Computational Geometry with Shapely When to Use Creating geometric shapes (points, lines, polygons) Boolean operations (intersection, union, difference) Spatial predicates (contains, intersects, within) Measurements (area, length, distance, centroid) Geometry transformations (translate, rotate, scale) Validating and fixing invalid geometries Quick Reference I want to... Command Example Create geometry create create polygon --coords "0,0 1,0 1,1 0,1" Intersection op intersection op intersection --g1 "POLYGON(...)" --g2 "POLYGON(...)" Check contains pred contains pred contains --g1 "POLYGON(...)" --g2 "POINT(0.5 0.5)" Calculate area measure area measure area --geom "POLYGON(...)" Distance distance distance --g1 "POINT(0 0)" --g2 "POINT(3 4)" Transform transform translate transform translate --geom "..." --params "1,2" Validate validate validate --geom "POLYGON(...)" Commands create
Create geometric objects from coordinates.
Point
uv run python scripts/shapely_compute.py create point --coords "1,2"
Line (2+ points)
uv run python scripts/shapely_compute.py create line --coords "0,0 1,1 2,0"
Polygon (3+ points, auto-closes)
uv run python scripts/shapely_compute.py create polygon --coords "0,0 1,0 1,1 0,1"
Polygon with hole
uv run python scripts/shapely_compute.py create polygon --coords "0,0 10,0 10,10 0,10" --holes "2,2 8,2 8,8 2,8"
MultiPoint
uv run python scripts/shapely_compute.py create multipoint --coords "0,0 1,1 2,2"
MultiLineString (pipe-separated lines)
uv run python scripts/shapely_compute.py create multilinestring --coords "0,0 1,1|2,2 3,3"
MultiPolygon (pipe-separated polygons)
uv run python scripts/shapely_compute.py create multipolygon --coords "0,0 1,0 1,1 0,1|2,2 3,2 3,3 2,3"
op (operations)
Boolean geometry operations.
Intersection of two polygons
uv run python scripts/shapely_compute.py op intersection \ --g1 "POLYGON((0 0,2 0,2 2,0 2,0 0))" \ --g2 "POLYGON((1 1,3 1,3 3,1 3,1 1))"
Union
uv run python scripts/shapely_compute.py op union --g1 "POLYGON(...)" --g2 "POLYGON(...)"
Difference (g1 - g2)
uv run python scripts/shapely_compute.py op difference --g1 "POLYGON(...)" --g2 "POLYGON(...)"
Symmetric difference (XOR)
uv run python scripts/shapely_compute.py op symmetric_difference --g1 "..." --g2 "..."
Buffer (expand/erode)
uv run python scripts/shapely_compute.py op buffer --g1 "POINT(0 0)" --g2 "1.5"
Convex hull
uv run python scripts/shapely_compute.py op convex_hull --g1 "MULTIPOINT((0 0),(1 1),(0 2),(2 0))"
Envelope (bounding box)
uv run python scripts/shapely_compute.py op envelope --g1 "POLYGON(...)"
Simplify (reduce points)
uv run python scripts/shapely_compute.py op simplify --g1 "LINESTRING(...)" --g2 "0.5"
pred (predicates)
Spatial relationship tests (returns boolean).
Does polygon contain point?
uv run python scripts/shapely_compute.py pred contains \ --g1 "POLYGON((0 0,2 0,2 2,0 2,0 0))" \ --g2 "POINT(1 1)"
Do geometries intersect?
uv run python scripts/shapely_compute.py pred intersects --g1 "..." --g2 "..."
Is g1 within g2?
uv run python scripts/shapely_compute.py pred within --g1 "POINT(1 1)" --g2 "POLYGON(...)"
Do geometries touch (share boundary)?
uv run python scripts/shapely_compute.py pred touches --g1 "..." --g2 "..."
Do geometries cross?
uv run python scripts/shapely_compute.py pred crosses --g1 "LINESTRING(...)" --g2 "LINESTRING(...)"
Are geometries disjoint (no intersection)?
uv run python scripts/shapely_compute.py pred disjoint --g1 "..." --g2 "..."
