.02	2064	880	POLYGON ((-77.00057 38.8309…
179	009803	11001009803	531060	3756	DC	140	11001009803	11	Census Tract 98.03	2968	1480	POLYGON ((-77.00841 38.8336…
180	009804	11001009804	518363	5609	DC	140	11001009804	11	Census Tract 98.04	2517	1133	POLYGON ((-77.00422 38.8404…
181	009807	11001009807	1037012	0	DC	140	11001009807	11	Census Tract 98.07	3523	1682	POLYGON ((-77.01737 38.8239…
182	009810	11001009810	398419	14058	DC	140	11001009810	11	Census Tract 98.10	2461	1243	POLYGON ((-77.00768 38.8314…
183	009811	11001009811	467511	0	DC	140	11001009811	11	Census Tract 98.11	4438	1939	POLYGON ((-77.00242 38.8274…
184	009901	11001009901	2102150	0	DC	140	11001009901	11	Census Tract 99.01	2364	1066	POLYGON ((-76.96481 38.8764…
185	009902	11001009902	1294556	0	DC	140	11001009902	11	Census Tract 99.02	2774	1289	POLYGON ((-76.95291 38.8664…
186	009903	11001009903	383679	0	DC	140	11001009903	11	Census Tract 99.03	2004	743	POLYGON ((-76.93006 38.8898…
187	009904	11001009904	426198	0	DC	140	11001009904	11	Census Tract 99.04	2886	1276	POLYGON ((-76.93578 38.8859…
188	009905	11001009905	431558	0	DC	140	11001009905	11	Census Tract 99.05	2790	1344	POLYGON ((-76.92932 38.8807…
189	009906	11001009906	252684	0	DC	140	11001009906	11	Census Tract 99.06	1773	896	POLYGON ((-76.94056 38.8865…
190	009907	11001009907	466954	0	DC	140	11001009907	11	Census Tract 99.07	2259	1146	POLYGON ((-76.94577 38.8808…
191	010100	11001010100	579230	0	DC	140	11001010100	11	Census Tract 101	2699	2022	POLYGON ((-77.03655 38.9007…
192	010201	11001010201	174884	0	DC	140	11001010201	11	Census Tract 102.01	3341	2471	POLYGON ((-77.02207 38.8791…
193	010202	11001010202	1069479	136323	DC	140	11001010202	11	Census Tract 102.02	2631	2042	POLYGON ((-77.0327 38.88262…
194	010300	11001010300	1084591	0	DC	140	11001010300	11	Census Tract 103	3604	1483	POLYGON ((-77.03637 38.9731…
195	010400	11001010400	2602393	7006	DC	140	11001010400	11	Census Tract 104	4616	1894	POLYGON ((-77.00919 38.8391…
196	010500	11001010500	749891	0	DC	140	11001010500	11	Census Tract 105	3712	2440	POLYGON ((-77.01756 38.8823…
197	010601	11001010601	224811	0	DC	140	11001010601	11	Census Tract 106.01	2130	1486	POLYGON ((-77.009 38.90576,…
198	010602	11001010602	542509	0	DC	140	11001010602	11	Census Tract 106.02	6594	3730	POLYGON ((-77.00444 38.9025…
199	010603	11001010603	464270	0	DC	140	11001010603	11	Census Tract 106.03	3068	2004	POLYGON ((-77.00907 38.8978…
200	010700	11001010700	891588	0	DC	140	11001010700	11	Census Tract 107	2296	1556	POLYGON ((-77.04973 38.9029…
201	010800	11001010800	661580	0	DC	140	11001010800	11	Census Tract 108	6879	1501	POLYGON ((-77.05014 38.8989…
202	010900	11001010900	2381015	2933566	DC	140	11001010900	11	Census Tract 109	3333	1378	POLYGON ((-77.03919 38.8005…
203	011001	11001011001	152450	0	DC	140	11001011001	11	Census Tract 110.01	2423	1636	POLYGON ((-77.01757 38.8764…
204	011002	11001011002	498122	367023	DC	140	11001011002	11	Census Tract 110.02	1859	1471	POLYGON ((-77.02188 38.8765…
205	011100	11001011100	5718693	366232	DC	140	11001011100	11	Census Tract 111	5903	1952	POLYGON ((-76.97913 38.9277…
206	980000	11001980000	6514228	4996439	DC	140	11001980000	11	Census Tract 9800	176	12	POLYGON ((-77.0647 38.89186…

What Are These `POLYGON` Objects?

