Geometry & Spatial Modeling¶
Geometry and spatial modeling techniques deal with mathematical problems involving points, lines, polygons, and other geometric objects. These algorithms are crucial for computer graphics, computational geometry, and spatial data analysis.
Techniques in This Category¶
| Technique | Description | Link |
|---|---|---|
| Sweep Line | An algorithmic technique that processes geometric events in a sorted order, commonly used for line intersection problems and geometric computations. | Sweep Line |
| Convex Hull | Finding the minimal convex polygon that contains all given points, with applications in optimization and geometric analysis. | Convex Hull |
When to Use Geometric Algorithms¶
Geometric techniques are essential when: - Working with spatial data or coordinates - Solving problems involving points, lines, or polygons - Need to determine geometric relationships - Optimizing spatial queries or computations
Common Geometric Problems¶
- Point-in-Polygon: Determining if a point lies inside a polygon
- Line Intersection: Finding intersection points between lines or line segments
- Convex Hull: Finding the smallest convex polygon containing all points
- Closest Pair: Finding the two closest points in a set
- Area Calculations: Computing areas of polygons or regions
- Spatial Indexing: Organizing geometric data for efficient queries
Complexity Considerations¶
Many geometric algorithms have specific complexity characteristics: - Sweep line algorithms often achieve O(n log n) complexity - Convex hull algorithms typically run in O(n log n) time - Spatial data structures can provide O(log n) query times