Dataset
All roads in Georgia from TIGER 2022
TIGER is the Census’s road data
I am only considering roads which fit inside the bounds of figures two and three
The outline of Georgia traced by its primary and secondary roads from TIGER 2022: all 11,737 of them.
The 397 primary and secondary roads that fit entirely inside the Atlanta bounding box.
Every one of the 27,709 roads TIGER knows about inside the box, down to the cul-de-sacs.
Calculating length of road
This is pretty straightforward.
Histogram of road lengths on a log x-axis and log-scaled frequency.
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[1.6e-05, 2e-05): 2 [2e-05, 2.5e-05): 2 [2.5e-05, 3.2e-05): 2 [3.2e-05, 3.9e-05): 1 [3.9e-05, 5e-05): 4 [5e-05, 6.2e-05): 8 [6.2e-05, 7.8e-05): 13 [7.8e-05, 9.7e-05): 16 [9.7e-05, 0.00012): 37 [0.00012, 0.00015): 72 [0.00015, 0.00019): 107 [0.00019, 0.00024): 161 [0.00024, 0.0003): 250 [0.0003, 0.00038): 422 [0.00038, 0.00047): 586 [0.00047, 0.00059): 868 [0.00059, 0.00074): 992 [0.00074, 0.00093): 1158 [0.00093, 0.0012): 1356 [0.0012, 0.0015): 1574 [0.0015, 0.0018): 1619 [0.0018, 0.0023): 1808 [0.0023, 0.0029): 1863 [0.0029, 0.0036): 1762 [0.0036, 0.0045): 1723 [0.0045, 0.0057): 1400 [0.0057, 0.0071): 1102 [0.0071, 0.0089): 821 [0.0089, 0.011): 603 [0.011, 0.014): 397 [0.014, 0.018): 246 [0.018, 0.022): 212 [0.022, 0.028): 141 [0.028, 0.035): 90 [0.035, 0.043): 73 [0.043, 0.054): 41 [0.054, 0.068): 45 [0.068, 0.086): 26 [0.086, 0.11): 23 [0.11, 0.13): 14 [0.13, 0.17): 12 [0.17, 0.21): 6 [0.21, 0.26): 8 [0.26, 0.33): 3 [0.33, 0.42): 4
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Road length (Euclidean lat/long distance)
Frequency
Calculating Curvature of Road
Call curvature \(\sigma\).
\[\sigma = \frac{l_{road} - l_{EndpointLine}}{l_{EndpointLine}}\]
One curved road drawn in blue with the straight chord between its endpoints in orange; short dashed rungs connect the road to the chord, inside a latitude/longitude axis frame.
-84.31
-84.30
-84.29
33.89
33.90
33.91
Road: length along the asphalt
Endpoint line: straight-line distance
Road
Endpoint Line
Distance
Histogram of road curvature on a log x-axis and log-scaled frequency.
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[1.3e-11, 2.6e-11): 2 [2.6e-11, 5.5e-11): 5 [5.5e-11, 1.1e-10): 9 [1.1e-10, 2.4e-10): 6 [2.4e-10, 5e-10): 10 [5e-10, 1e-09): 9 [1e-09, 2.1e-09): 14 [2.1e-09, 4.5e-09): 18 [4.5e-09, 9.3e-09): 28 [9.3e-09, 1.9e-08): 59 [1.9e-08, 4e-08): 70 [4e-08, 8.4e-08): 76 [8.4e-08, 1.7e-07): 104 [1.7e-07, 3.6e-07): 102 [3.6e-07, 7.5e-07): 94 [7.5e-07, 1.6e-06): 95 [1.6e-06, 3.3e-06): 103 [3.3e-06, 6.8e-06): 116 [6.8e-06, 1.4e-05): 116 [1.4e-05, 2.9e-05): 164 [2.9e-05, 6.1e-05): 223 [6.1e-05, 0.00013): 316 [0.00013, 0.00026): 435 [0.00026, 0.00055): 480 [0.00055, 0.0011): 546 [0.0011, 0.0024): 686 [0.0024, 0.005): 872 [0.005, 0.01): 1254 [0.01, 0.021): 1667 [0.021, 0.045): 2126 [0.045, 0.093): 2139 [0.093, 0.19): 2004 [0.19, 0.4): 1940 [0.4, 0.84): 873 [0.84, 1.7): 492 [1.7, 3.6): 305 [3.6, 7.5): 130 [7.5, 16): 47 [16, 33): 8 [33, 68): 2 [68, 1.4e+02): 3
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Road curvature
Frequency
Now we’re getting somewhere
A dense scatter of every named road in the box, length on a log x-axis against curvature on a log y-axis.
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length
curvature
Pareto
We want the straightest, longest road. We must make a tradeoff between length and curvature. Any road which is both shorter and curvier than another road cannot be our straightest, longest road. The grouping of roads which are not both shorter and curvier than another road are our Pareto Front.