Code

head(dc_sf)

OBJECTID	TRACT	GEOID	ALAND	AWATER	STUSAB	SUMLEV	GEOCODE	STATE	NAME	POP100	HU100	geometry
1	002002	11001002002	849376	0	DC	140	11001002002	11	Census Tract 20.02	4072	1532	POLYGON ((-77.03642 38.9497…
2	002101	11001002101	600992	0	DC	140	11001002101	11	Census Tract 21.01	5687	2335	POLYGON ((-77.02824 38.9581…
3	002102	11001002102	725975	0	DC	140	11001002102	11	Census Tract 21.02	5099	2221	POLYGON ((-77.01997 38.9581…
4	002201	11001002201	415173	0	DC	140	11001002201	11	Census Tract 22.01	3485	1229	POLYGON ((-77.02743 38.9518…
5	002202	11001002202	698895	566	DC	140	11001002202	11	Census Tract 22.02	3339	1454	POLYGON ((-77.01968 38.9520…
6	000101	11001000101	199776	5261	DC	140	11001000101	11	Census Tract 1.01	1406	999	POLYGON ((-77.05714 38.9105…

Zoom… Enhance…

Let’s try printing just the first row?

Code

rmarkdown::paged_table(dc_sf[1,])

OBJECTID	TRACT	GEOID	ALAND	AWATER	STUSAB	SUMLEV	GEOCODE	STATE	NAME	POP100	HU100	geometry
1	002002	11001002002	849376	0	DC	140	11001002002	11	Census Tract 20.02	4072	1532	POLYGON ((-77.03642 38.9497…

Printing the special geometry column?

Code

rmarkdown::paged_table(dc_sf[1, "geometry"])

geometry
POLYGON ((-77.03642 38.9497…

Nope, we’ll have to open the “black box” using the st_coordinates() function from the sf library →

Code

sf::st_coordinates(dc_sf[1,"geometry"])

