Understanding spatial relationships is fundamental to GIS analysis. PostGIS provides a comprehensive set of functions to determine how geometries interact with each other - whether they intersect, contain one another, touch at boundaries, or overlap partially. These relationship functions form the backbone of spatial queries, enabling complex location-based analysis and decision-making.
Introduction to Spatial Relationships
Spatial relationship functions allow you to compare geometries and determine their spatial interactions. These functions are essential for:
- Finding points within polygons (e.g., buildings within districts)
- Detecting spatial conflicts (e.g., overlapping land claims)
- Identifying adjacent features (e.g., neighboring properties)
- Performing spatial joins between datasets
- Implementing spatial business rules and constraints
| Function | Description | Returns True When | Common Use Case |
|---|---|---|---|
| ST_Intersects | Geometries share any space | Any part touches or overlaps | General spatial filtering |
| ST_Within | First geometry is inside second | Completely contained within | Point-in-polygon queries |
| ST_Contains | First geometry contains second | Completely contains other | Finding features within areas |
| ST_Touches | Geometries share boundary only | Touch at edges, no interior overlap | Finding adjacent features |
| ST_Overlaps | Partial overlap of same dimension | Some but not all area overlaps | Detecting conflicts |
| ST_Disjoint | Geometries don't interact | No spatial relationship | Exclusion queries |
Setting Up Sample Data
Let's create realistic sample data representing parcels and buildings with real-world coordinates:
-- Create parcels table
CREATE TABLE parcels (
id SERIAL PRIMARY KEY,
name TEXT,
district TEXT,
area_hectares NUMERIC,
geom GEOMETRY(POLYGON, 4326)
);
-- Create buildings table
CREATE TABLE buildings (
id SERIAL PRIMARY KEY,
name TEXT,
building_type TEXT,
floors INTEGER,
geom GEOMETRY(POINT, 4326)
);
-- Create roads table
CREATE TABLE roads (
id SERIAL PRIMARY KEY,
name TEXT,
road_type TEXT,
geom GEOMETRY(LINESTRING, 4326)
);
-- Insert sample parcel geometries (Delhi area)
INSERT INTO parcels (name, district, area_hectares, geom) VALUES
('Parcel A', 'Central Delhi', 5.2, ST_GeomFromText('POLYGON((77.20 28.60, 77.25 28.60, 77.25 28.65, 77.20 28.65, 77.20 28.60))', 4326)),
('Parcel B', 'Central Delhi', 3.8, ST_GeomFromText('POLYGON((77.25 28.60, 77.30 28.60, 77.30 28.65, 77.25 28.65, 77.25 28.60))', 4326)),
('Parcel C', 'South Delhi', 4.1, ST_GeomFromText('POLYGON((77.22 28.55, 77.27 28.55, 77.27 28.60, 77.22 28.60, 77.22 28.55))', 4326)),
('Parcel D', 'North Delhi', 6.3, ST_GeomFromText('POLYGON((77.15 28.65, 77.22 28.65, 77.22 28.72, 77.15 28.72, 77.15 28.65))', 4326));
-- Insert sample building locations
INSERT INTO buildings (name, building_type, floors, geom) VALUES
('Building 1', 'Office', 12, ST_Point(77.22, 28.62)),
('Building 2', 'Residential', 8, ST_Point(77.28, 28.62)),
('Building 3', 'Commercial', 15, ST_Point(77.24, 28.57)),
('Building 4', 'Industrial', 4, ST_Point(77.18, 28.68)),
('Building 5', 'Residential', 6, ST Point(77.35, 28.66)),
('Building 6', 'Office', 10, ST_Point(77.26, 28.63));
-- Insert sample roads
INSERT INTO roads (name, road_type, geom) VALUES
('Main Road', 'Highway', ST_GeomFromText('LINESTRING(77.18 28.58, 77.32 28.64)', 4326)),
('Side Street', 'Local', ST_GeomFromText('LINESTRING(77.21 28.60, 77.21 28.70)', 4326)),
('Ring Road', 'Arterial', ST_GeomFromText('LINESTRING(77.15 28.65, 77.30 28.65)', 4326));
-- Create spatial indexes
CREATE INDEX idx_parcels_geom ON parcels USING GIST (geom);
CREATE INDEX idx_buildings_geom ON buildings USING GIST (geom);
CREATE INDEX idx_roads_geom ON roads USING GIST (geom);
ST_Intersects - General Spatial Intersection
ST_Intersects is the most commonly used spatial relationship function. It returns true if geometries share any space, including touching at boundaries.
