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skills/geopandas/references/geometric-operations.md

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+# Geometric Operations
+
+GeoPandas provides extensive geometric manipulation through Shapely integration.
+
+## Constructive Operations
+
+Create new geometries from existing ones:
+
+### Buffer
+
+Create geometries representing all points within a distance:
+
+```python
+# Buffer by fixed distance
+buffered = gdf.geometry.buffer(10)
+
+# Negative buffer (erosion)
+eroded = gdf.geometry.buffer(-5)
+
+# Buffer with resolution parameter
+smooth_buffer = gdf.geometry.buffer(10, resolution=16)
+```
+
+### Boundary
+
+Get lower-dimensional boundary:
+
+```python
+# Polygon -> LineString, LineString -> MultiPoint
+boundaries = gdf.geometry.boundary
+```
+
+### Centroid
+
+Get center point of each geometry:
+
+```python
+centroids = gdf.geometry.centroid
+```
+
+### Convex Hull
+
+Smallest convex polygon containing all points:
+
+```python
+hulls = gdf.geometry.convex_hull
+```
+
+### Concave Hull
+
+Smallest concave polygon containing all points:
+
+```python
+# ratio parameter controls concavity (0 = convex hull, 1 = most concave)
+concave_hulls = gdf.geometry.concave_hull(ratio=0.5)
+```
+
+### Envelope
+
+Smallest axis-aligned rectangle:
+
+```python
+envelopes = gdf.geometry.envelope
+```
+
+### Simplify
+
+Reduce geometric complexity:
+
+```python
+# Douglas-Peucker algorithm with tolerance
+simplified = gdf.geometry.simplify(tolerance=10)
+
+# Preserve topology (prevents self-intersections)
+simplified = gdf.geometry.simplify(tolerance=10, preserve_topology=True)
+```
+
+### Segmentize
+
+Add vertices to line segments:
+
+```python
+# Add vertices with maximum segment length
+segmented = gdf.geometry.segmentize(max_segment_length=5)
+```
+
+### Union All
+
+Combine all geometries into single geometry:
+
+```python
+# Union all features
+unified = gdf.geometry.union_all()
+```
+
+## Affine Transformations
+
+Mathematical transformations of coordinates:
+
+### Rotate
+
+```python
+# Rotate around origin (0, 0) by angle in degrees
+rotated = gdf.geometry.rotate(angle=45, origin='center')
+
+# Rotate around custom point
+rotated = gdf.geometry.rotate(angle=45, origin=(100, 100))
+```
+
+### Scale
+
+```python
+# Scale uniformly
+scaled = gdf.geometry.scale(xfact=2.0, yfact=2.0)
+
+# Scale with origin
+scaled = gdf.geometry.scale(xfact=2.0, yfact=2.0, origin='center')
+```
+
+### Translate
+
+```python
+# Shift coordinates
+translated = gdf.geometry.translate(xoff=100, yoff=50)
+```
+
+### Skew
+
+```python
+# Shear transformation
+skewed = gdf.geometry.skew(xs=15, ys=0, origin='center')
+```
+
+### Custom Affine Transform
+
+```python
+from shapely import affinity
+
+# Apply 6-parameter affine transformation matrix
+# [a, b, d, e, xoff, yoff]
+transformed = gdf.geometry.affine_transform([1, 0, 0, 1, 100, 50])
+```
+
+## Geometric Properties
+
+Access geometric properties (returns pandas Series):
+
+```python
+# Area
+areas = gdf.geometry.area
+
+# Length/perimeter
+lengths = gdf.geometry.length
+
+# Bounding box coordinates
+bounds = gdf.geometry.bounds  # Returns DataFrame with minx, miny, maxx, maxy
+
+# Total bounds for entire GeoSeries
+total_bounds = gdf.geometry.total_bounds  # Returns array [minx, miny, maxx, maxy]
+
+# Check geometry types
+geom_types = gdf.geometry.geom_type
+
+# Check if valid
+is_valid = gdf.geometry.is_valid
+
+# Check if empty
+is_empty = gdf.geometry.is_empty
+```
+
+## Geometric Relationships
+
+Binary predicates testing relationships:
+
+```python
+# Within
+gdf1.geometry.within(gdf2.geometry)
+
+# Contains
+gdf1.geometry.contains(gdf2.geometry)
+
+# Intersects
+gdf1.geometry.intersects(gdf2.geometry)
+
+# Touches
+gdf1.geometry.touches(gdf2.geometry)
+
+# Crosses
+gdf1.geometry.crosses(gdf2.geometry)
+
+# Overlaps
+gdf1.geometry.overlaps(gdf2.geometry)
+
+# Covers
+gdf1.geometry.covers(gdf2.geometry)
+
+# Covered by
+gdf1.geometry.covered_by(gdf2.geometry)
+```
+
+## Point Extraction
+
+Extract specific points from geometries:
+
+```python
+# Representative point (guaranteed to be within geometry)
+rep_points = gdf.geometry.representative_point()
+
+# Interpolate point along line at distance
+points = line_gdf.geometry.interpolate(distance=10)
+
+# Interpolate point at normalized distance (0 to 1)
+midpoints = line_gdf.geometry.interpolate(distance=0.5, normalized=True)
+```
+
+## Delaunay Triangulation
+
+```python
+# Create triangulation
+triangles = gdf.geometry.delaunay_triangles()
+```