               X        Y L1 L2
  [1,] -77.03642 38.94975  1  1
  [2,] -77.03643 38.94827  1  1
  [3,] -77.03628 38.94827  1  1
  [4,] -77.03539 38.94827  1  1
  [5,] -77.03452 38.94827  1  1
  [6,] -77.03442 38.94827  1  1
  [7,] -77.03375 38.94827  1  1
  [8,] -77.03309 38.94827  1  1
  [9,] -77.03287 38.94827  1  1
 [10,] -77.03273 38.94827  1  1
 [11,] -77.03170 38.94824  1  1
 [12,] -77.03163 38.94819  1  1
 [13,] -77.03146 38.94802  1  1
 [14,] -77.03112 38.94769  1  1
 [15,] -77.03109 38.94767  1  1
 [16,] -77.03107 38.94765  1  1
 [17,] -77.03104 38.94762  1  1
 [18,] -77.03098 38.94753  1  1
 [19,] -77.03080 38.94735  1  1
 [20,] -77.03071 38.94726  1  1
 [21,] -77.03069 38.94724  1  1
 [22,] -77.03044 38.94699  1  1
 [23,] -77.03023 38.94679  1  1
 [24,] -77.03005 38.94661  1  1
 [25,] -77.02985 38.94642  1  1
 [26,] -77.02982 38.94640  1  1
 [27,] -77.02965 38.94613  1  1
 [28,] -77.02893 38.94614  1  1
 [29,] -77.02821 38.94613  1  1
 [30,] -77.02780 38.94613  1  1
 [31,] -77.02747 38.94613  1  1
 [32,] -77.02702 38.94613  1  1
 [33,] -77.02660 38.94613  1  1
 [34,] -77.02667 38.94641  1  1
 [35,] -77.02679 38.94720  1  1
 [36,] -77.02681 38.94738  1  1
 [37,] -77.02694 38.94826  1  1
 [38,] -77.02695 38.94834  1  1
 [39,] -77.02695 38.94840  1  1
 [40,] -77.02696 38.94847  1  1
 [41,] -77.02701 38.94877  1  1
 [42,] -77.02702 38.94884  1  1
 [43,] -77.02704 38.94900  1  1
 [44,] -77.02705 38.94909  1  1
 [45,] -77.02708 38.94934  1  1
 [46,] -77.02714 38.94974  1  1
 [47,] -77.02716 38.94993  1  1
 [48,] -77.02721 38.95028  1  1
 [49,] -77.02723 38.95037  1  1
 [50,] -77.02724 38.95046  1  1
 [51,] -77.02725 38.95055  1  1
 [52,] -77.02726 38.95063  1  1
 [53,] -77.02728 38.95072  1  1
 [54,] -77.02729 38.95081  1  1
 [55,] -77.02740 38.95163  1  1
 [56,] -77.02743 38.95188  1  1
 [57,] -77.02756 38.95281  1  1
 [58,] -77.02756 38.95283  1  1
 [59,] -77.02757 38.95291  1  1
 [60,] -77.02773 38.95400  1  1
 [61,] -77.02774 38.95409  1  1
 [62,] -77.02779 38.95451  1  1
 [63,] -77.02783 38.95476  1  1
 [64,] -77.02787 38.95505  1  1
 [65,] -77.02788 38.95516  1  1
 [66,] -77.02789 38.95523  1  1
 [67,] -77.02796 38.95572  1  1
 [68,] -77.02800 38.95602  1  1
 [69,] -77.02802 38.95612  1  1
 [70,] -77.02803 38.95622  1  1
 [71,] -77.02807 38.95653  1  1
 [72,] -77.02812 38.95687  1  1
 [73,] -77.02814 38.95703  1  1
 [74,] -77.02816 38.95718  1  1
 [75,] -77.02818 38.95729  1  1
 [76,] -77.02821 38.95750  1  1
 [77,] -77.02821 38.95758  1  1
 [78,] -77.02822 38.95765  1  1
 [79,] -77.02823 38.95781  1  1
 [80,] -77.02824 38.95797  1  1
 [81,] -77.02824 38.95805  1  1
 [82,] -77.02824 38.95813  1  1
 [83,] -77.02824 38.95829  1  1
 [84,] -77.02824 38.95836  1  1
 [85,] -77.02823 38.95851  1  1
 [86,] -77.02822 38.95872  1  1
 [87,] -77.02817 38.95935  1  1
 [88,] -77.02811 38.96003  1  1
 [89,] -77.02806 38.96074  1  1
 [90,] -77.02803 38.96102  1  1
 [91,] -77.02803 38.96105  1  1
 [92,] -77.02802 38.96120  1  1
 [93,] -77.02802 38.96123  1  1
 [94,] -77.02806 38.96127  1  1
 [95,] -77.02816 38.96130  1  1
 [96,] -77.02852 38.96135  1  1
 [97,] -77.02851 38.96130  1  1
 [98,] -77.02851 38.96128  1  1
 [99,] -77.02851 38.96126  1  1
[100,] -77.02854 38.96121  1  1
[101,] -77.02855 38.96119  1  1
[102,] -77.02859 38.96115  1  1
[103,] -77.02876 38.96100  1  1
[104,] -77.02925 38.96054  1  1
[105,] -77.02948 38.96033  1  1
[106,] -77.02952 38.96030  1  1
[107,] -77.02953 38.96028  1  1
[108,] -77.02958 38.96026  1  1
[109,] -77.02962 38.96024  1  1
[110,] -77.02965 38.96023  1  1
[111,] -77.02967 38.96022  1  1
[112,] -77.02970 38.96022  1  1
[113,] -77.02999 38.96003  1  1
[114,] -77.03003 38.96000  1  1
[115,] -77.03011 38.95994  1  1
[116,] -77.03013 38.95992  1  1
[117,] -77.03016 38.95989  1  1
[118,] -77.03038 38.95966  1  1
[119,] -77.03061 38.95938  1  1
[120,] -77.03073 38.95925  1  1
[121,] -77.03081 38.95915  1  1
[122,] -77.03115 38.95874  1  1
[123,] -77.03138 38.95847  1  1
[124,] -77.03148 38.95836  1  1
[125,] -77.03158 38.95824  1  1
[126,] -77.03172 38.95807  1  1
[127,] -77.03181 38.95796  1  1
[128,] -77.03204 38.95770  1  1
[129,] -77.03224 38.95745  1  1
[130,] -77.03231 38.95737  1  1
[131,] -77.03238 38.95729  1  1
[132,] -77.03252 38.95712  1  1
[133,] -77.03257 38.95706  1  1
[134,] -77.03266 38.95695  1  1
[135,] -77.03271 38.95689  1  1
[136,] -77.03294 38.95662  1  1
[137,] -77.03298 38.95658  1  1
[138,] -77.03318 38.95637  1  1
[139,] -77.03341 38.95620  1  1
[140,] -77.03376 38.95566  1  1
[141,] -77.03379 38.95563  1  1
[142,] -77.03420 38.95514  1  1
[143,] -77.03460 38.95466  1  1
[144,] -77.03504 38.95413  1  1
[145,] -77.03520 38.95394  1  1
[146,] -77.03560 38.95347  1  1
[147,] -77.03588 38.95314  1  1
[148,] -77.03604 38.95295  1  1
[149,] -77.03612 38.95285  1  1
[150,] -77.03625 38.95271  1  1
[151,] -77.03642 38.95254  1  1
[152,] -77.03642 38.95188  1  1
[153,] -77.03642 38.95081  1  1
[154,] -77.03642 38.95053  1  1
[155,] -77.03642 38.94975  1  1

