Road Curvature from OS Open Roads

1 Purpose

This page turns the curvature research note into a concrete, reproducible inspection of the Open Roads geometry. The aim is not to produce engineering-grade curve radius. It is to check whether the centreline geometry can support a conservative link-level ranking signal for the collision model.

The background argument is:

Horizontal curves are a recognised crash-risk factor, especially for roadway-departure crashes.
OS Open Roads gives broad coverage and stable enough link geometry for feature engineering, but it is a generalised 1:25,000-scale product.
Curvature should therefore be treated as a screening/ranking proxy rather than a survey-grade design measure.
The implementation uses a vertex-density gate by road class so sparse geometry is left as missing instead of being silently interpreted as straight.

The full background note is in docs/notes/deep-research-roadcurvature.md.

2 Method

For each road link, the curvature module does the following:

Load OS Open Roads geometry and reproject it to a metre-based CRS if needed.
Normalise the geometry to a single LineString; disjoint MultiLineString geometries keep the longest part.
Count original geometry vertices and calculate vertices_per_km.
Decide which road classes pass the operational geometry-quality gate: median vertices_per_km >= 40 and 25th percentile vertices_per_km >= 20.
Resample eligible links at 15 m spacing.
Calculate absolute turning angle at each interior resampled point.
Store three features: mean_curvature_deg_per_km, max_curvature_deg_per_km, and sinuosity.

mean_curvature_deg_per_km is total absolute turning angle per kilometre of link. It is therefore interpretable as “how much the link turns overall”. max_curvature_deg_per_km is the sharpest local turning-angle density found on the resampled line, capped at 10,000 deg/km to suppress single-vertex artefacts. sinuosity is link_length / straight_line_distance, clipped at 5.0 for near-closed loop-like geometries.

if not OPENROADS_PATH.exists():
    raise FileNotFoundError(f"Open Roads parquet not found: {OPENROADS_PATH}")

openroads = gpd.read_parquet(OPENROADS_PATH)
print(f"Loaded {len(openroads):,} OS Open Roads links from {OPENROADS_PATH.relative_to(ROOT)}")
print(f"Source CRS: {openroads.crs}")

Loaded 2,167,557 OS Open Roads links from data/processed/shapefiles/openroads.parquet
Source CRS: {"$schema": "https://proj.org/schemas/v0.7/projjson.schema.json", "type": "GeographicCRS", "name": "WGS 84", "datum_ensemble": {"name": "World Geodetic System 1984 ensemble", "members": [{"name": "World Geodetic System 1984 (Transit)"}, {"name": "World Geodetic System 1984 (G730)"}, {"name": "World Geodetic System 1984 (G873)"}, {"name": "World Geodetic System 1984 (G1150)"}, {"name": "World Geodetic System 1984 (G1674)"}, {"name": "World Geodetic System 1984 (G1762)"}, {"name": "World Geodetic System 1984 (G2139)"}, {"name": "World Geodetic System 1984 (G2296)"}], "ellipsoid": {"name": "WGS 84", "semi_major_axis": 6378137, "inverse_flattening": 298.257223563}, "accuracy": "2.0", "id": {"authority": "EPSG", "code": 6326}}, "coordinate_system": {"subtype": "ellipsoidal", "axis": [{"name": "Geodetic latitude", "abbreviation": "Lat", "direction": "north", "unit": "degree"}, {"name": "Geodetic longitude", "abbreviation": "Lon", "direction": "east", "unit": "degree"}]}, "scope": "Horizontal component of 3D system.", "area": "World.", "bbox": {"south_latitude": -90, "west_longitude": -180, "north_latitude": 90, "east_longitude": 180}, "id": {"authority": "EPSG", "code": 4326}}

gdf = openroads.copy()
gdf["geometry"] = gdf.geometry.apply(normalise_linestring)
gdf = gdf.loc[gdf.geometry.notna()].copy()

if gdf.crs is None:
    raise ValueError("Input CRS is missing; curvature needs a metric CRS.")