The scatter with the longest-straightest Pareto front drawn as a rising staircase along the lower-right edge of the cloud.
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Royal Dr · length 0.007, curvature 0e+00
Burroughs Ave SE · length 0.008, curvature 8e-09
Walker Ave · length 0.011, curvature 4e-08
Woodward Ave SE · length 0.017, curvature 1e-07
Joseph E Boone St · length 0.020, curvature 5e-06
Constitution Rd SE · length 0.031, curvature 2e-05
McAfee Rd · length 0.057, curvature 9e-05
Glenwood Rd · length 0.074, curvature 1e-04
State Rte 260 · length 0.133, curvature 2e-03
I- 20 · length 0.198, curvature 3e-02
I- 85 · length 0.414, curvature 2e-01
Pareto Front
length
curvature
Longest Straightest Lines
Here are the Pareto Front roads in table form. Looks reasonable.
name rttyp length curvature
Royal Dr M 0.007 0E+00 Burroughs Ave SE M 0.008 8E-09 Walker Ave M 0.011 4E-08 Woodward Ave SE M 0.017 1E-07 Joseph E Boone St M 0.020 5E-06 Constitution Rd SE M 0.031 2E-05 McAfee Rd M 0.057 9E-05 Glenwood Rd M 0.074 1E-04 State Rte 260 S 0.133 2E-03 I- 20 I 0.198 3E-02 I- 85 I 0.414 2E-01
The longest-straightest candidate roads drawn dark over the interstates of the Atlanta box in cyan for orientation.
Royal Dr · M
Burroughs Ave SE · M
Walker Ave · M
Woodward Ave SE · M
Joseph E Boone St · M
Constitution Rd SE · M
McAfee Rd · M
Glenwood Rd · M
State Rte 260 · S
I- 20 · I
I- 85 · I
Interstates
Candidates
Shortest Curviest Lines
The scatter with the shortest-curviest Pareto front drawn along the upper-left edge of the cloud, where roads are short but sharply curved.
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Atlantia Rd SE · length 0.000, curvature 0e+00
Vinings Forest Ln · length 0.000, curvature 9e-03
Cross Creek Pkwy NW · length 0.000, curvature 6e-02
Broad St · length 0.000, curvature 4e-01
Brookhaven Heights Ct · length 0.000, curvature 5e-01
Dupont Commons Dr NW · length 0.000, curvature 7e-01
Dupont Commons Dr NW · length 0.000, curvature 8e-01
Parkside Cir · length 0.000, curvature 1e+00
Vinings Central Dr · length 0.000, curvature 2e+00
Cabretta Dr SE · length 0.001, curvature 2e+00
Duncan Dr · length 0.001, curvature 3e+00
Wild Turkey Ct · length 0.001, curvature 1e+01
Bascala Cir · length 0.002, curvature 1e+01
Beatrice Ct · length 0.002, curvature 3e+01
Telfair Ln · length 0.004, curvature 3e+01
Conifer Park Ln · length 0.005, curvature 6e+01
Highland Parc Pl SE · length 0.007, curvature 7e+01
Phoenix Blvd · length 0.022, curvature 1e+02
Pareto Front
length
curvature
name rttyp length curvature
Atlantia Rd SE M 0.0000 0E+00 Vinings Forest Ln M 0.0000 9E-03 Cross Creek Pkwy NW M 0.0001 6E-02 Broad St M 0.0001 4E-01 Brookhaven Heights Ct M 0.0003 5E-01 Dupont Commons Dr NW M 0.0003 7E-01 Parkside Cir M 0.0004 1E+00 Vinings Central Dr M 0.0004 2E+00 Cabretta Dr SE M 0.0005 2E+00 Duncan Dr M 0.0006 3E+00 Wild Turkey Ct M 0.0008 1E+01 Bascala Cir M 0.0018 1E+01 Beatrice Ct M 0.0023 3E+01 Telfair Ln M 0.0037 3E+01 Conifer Park Ln M 0.0047 6E+01 Highland Parc Pl SE M 0.0073 7E+01 Phoenix Blvd M 0.0220 1E+02
The shortest-curviest candidate roads, tiny loops and cul-de-sacs, over the interstates of the box in cyan.
Atlantia Rd SE · M
Vinings Forest Ln · M
Cross Creek Pkwy NW · M
Broad St · M
Brookhaven Heights Ct · M
Dupont Commons Dr NW · M
Dupont Commons Dr NW · M
Parkside Cir · M
Vinings Central Dr · M
Cabretta Dr SE · M
Duncan Dr · M
Wild Turkey Ct · M
Bascala Cir · M
Beatrice Ct · M
Telfair Ln · M
Conifer Park Ln · M
Highland Parc Pl SE · M
Interstates
Candidates
Explorer
Click a point, a row, or the map itself.