shapely-compute

• 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

| 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(...)" |

create

Create geometric objects from coordinates.

```bash

# 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.

```bash

# 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).

```bash

# 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.

```bash

# 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.

```bash

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.

```bash

# 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.

```bash

# 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.

```bash

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.

```bash

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, ...}

```

• 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

• 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))"

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.)

| 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 |

• /math-mode - Full math orchestration (SymPy, Z3)
• /math-plot - Visualization with matplotlib