units = (
    getattr(gdf.crs.axis_info[0], "unit_name", "").lower()
    if gdf.crs.axis_info
    else ""
)
if "metre" not in units and "meter" not in units:
    gdf = gdf.to_crs(27700)

gdf["calc_length_m"] = gdf.geometry.length
gdf = gdf.loc[gdf["calc_length_m"] > 0].copy()
gdf["vertex_count"] = gdf.geometry.apply(vertex_count)
gdf["vertices_per_km"] = gdf["vertex_count"] / (gdf["calc_length_m"] / 1000)

print(f"Metric CRS used for curvature: {gdf.crs}")
print(f"Usable non-empty LineString links: {len(gdf):,}")

Metric CRS used for curvature: EPSG:27700
Usable non-empty LineString links: 2,167,557

3 Geometry Quality Gate

The gate is deliberately operational. It is not an OS-published standard; it is a guardrail for using 15 m resampling on already-generalised Open Roads centreline geometry. Classes that fail the gate should keep curvature as NaN so sparse linework does not become a false zero-curvature signal.

vertex_summary = (
    gdf.groupby("road_classification", dropna=False)["vertices_per_km"]
    .describe()
    .sort_index()
)

valid_classes = vertex_summary.index[
    (vertex_summary["50%"] >= MEDIAN_VERTICES_PER_KM_MIN)
    & (vertex_summary["25%"] >= P25_VERTICES_PER_KM_MIN)
].tolist()

strategy = (
    "all_classes"
    if set(valid_classes) == set(vertex_summary.index.tolist())
    else "gated_by_road_classification"
)

gate_table = vertex_summary.reset_index().rename(
    columns={
        "road_classification": "road_class",
        "50%": "median_vertices_per_km",
        "25%": "p25_vertices_per_km",
        "75%": "p75_vertices_per_km",
    }
)
gate_table["passes_gate"] = gate_table["road_class"].isin(valid_classes)
show_cols = [
    "road_class",
    "count",
    "mean",
    "p25_vertices_per_km",
    "median_vertices_per_km",
    "p75_vertices_per_km",
    "passes_gate",
]
gate_table[show_cols].round(2)

	road_class	count	mean	p25_vertices_per_km	median_vertices_per_km	p75_vertices_per_km	passes_gate
0	A Road	155538.0	148.78	30.62	65.65	130.07	True
1	B Road	89286.0	96.59	27.29	55.42	104.01	True
2	Classified Unnumbered	190921.0	78.15	21.42	43.97	88.49	True
3	Motorway	4084.0	128.83	15.78	24.32	53.90	False
4	Not Classified	224878.0	81.60	41.74	63.34	94.99	True
5	Unclassified	1060014.0	84.11	41.65	63.68	97.54	True
6	Unknown	442836.0	77.58	36.34	60.61	93.52	True

Original geometry vertex density by road class. Dashed lines show the p25 and median gate thresholds.

4 Seeded Random Road-Section Sample

The table and plots below use a reproducible random sample from the actual OS Open Roads parquet. The sample is restricted to links with at least three vertices and length between 30 m and 2 km, so every plotted section has enough geometry to inspect. Curvature is calculated for every sampled section for diagnostic visibility; the passes_class_gate column shows whether production code would persist those values or leave them missing.

sample_pool = gdf.loc[
    (gdf["vertex_count"] >= 3)
    & (gdf["calc_length_m"].between(30, 2000))
].copy()

sample_links = sample_pool.sample(
    n=min(N_SAMPLE, len(sample_pool)),
    random_state=RANDOM_SEED,
).copy()

feature_rows = []
for idx, row in sample_links.iterrows():
    features = turning_angle_features(row.geometry, spacing_m=SPACING_M)
    feature_rows.append(
        {
            "link_id": row["link_id"],
            MEAN_CURVATURE_COL: features[MEAN_CURVATURE_COL],
            MAX_CURVATURE_COL: features[MAX_CURVATURE_COL],
            SINUOSITY_COL: features[SINUOSITY_COL],
            "passes_class_gate": row["road_classification"] in valid_classes,
        }
    )

sample_features = pd.DataFrame(feature_rows)
sample_links = sample_links.merge(sample_features, on="link_id", how="left")

print(
    f"Seed {RANDOM_SEED} selected {len(sample_links)} links "
    f"from {len(sample_pool):,} eligible road sections."
)