Working With `sf` Objects

Code

# Select column by name
head(dc_sf$NAME)

[1] "Census Tract 20.02" "Census Tract 21.01" "Census Tract 21.02"
[4] "Census Tract 22.01" "Census Tract 22.02" "Census Tract 1.01"

Code

# Select column by index
head(dc_sf[,4])

ALAND	geometry
849376	POLYGON ((-77.03642 38.9497…
600992	POLYGON ((-77.02824 38.9581…
725975	POLYGON ((-77.01997 38.9581…
415173	POLYGON ((-77.02743 38.9518…
698895	POLYGON ((-77.01968 38.9520…
199776	POLYGON ((-77.05714 38.9105…

And… Actually Displaying the Map!

Code

# We can extract *just* the geometry column with the st_geometry function...
dc_geo <- sf::st_geometry(dc_sf)
# This produces an object of type "sfc"
class(dc_geo)

[1] "sfc_POLYGON" "sfc"

Code

# Plot the geometry with base R's plot() function
plot(dc_geo)

More “Modern” Plots with `ggplot2`!

Code

library(ggplot2)
dc_sf |>
  ggplot2::ggplot() +
  ggplot2::geom_sf() +
  ggplot2::theme_classic()

Code

dc_sf |>
  ggplot2::ggplot() +
  ggplot2::geom_sf() +
  ggplot2::theme_classic()

How to Do Things with Geometries

HW1 \(\rightarrow\) HW2

Once you finish HW1, you’ll know how to create geometries with sf and terra
So now, what can you do with them?
For example, we’d like to be able to say things like:
- “The new lamppost cannot be placed at \((x, y)\), since there is already a building there!”
- “There are \(N_1\) lampposts in County 1, and \(N_2\) lampposts in County 2”
- “The average resident in Neighborhood A lives 2 km away from their nearest bus stop

First Things First: Loading and Saving

Note how there were no data files in HW1 😱
From HW2 onwards (and in your GIS life), we’ll:
- Download from e.g. city Open Data Portals: geo data files, but also loading on-the-fly (this week)
- Summarize/aggregate (this week and next week)
- Visualize findings (“Mapping Libraries” unit)

Vector Formats

Shapefiles (`.shp` et al.)

A shape“file” is actually (at least) three separate files bundled together:

Mandatory .shp: Containing feature geometries
Mandatory .shx: Positional indices
Mandatory .dbf: Data attributes
Optional .prj: Coordinate reference system
Optional .xml: Metadata

Shapefiles

Let’s see what’s inside the shapefile we first saw in Week 1, containing data on DC’s Census Tracts: Census Tracts in 2020

DC Census Tracts (with the Georgetown campus tract highlighted!) from OpenData.DC.gov

Shapefile Anatomy

GeoJSON / TopoJSON (`.geojson`)

JavaScript Object Notation: General cross-platform format
Useful when data is too complex for e.g. .csv
TopoJSON = Memory-efficient GeoJSON
Bonus: Inline preview on GitHub!

