shapely-compute

使用 Shapely 进行计算几何

适用场景

• 创建几何形状（点、线、多边形）
• 布尔运算（交集、并集、差集）
• 空间谓词（包含、相交、位于内部）
• 测量（面积、长度、距离、质心）
• 几何变换（平移、旋转、缩放）
• 验证并修复无效几何

快速参考

我想要……	命令	示例
创建几何图形	create	create polygon --coords "0,0 1,0 1,1 0,1"
求交集	op intersection	op intersection --g1 "POLYGON(...)" --g2 "POLYGON(...)"
检查是否包含	pred contains	pred contains --g1 "POLYGON(...)" --g2 "POINT(0.5 0.5)"
计算面积	measure area	measure area --geom "POLYGON(...)"
计算距离	distance	distance --g1 "POINT(0 0)" --g2 "POINT(3 4)"
变换几何图形	transform translate	transform translate --geom "..." --params "1,2"
验证几何图形	validate	validate --geom "POLYGON(...)"

命令

create

根据坐标创建几何对象。

# 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（运算）

执行几何布尔运算。

# 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（谓词）

测试空间关系（返回布尔值）。

# 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

测量几何属性。

# 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

计算几何图形之间的距离。

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

执行仿射变换。

# 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

检查并修复几何图形的有效性。

# 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

从几何图形中提取坐标。

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

解析 WKT 并获取几何图形信息。

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, ...}

几何类型

• point - 单个坐标 (x, y) 或 (x, y, z)
• line/linestring - 由相连点组成的序列
• polygon - 带有可选孔洞的闭合形状
• multipoint、multilinestring、multipolygon - 几何集合

输入格式

• 坐标字符串："0,0 1,0 1,1 0,1"（以空格分隔的 x,y 坐标对）
• WKT："POLYGON((0 0, 1 0, 1 1, 0 1, 0 0))"

输出格式

所有命令均返回 JSON，包含：

• wkt：结果几何图形的 WKT 表示
• type：几何类型（Point、LineString、Polygon 等）
• bounds：(minx, miny, maxx, maxy)
• is_valid、is_empty：有效性标记
• 与测量相关的字段（area、length、distance 等）

常见用例

用例	命令
碰撞检测	pred intersects
点在多边形内	pred contains
面积计算	measure area
缓冲区	op buffer
形状合并	op union
形状相减	op difference
边界框	op envelope 或 measure bounds
简化路径	op simplify

相关技能

• /math-mode - 完整的数学编排（SymPy、Z3）
• /math-plot - 使用 matplotlib 进行可视化