Seed 20260421 selected 8 links from 1,845,997 eligible road sections.

	link_id	road_classification	form_of_way	road_name	start_node	end_node	calc_length_m	vertex_count	vertices_per_km	passes_class_gate	mean_curvature_deg_per_km	max_curvature_deg_per_km	sinuosity
0	44280356-A6F5-4FF8-AB95-713DD95CD4CC	Unclassified	Single Carriageway		3C3A4374-1ED0-451D-ACF4-175CD790F9EF	C67E4253-6E96-464D-9B70-5CA4D67946AD	79.164	4	50.528	True	998.386	3608.360	1.210
5	3CB73090-FF8F-417C-B46C-6AD368C3A54B	Not Classified	Single Carriageway	Pasture Close	5A9E2542-979C-4CD6-B087-C6C25E2594B7	E491F454-80E8-4A86-B208-EFF89A237EE4	151.464	9	59.420	True	872.444	2481.432	1.478
4	BE3CE2CE-C1CB-443E-ABE2-7C9D48279163	Unclassified	Single Carriageway	Wrightson Avenue	645C4237-F279-4D59-968F-C7CF9283C2D9	CD39309E-62E6-4000-B2C9-5FC9F842CF8A	154.342	4	25.916	True	113.225	1174.140	1.006
3	F1BE01C7-E58C-4093-8014-85B9CFFEED18	Unclassified	Single Carriageway	Gregory Street	10380C8B-4137-4B96-96CB-0056E6B70E34	C40FDD24-F378-4E0B-98E8-F7528FF7D285	108.148	7	64.726	True	41.738	231.213	1.001
1	C4B7A336-9E0F-4446-916B-E943F9E244CB	Classified Unnumbered	Single Carriageway	Gipsy Lane	AC3C7397-2AE5-49A3-AEB5-74A9C2A9D8C0	84CC2165-9BD5-43A7-BC6B-91333C7FC8FC	156.340	9	57.567	True	5.611	26.189	1.000
7	9AC3CFA6-7FDA-446F-9395-7343CE6C2815	Unclassified	Single Carriageway	Dalewood	859686FD-5C36-4167-98E7-8807276BBBCD	D46680DA-2623-424F-B494-B2DAFDAC895D	49.906	5	100.188	True	0.476	0.890	1.000
2	80FA9366-B954-4A23-A0F3-4D87149FDCDC	Unclassified	Single Carriageway	Cedarway	A13E47E6-409B-47D4-90EF-41519EE409DD	3FF8A033-483B-45E3-9AF7-2A310955F405	34.929	3	85.888	True	0.000	0.000	1.000
6	8491CCDF-EF5F-4A21-8F49-BF7E9022ECE3	Unclassified	Single Carriageway	Byward Drive	958B158C-89DC-4616-9E57-54B5B19DABC9	F3B26BEE-8E49-473C-86BE-0B4277675EBB	62.611	3	47.915	True	0.000	0.000	1.000

4.1 Sample Section Plots

Black lines are the original OS Open Roads link geometry. Blue points are the 15 m resampled points used for turning-angle calculation. Red points are the start and end nodes.

Seeded random sample of Open Roads links with original geometry and 15 m resampled points.