my_data.geojson

{
  "type": "FeatureCollection",
  "features": [
    {
      "type": "Feature",
      "geometry": {
        "type": "Polygon",
        "coordinates": [
          [
            [30, 20], [45, 40],
            [10, 40], [30, 20]
          ]
        ]
      },
      "properties": {
        "color": "green",
        "area": 3565747
      }
    },
    {
      "type": "Feature",
      "geometry": {
        "type": "Polygon",
        "coordinates": [
          [
            [15, 5], [40, 10],
            [10, 20], [5, 10], 
            [15, 5]
          ]
        ]
      },
      "properties": {
        "color": "red",
        "area": 3272386
      }
    }
  ]
}

GeoPackage (`.gpkg`)

Open-source (non-proprietary) data format standard

Raster Formats

GeoTIFF (.tif or .tiff)
- Based on TIFF format developed at NASA
NetCDF (.nc4)
- Used in earth sciences, as format for data sources measured and distributed multiple times per day over large full-country or full-continent areas.

Coordinate Reference Systems (CRS)

EPSG (European Petroleum Survey Group) Registry: Most common way to specify a CRS
- For example, 4326 is the EPSG code for the WGS84 coordinate system
PROJ: Rather than opaque numeric code like EPSG, uses plaintext “proj-strings” containing parameter info: datum, ellipsoid, projection, and units (e.g. meters). Example: PROJ4 code EPSG:4326 is represented as
```
+proj=longlat +ellps=WGS84 +datum=WGS84 +no_defs
```
WKT: Lengthy but human-readable descriptions

Geospatial Operations 1: Unary Operations

Getting the Geometries

Using rnaturalearth with mapview

Code

set.seed(6805)
library(tidyverse)
library(sf)
library(rnaturalearth)
library(mapview)
france_sf <- ne_countries(country = "France", scale = 50)
(france_map <- mapview(france_sf, label = "geounit", legend = FALSE))

Centroid of France

Code

france_cent_sf <- sf::st_centroid(france_sf)

Warning: st_centroid assumes attributes are constant over geometries

Code

france_map + mapview(france_cent_sf, label = "Centroid", legend = FALSE)

One We Already Saw: Union

Computing the union of all geometries in the sf via sf::st_union()

Code

library(leaflet.extras2)

Loading required package: leaflet

Code

africa_sf <- ne_countries(continent = "Africa", scale = 50)
africa_union_sf <- sf::st_union(africa_sf)
africa_map <- mapview(africa_sf, label="geounit", legend=FALSE)
africa_union_map <- mapview(africa_union_sf, label="st_union(africa)", legend=FALSE)
africa_map | africa_union_map

Helpful for Rasterizing: BBox

Code

africa_bbox_sf <- sf::st_bbox(africa_sf)
africa_bbox_map <- mapview(africa_bbox_sf, label="st_bbox(africa)", legend=FALSE)
africa_map | africa_bbox_map

Convex Hulls by Country

Code

africa_countries_cvx <- sf::st_convex_hull(africa_sf)
africa_countries_cvx_map <- mapview(africa_countries_cvx, label="geounit", legend=FALSE)
africa_map | africa_countries_cvx_map

Convex Hull of Continent

Use st_union() first:

Code

africa_cvx <- africa_sf |> st_union() |> st_convex_hull()
africa_cvx_map <- mapview(africa_cvx, label="geounit", legend=FALSE)
africa_map | africa_cvx_map

One We Already Saw: Centroids

Computing the centroid of all geometries in the sf via sf::st_centroid()

Code

africa_cents_sf <- sf::st_centroid(africa_sf)

Warning: st_centroid assumes attributes are constant over geometries

Code

africa_cents_map <- mapview(africa_cents_sf, label="geounit", legend=FALSE)
africa_map | africa_cents_map