Basic Intersection Queries
-- Find buildings that intersect with parcels
SELECT
b.name AS building_name,
b.building_type,
p.name AS parcel_name,
p.district
FROM buildings b
JOIN parcels p ON ST_Intersects(b.geom, p.geom)
ORDER BY p.district, b.name;
-- Find roads that intersect with parcels
SELECT
r.name AS road_name,
r.road_type,
p.name AS parcel_name,
ST_Length(ST_Intersection(r.geom, p.geom)) AS intersection_length
FROM roads r
JOIN parcels p ON ST_Intersects(r.geom, p.geom)
ORDER BY intersection_length DESC;
Intersection with Distance Buffer
-- Find buildings within 500 meters of roads
SELECT
b.name AS building_name,
r.name AS road_name,
ST_Distance(b.geom, r.geom) * 111000 AS distance_meters
FROM buildings b
CROSS JOIN roads r
WHERE ST_Intersects(b.geom, ST_Buffer(r.geom, 0.005)) -- ~500m buffer
ORDER BY distance_meters;
-- Count buildings by district using intersection
SELECT
p.district,
COUNT(b.id) AS building_count,
array_agg(b.building_type) AS building_types
FROM parcels p
LEFT JOIN buildings b ON ST_Intersects(b.geom, p.geom)
GROUP BY p.district
ORDER BY building_count DESC;
ST_Within - Complete Containment
ST_Within returns true if the first geometry is completely inside the second geometry.
-- Find buildings completely within parcels
SELECT
b.name AS building_name,
b.building_type,
p.name AS parcel_name,
p.district,
p.area_hectares
FROM buildings b
JOIN parcels p ON ST_Within(b.geom, p.geom)
ORDER BY p.area_hectares DESC;
-- Buildings within specific districts
SELECT
p.district,
COUNT(b.id) AS buildings_within,
array_agg(DISTINCT b.building_type) AS building_types,
AVG(b.floors) AS avg_floors
FROM parcels p
LEFT JOIN buildings b ON ST_Within(b.geom, p.geom)
GROUP BY p.district
ORDER BY buildings_within DESC;
Nested Within Queries
-- Find buildings within parcels of a specific district
SELECT
b.name,
b.building_type,
b.floors
FROM buildings b
WHERE ST_Within(b.geom, (
SELECT ST_Union(geom)
FROM parcels
WHERE district = 'Central Delhi'
))
ORDER BY b.floors DESC;
-- Multi-level containment analysis
SELECT
p.district,
p.name AS parcel_name,
COUNT(b.id) AS building_count,
SUM(b.floors) AS total_floors,
AVG(b.floors) AS avg_floors,
MAX(b.floors) AS max_floors
FROM parcels p
LEFT JOIN buildings b ON ST_Within(b.geom, p.geom)
GROUP BY p.district, p.name, p.id
ORDER BY total_floors DESC NULLS LAST;
ST_Contains - Reverse Containment
ST_Contains is the inverse of ST_Within. It checks if the first geometry completely contains the second.
