shapely-compute

SKILL.md

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: {"distance": 5.0, "g1_type": "Point", "g2_type": "Point"}

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: {"is_valid": true, "type": "Polygon", ...}

# 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: {"coords": [[0,0],[1,0],[1,1],[0,1],[0,0]], "type": "Polygon"}

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: {"type": "Polygon", "bounds": [...], "area": 1.0, ...}

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