Do geometries overlap?
uv run python scripts/shapely_compute.py pred overlaps --g1 "..." --g2 "..."
Are geometries equal?
uv run python scripts/shapely_compute.py pred equals --g1 "..." --g2 "..."
Does g1 cover g2?
uv run python scripts/shapely_compute.py pred covers --g1 "..." --g2 "..."
Is g1 covered by g2?
uv run python scripts/shapely_compute.py pred covered_by --g1 "..." --g2 "..."
measure
Geometric measurements.
Area (polygons)
uv run python scripts/shapely_compute.py measure area --geom "POLYGON((0 0,1 0,1 1,0 1,0 0))"
Length (lines, polygon perimeter)
uv run python scripts/shapely_compute.py measure length --geom "LINESTRING(0 0,3 4)"
Centroid
uv run python scripts/shapely_compute.py measure centroid --geom "POLYGON((0 0,2 0,2 2,0 2,0 0))"
Bounds (minx, miny, maxx, maxy)
uv run python scripts/shapely_compute.py measure bounds --geom "POLYGON(...)"
Exterior ring (polygon only)
uv run python scripts/shapely_compute.py measure exterior_ring --geom "POLYGON(...)"
All measurements at once
uv run python scripts/shapely_compute.py measure all --geom "POLYGON((0 0,2 0,2 2,0 2,0 0))"
distance
Distance between geometries.
uv run python scripts/shapely_compute.py distance --g1 "POINT(0 0)" --g2 "POINT(3 4)"
Returns:
transform
Affine transformations.
Translate (move)
uv run python scripts/shapely_compute.py transform translate \ --geom "POLYGON((0 0,1 0,1 1,0 1,0 0))" --params "5,10"
params: dx,dy or dx,dy,dz
Rotate (degrees, around centroid by default)
uv run python scripts/shapely_compute.py transform rotate \ --geom "POLYGON((0 0,1 0,1 1,0 1,0 0))" --params "45"
params: angle or angle,origin_x,origin_y
Scale (from centroid by default)
uv run python scripts/shapely_compute.py transform scale \ --geom "POLYGON((0 0,1 0,1 1,0 1,0 0))" --params "2,2"
params: sx,sy or sx,sy,origin_x,origin_y
Skew
uv run python scripts/shapely_compute.py transform skew \ --geom "POLYGON(...)" --params "15,0"
params: xs,ys (degrees)
validate / makevalid
Check and fix geometry validity.
Check if valid
uv run python scripts/shapely_compute.py validate --geom "POLYGON((0 0,1 0,1 1,0 1,0 0))"
Returns:
Fix invalid geometry (self-intersecting, etc.)
uv run python scripts/shapely_compute.py makevalid --geom "POLYGON((0 0,2 2,2 0,0 2,0 0))"
coords
Extract coordinates from geometry.
uv run python scripts/shapely_compute.py coords --geom "POLYGON((0 0,1 0,1 1,0 1,0 0))"
Returns:
fromwkt
Parse WKT and get geometry information.
uv run python scripts/shapely_compute.py fromwkt "POLYGON((0 0,1 0,1 1,0 1,0 0))"
Returns:
Geometry Types point - Single coordinate (x, y) or (x, y, z) line/linestring - Sequence of connected points polygon - Closed shape with optional holes multipoint, multilinestring, multipolygon - Collections Input Formats Coordinates string: "0,0 1,0 1,1 0,1" (space-separated x,y pairs) WKT: "POLYGON((0 0, 1 0, 1 1, 0 1, 0 0))" Output Format
All commands return JSON with:
wkt: WKT representation of result geometry type: Geometry type (Point, LineString, Polygon, etc.) bounds: (minx, miny, maxx, maxy) is_valid, is_empty: Validity flags Measurement-specific fields (area, length, distance, etc.) Common Use Cases Use Case Command Collision detection pred intersects Point-in-polygon pred contains Area calculation measure area Buffer zones op buffer Shape combination op union Shape subtraction op difference Bounding box op envelope or measure bounds Simplify path op simplify Related Skills /math-mode - Full math orchestration (SymPy, Z3) /math-plot - Visualization with matplotlib