-- Find parcels that contain buildings
SELECT
p.name AS parcel_name,
p.district,
p.area_hectares,
COUNT(b.id) AS buildings_contained,
array_agg(b.name ORDER BY b.floors DESC) AS building_names,
SUM(b.floors) AS total_floors
FROM parcels p
LEFT JOIN buildings b ON ST_Contains(p.geom, b.geom)
GROUP BY p.id, p.name, p.district, p.area_hectares
ORDER BY buildings_contained DESC, total_floors DESC;
-- Parcels containing specific building types
SELECT
p.name AS parcel_name,
p.district,
b.building_type,
COUNT(b.id) AS count_of_type
FROM parcels p
JOIN buildings b ON ST_Contains(p.geom, b.geom)
WHERE b.building_type IN ('Office', 'Commercial')
GROUP BY p.name, p.district, b.building_type
ORDER BY p.district, count_of_type DESC;
ST_Touches - Boundary Relationships
ST_Touches returns true when geometries share a boundary but don't overlap in their interiors.
-- Find adjacent parcels
SELECT
p1.name AS parcel1,
p2.name AS parcel2,
p1.district AS district1,
p2.district AS district2,
ST_Length(ST_Intersection(p1.geom, p2.geom)) AS shared_boundary_length
FROM parcels p1
JOIN parcels p2 ON p1.id < p2.id AND ST_Touches(p1.geom, p2.geom)
ORDER BY shared_boundary_length DESC;
-- Buildings touching parcel boundaries
SELECT
b.name AS building_name,
p.name AS parcel_name,
'Boundary Location' AS relationship_type
FROM buildings b
JOIN parcels p ON ST_Touches(b.geom, p.geom)
ORDER BY p.name;
-- Roads touching parcel boundaries
SELECT
r.name AS road_name,
p.name AS parcel_name,
ST_Length(ST_Intersection(r.geom, ST_Boundary(p.geom))) AS boundary_contact_length
FROM roads r
JOIN parcels p ON ST_Touches(r.geom, p.geom)
ORDER BY boundary_contact_length DESC;
ST_Overlaps - Partial Overlapping
ST_Overlaps returns true when geometries of the same dimension share some but not all of their area.
-- Create overlapping parcels for demonstration
INSERT INTO parcels (name, district, area_hectares, geom) VALUES
('Overlapping Parcel', 'Central Delhi', 2.1,
ST_GeomFromText('POLYGON((77.23 28.61, 77.28 28.61, 77.28 28.64, 77.23 28.64, 77.23 28.61))', 4326));
-- Find overlapping parcels
SELECT
p1.name AS parcel1,
p2.name AS parcel2,
ST_Area(ST_Intersection(p1.geom, p2.geom)) AS overlap_area,
ST_Area(ST_Intersection(p1.geom, p2.geom)) / ST_Area(p1.geom) * 100 AS overlap_percent_p1,
ST_Area(ST_Intersection(p1.geom, p2.geom)) / ST_Area(p2.geom) * 100 AS overlap_percent_p2
FROM parcels p1
JOIN parcels p2 ON p1.id < p2.id AND ST_Overlaps(p1.geom, p2.geom)
ORDER BY overlap_area DESC;
-- Detect potential land use conflicts
SELECT
p1.name AS parcel1,
p1.district AS district1,
p2.name AS parcel2,
p2.district AS district2,
'Potential Conflict' AS issue_type,
ST_Area(ST_Intersection(p1.geom, p2.geom)) * 111000 * 111000 AS overlap_area_m2
FROM parcels p1
JOIN parcels p2 ON p1.id != p2.id AND ST_Overlaps(p1.geom, p2.geom)
ORDER BY overlap_area_m2 DESC;
ST_Disjoint - No Spatial Relationship
ST_Disjoint returns true when geometries have no spatial relationship whatsoever.