Geospatial Operations 2: Binary Operations

Spatial Joins

Code

nc <- system.file("shape/nc.shp", package="sf") |>
  read_sf() |>
  st_transform('EPSG:2264')
gr <- st_sf(
         label = apply(expand.grid(1:10, LETTERS[10:1])[,2:1], 1, paste0, collapse = ""),
         geom = st_make_grid(nc))
gr$col <- sf.colors(10, categorical = TRUE, alpha = .3)
# cut, to verify that NA's work out:
gr <- gr[-(1:30),]
suppressWarnings(nc_j <- st_join(nc, gr, largest = TRUE))
par(mfrow = c(2,1), mar = rep(0,4))
plot(st_geometry(nc_j), border = 'grey')
plot(st_geometry(gr), add = TRUE, col = gr$col)
text(st_coordinates(st_centroid(st_geometry(gr))), labels = gr$label, cex = .85)
# the joined dataset:
plot(st_geometry(nc_j), border = 'grey', col = nc_j$col)
text(st_coordinates(st_centroid(st_geometry(nc_j))), labels = nc_j$label, cex = .7)
plot(st_geometry(gr), border = '#88ff88aa', add = TRUE)

Spatial Sampling

Code

# Sample random points
africa_points_list <- sf::st_sample(africa_union_sf, 10)
africa_points_sf <- sf::st_sf(africa_points_list)
africa_points_map <- mapview(africa_points_sf, label="Random Point", col.regions=cb_palette[1], legend=FALSE)

Warning in cbind(`Feature ID` = fid, mat): number of rows of result is not a
multiple of vector length (arg 1)

Code

africa_map + africa_points_map

The “Default” Predicate: `st_intersects`

Code

countries_w_points <- africa_sf[africa_points_sf,]
mapview(countries_w_points, label="geounit", legend=FALSE) + africa_points_map

Counting with `lengths()`

Code

country_inter <- sf::st_intersects(africa_sf, africa_points_sf)
# Computes point counts for each polygon
(num_intersections <- lengths(country_inter))

 [1] 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0
[39] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2

Code

africa_sf <- africa_sf |> mutate(
  num_points = num_intersections
) |> arrange(geounit)
africa_sf |> select(geounit, num_points) |> head()

geounit	num_points	geometry
Algeria	2	MULTIPOLYGON (((8.576563 36…
Angola	2	MULTIPOLYGON (((13.07275 -4…
Benin	0	MULTIPOLYGON (((1.622656 6….
Botswana	0	MULTIPOLYGON (((25.25879 -1…
Burkina Faso	0	MULTIPOLYGON (((0.9004883 1…
Burundi	0	MULTIPOLYGON (((30.55361 -2…

Plotting with `mapview`

Code

mapview(africa_sf, zcol="num_points")

Plotting with `ggplot2`

Since we’re starting to get into data attributes rather than geometric features, switching to ggplot2 is recommended!

Code

africa_sf |> ggplot(aes(fill=num_points)) +
  geom_sf() +
  theme_classic()

Getting Fancier…

To do fancier geospatial operations, we’ll need to start overthinking the different possible relationships between two or more geometries!
To this end: predicates

References

Rodrigue, Jean-Paul. 2016. The Geography of Transport Systems. Taylor & Francis.

Logistical Table-Setting

TA Intros

Where We Left Off: Let’s Make Some Dang Maps!

Our First Map: Polygons!

sf Objects

What Are These POLYGON Objects?

Zoom… Enhance…

Working With sf Objects

And… Actually Displaying the Map!

More “Modern” Plots with ggplot2!

How to Do Things with Geometries

HW1 \(\rightarrow\) HW2

First Things First: Loading and Saving

Vector Formats

Shapefiles (.shp et al.)

Shapefiles

Shapefile Anatomy

GeoJSON / TopoJSON (.geojson)

GeoPackage (.gpkg)

Raster Formats

Coordinate Reference Systems (CRS)

Geospatial Operations 1: Unary Operations

Getting the Geometries

Centroid of France

One We Already Saw: Union

Helpful for Rasterizing: BBox

Convex Hulls by Country

Convex Hull of Continent

One We Already Saw: Centroids

Geospatial Operations 2: Binary Operations

Spatial Joins

Spatial Sampling

The “Default” Predicate: st_intersects

Counting with lengths()

Plotting with mapview

Plotting with ggplot2

Getting Fancier…

References

`sf` Objects

What Are These `POLYGON` Objects?

Working With `sf` Objects

More “Modern” Plots with `ggplot2`!

Shapefiles (`.shp` et al.)

GeoJSON / TopoJSON (`.geojson`)

GeoPackage (`.gpkg`)

The “Default” Predicate: `st_intersects`

Counting with `lengths()`

Plotting with `mapview`

Plotting with `ggplot2`