5 Start/End Nodes and Geometry Coordinates

This table exposes the node-level geometry used by the plots. Coordinates are in the metric CRS used for curvature calculation, currently British National Grid if the source parquet is WGS84.

	link_id	node_role	node_id	x_m	y_m
0	44280356-A6F5-4FF8-AB95-713DD95CD4CC	start	3C3A4374-1ED0-451D-ACF4-175CD790F9EF	454596.137	518319.037
1	44280356-A6F5-4FF8-AB95-713DD95CD4CC	end	C67E4253-6E96-464D-9B70-5CA4D67946AD	454531.707	518307.597
2	C4B7A336-9E0F-4446-916B-E943F9E244CB	start	AC3C7397-2AE5-49A3-AEB5-74A9C2A9D8C0	460091.514	306885.928
3	C4B7A336-9E0F-4446-916B-E943F9E244CB	end	84CC2165-9BD5-43A7-BC6B-91333C7FC8FC	460230.022	306813.420
4	80FA9366-B954-4A23-A0F3-4D87149FDCDC	start	A13E47E6-409B-47D4-90EF-41519EE409DD	428108.818	560169.152
5	80FA9366-B954-4A23-A0F3-4D87149FDCDC	end	3FF8A033-483B-45E3-9AF7-2A310955F405	428140.819	560183.152
6	F1BE01C7-E58C-4093-8014-85B9CFFEED18	start	10380C8B-4137-4B96-96CB-0056E6B70E34	455232.797	338997.709
7	F1BE01C7-E58C-4093-8014-85B9CFFEED18	end	C40FDD24-F378-4E0B-98E8-F7528FF7D285	455228.798	338889.708
8	BE3CE2CE-C1CB-443E-ABE2-7C9D48279163	start	645C4237-F279-4D59-968F-C7CF9283C2D9	454346.577	400181.554
9	BE3CE2CE-C1CB-443E-ABE2-7C9D48279163	end	CD39309E-62E6-4000-B2C9-5FC9F842CF8A	454294.179	400325.815
10	3CB73090-FF8F-417C-B46C-6AD368C3A54B	start	5A9E2542-979C-4CD6-B087-C6C25E2594B7	334726.767	432524.459
11	3CB73090-FF8F-417C-B46C-6AD368C3A54B	end	E491F454-80E8-4A86-B208-EFF89A237EE4	334646.645	432588.347
12	8491CCDF-EF5F-4A21-8F49-BF7E9022ECE3	start	958B158C-89DC-4616-9E57-54B5B19DABC9	503121.067	484139.036
13	8491CCDF-EF5F-4A21-8F49-BF7E9022ECE3	end	F3B26BEE-8E49-473C-86BE-0B4277675EBB	503065.066	484111.035
14	9AC3CFA6-7FDA-446F-9395-7343CE6C2815	start	859686FD-5C36-4167-98E7-8807276BBBCD	496793.943	366650.528
15	9AC3CFA6-7FDA-446F-9395-7343CE6C2815	end	D46680DA-2623-424F-B494-B2DAFDAC895D	496842.613	366639.488

The next table lists the first few original geometry vertices per sampled road section. It is intentionally compact: enough to show the actual coordinate sequence, without printing every point for long links.