-- Find buildings not associated with any parcel
SELECT
b.name AS isolated_building,
b.building_type,
b.floors,
ST_X(b.geom) AS longitude,
ST_Y(b.geom) AS latitude
FROM buildings b
WHERE NOT EXISTS (
SELECT 1 FROM parcels p
WHERE ST_Intersects(b.geom, p.geom)
)
ORDER BY b.name;
-- Parcels with no buildings
SELECT
p.name AS empty_parcel,
p.district,
p.area_hectares
FROM parcels p
WHERE ST_Disjoint(p.geom, (SELECT ST_Union(geom) FROM buildings))
ORDER BY p.area_hectares DESC;
Advanced Spatial Relationship Analysis
Distance-Based Relationships
-- Find nearest parcel for each building
WITH building_parcel_distances AS (
SELECT
b.id AS building_id,
b.name AS building_name,
p.id AS parcel_id,
p.name AS parcel_name,
ST_Distance(b.geom, p.geom) AS distance,
ROW_NUMBER() OVER (PARTITION BY b.id ORDER BY ST_Distance(b.geom, p.geom)) AS rn
FROM buildings b
CROSS JOIN parcels p
)
SELECT
building_name,
parcel_name,
ROUND(distance * 111000, 2) AS distance_meters,
CASE
WHEN distance = 0 THEN 'Within'
WHEN distance < 0.001 THEN 'Very Close'
WHEN distance < 0.005 THEN 'Close'
ELSE 'Distant'
END AS proximity_category
FROM building_parcel_distances
WHERE rn = 1
ORDER BY distance;
Complex Spatial Queries
-- Multi-criteria spatial analysis
SELECT
b.name AS building_name,
b.building_type,
b.floors,
p.name AS parcel_name,
p.district,
CASE
WHEN ST_Within(b.geom, p.geom) THEN 'Inside Parcel'
WHEN ST_Touches(b.geom, p.geom) THEN 'On Boundary'
WHEN ST_DWithin(b.geom, p.geom, 0.001) THEN 'Very Close'
ELSE 'Distant'
END AS spatial_relationship,
ST_Distance(b.geom, p.geom) * 111000 AS distance_meters
FROM buildings b
LEFT JOIN parcels p ON ST_Intersects(b.geom, ST_Buffer(p.geom, 0.001))
ORDER BY b.name, distance_meters;
-- Comprehensive relationship matrix
SELECT
'Buildings vs Parcels' AS relationship_type,
COUNT(CASE WHEN ST_Within(b.geom, p.geom) THEN 1 END) AS within_count,
COUNT(CASE WHEN ST_Touches(b.geom, p.geom) THEN 1 END) AS touches_count,
COUNT(CASE WHEN ST_Intersects(b.geom, p.geom) AND NOT ST_Within(b.geom, p.geom) THEN 1 END) AS intersects_only,
COUNT(CASE WHEN ST_Disjoint(b.geom, p.geom) THEN 1 END) AS disjoint_count
FROM buildings b
CROSS JOIN parcels p;
Combining Spatial Relationships with Attribute Filters
-- Find office buildings within commercial districts
SELECT
b.name AS building_name,
b.floors,
p.name AS parcel_name,
p.district
FROM buildings b
JOIN parcels p ON ST_Within(b.geom, p.geom)
WHERE b.building_type = 'Office'
AND p.district LIKE '%Central%'
ORDER BY b.floors DESC;
-- High-rise buildings near major roads
SELECT
b.name AS building_name,
b.building_type,
b.floors,
r.name AS nearby_road,
ST_Distance(b.geom, r.geom) * 111000 AS distance_meters
FROM buildings b
CROSS JOIN roads r
WHERE b.floors >= 10
AND ST_DWithin(b.geom, r.geom, 0.002) -- ~200m
AND r.road_type IN ('Highway', 'Arterial')
ORDER BY b.floors DESC, distance_meters;
-- District-wise building analysis with spatial constraints
SELECT
p.district,
COUNT(DISTINCT p.id) AS total_parcels,
COUNT(b.id) AS total_buildings,
COUNT(CASE WHEN b.building_type = 'Residential' THEN 1 END) AS residential_buildings,
COUNT(CASE WHEN b.building_type = 'Office' THEN 1 END) AS office_buildings,
COUNT(CASE WHEN b.building_type = 'Commercial' THEN 1 END) AS commercial_buildings,
AVG(b.floors) AS avg_building_height,
SUM(p.area_hectares) AS total_area_hectares
FROM parcels p
