Shapely Geometry — Core Concepts

Shapely is a Python library for manipulating and analyzing planar geometric objects. It wraps the GEOS library (the same engine behind PostGIS) and provides Pythonic access to geometry creation, spatial predicates, and set-theoretic operations.

Geometry types

Shapely implements the core types from the Simple Features specification:

from shapely.geometry import Point, LineString, Polygon, MultiPoint

point = Point(2.0, 3.0)
line = LineString([(0, 0), (1, 1), (2, 0)])
polygon = Polygon([(0, 0), (4, 0), (4, 3), (0, 3)])

• Point — a single coordinate pair (or triple for 3D).
• LineString — an ordered sequence of points forming a path.
• LinearRing — a closed LineString (used as polygon boundaries).
• Polygon — an exterior ring with optional holes.
• Multi-variants — MultiPoint, MultiLineString, MultiPolygon for collections.

Polygons with holes

exterior = [(0, 0), (10, 0), (10, 10), (0, 10)]
hole = [(3, 3), (7, 3), (7, 7), (3, 7)]
polygon_with_hole = Polygon(exterior, [hole])
print(polygon_with_hole.area)  # 100 - 16 = 84

Spatial predicates

Predicates answer yes/no questions about spatial relationships:

park = Polygon([(0, 0), (5, 0), (5, 5), (0, 5)])
house = Point(3, 3)
river = LineString([(0, 6), (5, 6)])

park.contains(house)     # True — the point is inside the polygon
house.within(park)       # True — inverse of contains
park.intersects(river)   # False — they do not touch
park.touches(river)      # False
park.disjoint(river)     # True — completely separate

DE-9IM relationships

For complex spatial reasoning, Shapely exposes the DE-9IM (Dimensionally Extended 9-Intersection Model) matrix:

park.relate(house)  # "0FFFFF212" — encodes the full topological relationship

This is the same predicate system used in PostGIS spatial queries.

Set operations

Combine or subtract geometries like set operations:

a = Polygon([(0, 0), (3, 0), (3, 3), (0, 3)])
b = Polygon([(2, 0), (5, 0), (5, 3), (2, 3)])

a.intersection(b)   # The overlapping rectangle
a.union(b)           # Combined shape covering both
a.difference(b)      # Part of A not in B
a.symmetric_difference(b)  # Parts in either but not both

These operations return new geometry objects that you can inspect, measure, or pass to further operations.

Measurements

polygon = Polygon([(0, 0), (4, 0), (4, 3), (0, 3)])

polygon.area       # 12.0
polygon.perimeter  # 14.0 (use .length for lines)
polygon.centroid   # POINT (2 1.5)
polygon.bounds     # (0.0, 0.0, 4.0, 3.0) — bounding box

line = LineString([(0, 0), (3, 4)])
line.length        # 5.0

Important caveat: Shapely works in a flat Cartesian plane. If your coordinates are latitude/longitude, areas and distances are in degrees, not meters. For geographic calculations, project coordinates to a local CRS (e.g., UTM) first, or use libraries like pyproj for transformation.

Buffering

Create a zone around any geometry:

point = Point(0, 0)
buffer = point.buffer(1.0)  # Circle with radius 1.0
print(buffer.area)           # ~3.14

line = LineString([(0, 0), (5, 0)])
corridor = line.buffer(0.5)  # Rectangle-like corridor around the line

Buffering is how you answer questions like “what is within 500 meters of this road?” — buffer the road geometry by 500 meters, then check what intersects.

Common misconception

People often assume Shapely handles coordinate reference systems (CRS) and map projections. It does not — Shapely operates on raw numbers with no concept of units or projections. If you pass latitude/longitude, it computes areas in “square degrees,” which is meaningless. Always project to meters-based coordinates before measuring real-world areas and distances.

When to use Shapely

• Geofencing: Is a delivery driver inside the allowed zone?
• Overlap analysis: Which parcels overlap with the flood plain?
• Route buffers: What properties are within 200m of the proposed highway?
• Data cleaning: Remove points that fall outside valid boundaries.

The one thing to remember: Shapely gives Python the spatial math engine to create, test, and combine geometric shapes — but always project your coordinates to the right system before measuring real-world areas or distances.