	link_id	vertex_ix	x_m	y_m
0	44280356-A6F5-4FF8-AB95-713DD95CD4CC	0	454596.137	518319.037
1	44280356-A6F5-4FF8-AB95-713DD95CD4CC	1	454582.707	518335.327
2	44280356-A6F5-4FF8-AB95-713DD95CD4CC	2	454566.477	518326.507
3	44280356-A6F5-4FF8-AB95-713DD95CD4CC	3	454531.707	518307.597
4	C4B7A336-9E0F-4446-916B-E943F9E244CB	0	460091.514	306885.928
5	C4B7A336-9E0F-4446-916B-E943F9E244CB	1	460097.174	306882.878
6	C4B7A336-9E0F-4446-916B-E943F9E244CB	2	460102.834	306879.828
7	C4B7A336-9E0F-4446-916B-E943F9E244CB	3	460117.494	306872.078
8	C4B7A336-9E0F-4446-916B-E943F9E244CB	4	460132.153	306864.319
9	C4B7A336-9E0F-4446-916B-E943F9E244CB	5	460161.233	306849.199
10	80FA9366-B954-4A23-A0F3-4D87149FDCDC	0	428108.818	560169.152
11	80FA9366-B954-4A23-A0F3-4D87149FDCDC	1	428124.819	560176.152
12	80FA9366-B954-4A23-A0F3-4D87149FDCDC	2	428140.819	560183.152
13	F1BE01C7-E58C-4093-8014-85B9CFFEED18	0	455232.797	338997.709
14	F1BE01C7-E58C-4093-8014-85B9CFFEED18	1	455232.067	338988.219
15	F1BE01C7-E58C-4093-8014-85B9CFFEED18	2	455231.347	338978.729
16	F1BE01C7-E58C-4093-8014-85B9CFFEED18	3	455230.017	338959.359
17	F1BE01C7-E58C-4093-8014-85B9CFFEED18	4	455228.687	338939.988
18	F1BE01C7-E58C-4093-8014-85B9CFFEED18	5	455228.737	338914.848
19	BE3CE2CE-C1CB-443E-ABE2-7C9D48279163	0	454346.577	400181.554
20	BE3CE2CE-C1CB-443E-ABE2-7C9D48279163	1	454339.178	400189.814
21	BE3CE2CE-C1CB-443E-ABE2-7C9D48279163	2	454318.418	400252.545
22	BE3CE2CE-C1CB-443E-ABE2-7C9D48279163	3	454294.179	400325.815
23	3CB73090-FF8F-417C-B46C-6AD368C3A54B	0	334726.767	432524.459
24	3CB73090-FF8F-417C-B46C-6AD368C3A54B	1	334689.617	432505.779
25	3CB73090-FF8F-417C-B46C-6AD368C3A54B	2	334682.688	432502.299
26	3CB73090-FF8F-417C-B46C-6AD368C3A54B	3	334666.597	432507.528
27	3CB73090-FF8F-417C-B46C-6AD368C3A54B	4	334657.267	432521.628
28	3CB73090-FF8F-417C-B46C-6AD368C3A54B	5	334656.726	432540.868
29	8491CCDF-EF5F-4A21-8F49-BF7E9022ECE3	0	503121.067	484139.036
30	8491CCDF-EF5F-4A21-8F49-BF7E9022ECE3	1	503093.067	484125.036
31	8491CCDF-EF5F-4A21-8F49-BF7E9022ECE3	2	503065.066	484111.035
32	9AC3CFA6-7FDA-446F-9395-7343CE6C2815	0	496793.943	366650.528
33	9AC3CFA6-7FDA-446F-9395-7343CE6C2815	1	496810.033	366646.878
34	9AC3CFA6-7FDA-446F-9395-7343CE6C2815	2	496826.113	366643.228
35	9AC3CFA6-7FDA-446F-9395-7343CE6C2815	3	496834.363	366641.358
36	9AC3CFA6-7FDA-446F-9395-7343CE6C2815	4	496842.613	366639.488

6 How the Curvature Code Works

The production module lives at src/road_risk/features/road_curvature.py. The key pieces are:

normalise_linestring() handles empty geometry, LineString, and MultiLineString cases before feature calculation.
ensure_metric_crs() converts longitude/latitude geometry to EPSG:27700 so spacing and length calculations are in metres.
resample_linestring() interpolates points every 15 m and keeps the link end point, so short residual segments are still represented.
turning_angle_features() computes angle changes between consecutive resampled segments, converts those into degrees per kilometre, and returns: mean_curvature_deg_per_km, max_curvature_deg_per_km, and sinuosity.
main() runs the vertex-density gate by road_classification, computes features only for passing classes, writes the columns to data/features/network_features.parquet, and writes QA CSV summaries.

The deliberate modelling choice is missingness over false certainty. If a road class fails the vertex-density gate, its curvature features stay NaN rather than being filled with zero. That preserves the distinction between “this link is straight in usable geometry” and “the source geometry is too sparse to support curvature”.

7 Interpretation

For modelling, the expected useful signal is relative rather than absolute: links with more turning per kilometre should rank above straighter links. The numbers should not be read as design-speed radius or engineering inventory values. That limitation is acceptable for a link-level risk model as long as the feature is documented, quality-gated, and evaluated against held-out collision outcomes before being promoted into the main model feature lists.