LEFT JOIN buildings b ON ST_Within(b.geom, p.geom)
GROUP BY p.district
ORDER BY total_buildings DESC;
Performance Optimization
Using Spatial Indexes Effectively
-- Check index usage
EXPLAIN ANALYZE
SELECT b.name, p.name
FROM buildings b
JOIN parcels p ON ST_Within(b.geom, p.geom);
-- Optimize with bounding box pre-filter
EXPLAIN ANALYZE
SELECT b.name, p.name
FROM buildings b
JOIN parcels p ON b.geom && p.geom AND ST_Within(b.geom, p.geom);
Performance Best Practices
| Technique | Description | When to Use |
|---|---|---|
| Bounding box filter | Use && operator before spatial function | Large datasets |
| Spatial indexes | GIST indexes on geometry columns | Always |
| Attribute pre-filtering | Filter by attributes before spatial operations | When attributes are selective |
| Geometry simplification | Use ST_Simplify for approximate queries | Visualization and rough analysis |
| Appropriate functions | Use most specific function for your needs | Always |
Real-World Applications
Urban Planning
-- Zoning compliance check
SELECT
b.name AS building_name,
b.building_type,
b.floors,
p.district,
CASE
WHEN b.building_type = 'Industrial' AND p.district LIKE '%Central%' THEN 'Zoning Violation'
WHEN b.floors > 15 AND p.district = 'Residential' THEN 'Height Violation'
ELSE 'Compliant'
END AS compliance_status
FROM buildings b
JOIN parcels p ON ST_Within(b.geom, p.geom)
WHERE ST_Within(b.geom, p.geom)
ORDER BY compliance_status, b.floors DESC;
Emergency Services Planning
-- Find buildings within emergency response zones
WITH emergency_zones AS (
SELECT
name,
ST_Buffer(geom, 0.01) AS response_zone -- ~1km radius
FROM buildings
WHERE building_type = 'Emergency Services'
)
SELECT
b.name AS building_name,
b.building_type,
ez.name AS nearest_emergency_service,
'Within Response Zone' AS status
FROM buildings b
JOIN emergency_zones ez ON ST_Within(b.geom, ez.response_zone)
WHERE b.building_type != 'Emergency Services'
ORDER BY b.building_type, b.name;
Common Pitfalls and Solutions
| Pitfall | Problem | Solution |
|---|---|---|
| Precision issues | Floating-point precision affects relationships | Use ST_Snap or tolerance-based functions |
| Invalid geometries | Invalid geometries cause unexpected results | Use ST_IsValid and ST_MakeValid |
| Mixed coordinate systems | Comparing geometries in different SRIDs | Transform to common coordinate system |
| Performance issues | Slow queries on large datasets | Use spatial indexes and bounding box filters |
| Boundary cases | Unclear behavior at exact boundaries | Understand function definitions and test edge cases |
Testing and Validation
-- Validate spatial relationships
SELECT
'Relationship Validation' AS test_type,
COUNT(*) AS total_tests,
COUNT(CASE WHEN ST_Within(b.geom, p.geom) THEN 1 END) AS within_relationships,
COUNT(CASE WHEN ST_Intersects(b.geom, p.geom) AND NOT ST_Within(b.geom, p.geom) THEN 1 END) AS intersect_only,
COUNT(CASE WHEN NOT ST_Intersects(b.geom, p.geom) THEN 1 END) AS no_relationship
FROM buildings b
CROSS JOIN parcels p;
-- Geometry validation
SELECT
'Buildings' AS table_name,
COUNT(*) AS total_geometries,
COUNT(CASE WHEN ST_IsValid(geom) THEN 1 END) AS valid_geometries,
COUNT(CASE WHEN NOT ST_IsValid(geom) THEN 1 END) AS invalid_geometries
FROM buildings
UNION ALL
SELECT
'Parcels',
COUNT(*),
COUNT(CASE WHEN ST_IsValid(geom) THEN 1 END),
COUNT(CASE WHEN NOT ST_IsValid(geom) THEN 1 END)
FROM parcels;