📐 Computational Geometry

Convex Hull • Sweep Line • Triangulation • Spatial Algorithms

Master geometric algorithms for points, lines, polygons, and spatial data structures — from convex hull to Voronoi diagrams and beyond.

48+

Geometric Algorithms & Spatial Data Structures

Beginner

🔢

Orientation & Cross Product

Determining clockwise/counterclockwise, collinearity.

Primitive

Beginner

✖️

Segment Intersection

Orientation test, bounding boxes, proper/improper intersection.

Point in Polygon (Ray Casting)

Even-odd rule, winding number, edge cases.

Graham Scan

Angle sorting, stack-based convex hull, O(n log n).

Convex Hull

Intermediate

🎁

Jarvis March (Gift Wrapping)

Output-sensitive, O(nh), simple to implement.

Convex Hull

Advanced

⚡

Quickhull

Divide-and-conquer, randomized expected O(n log n).

3D Convex Hull

Preparate and Hong, incremental algorithm, faces.

Extension

Advanced

📏

Line Segment Intersection (Sweep Line)

Bentley-Ottmann, event queue, status structure, O((n+k) log n).

Fortune's Algorithm (Voronoi)

Sweep line, beach line, parabola, O(n log n).

Closest Pair of Points

Divide-and-conquer, sweep line, O(n log n).

Polygon Triangulation

Ear clipping, monotone polygon triangulation, O(n log n).

Art Gallery Problem & Guards

Fisk's proof, triangulation coloring, NP-hard variations.

K-D Trees

Space partitioning, nearest neighbor search, O(log n) avg.

Quadtrees & Octrees

Hierarchical subdivision, image compression, collision detection.

R-Trees (Spatial Indexing)

Minimum bounding boxes, GIS databases, query optimization.

Orthogonal Range Searching

Range trees, fractional cascading, counting queries.

Query

Intermediate

📈

Convex Hull Trick (DP Optimization)

Dynamic programming optimization for line functions.

Optimization

Advanced

🔄

Rotating Calipers

Diameter of convex polygon, width, distance, O(n).

Minkowski Sum

Convolution of polygons, collision detection, configuration space.

Delaunay Triangulation

Empty circumcircle, max-min angle, Lawson flip algorithm.

Voronoi Diagrams

Dual to Delaunay, nearest neighbor regions, applications.

Arrangements of Lines

Combinatorial complexity, zone theorem, doubly connected edge lists (DCEL).

Boolean Operations (Polygon Union/Intersection)

Weiler–Atherton, Vatti clipping, Greiner-Hormann.

Visibility Graphs

Shortest path among obstacles, Euclidean shortest path.

Convex Hull Variations

Melkman's algorithm (simple polygon), online hull.

Ham Sandwich Theorem & Cuts

Bisecting measures, computational complexity.

Theory

Discrepancy

📐 Geometric Algorithms Roadmap

🔰 Foundation

Points, vectors, orientation, segment intersection, point in polygon

📏 Practitioner

Graham Scan, Jarvis March, K-D trees, range searching

⚙️ Expert

Sweep line algorithms, Fortune's Voronoi, triangulation, rotating calipers

🏆 Researcher

Delaunay, DCEL arrangements, boolean ops, visibility graphs, 3D hull

⚡ Solve Spatial Problems Efficiently

Interactive geometric visualizations, algorithm walkthroughs, and coding challenges.

Back to Home Geometry Services

📐 Computational Geometry

Orientation & Cross Product

Segment Intersection

Point in Polygon (Ray Casting)

Graham Scan

Jarvis March (Gift Wrapping)

Quickhull

3D Convex Hull

Line Segment Intersection (Sweep Line)

Fortune's Algorithm (Voronoi)

Closest Pair of Points

Polygon Triangulation

Art Gallery Problem & Guards

K-D Trees

Quadtrees & Octrees

R-Trees (Spatial Indexing)

Orthogonal Range Searching

Convex Hull Trick (DP Optimization)

Rotating Calipers

Minkowski Sum

Delaunay Triangulation

Voronoi Diagrams

Arrangements of Lines

Boolean Operations (Polygon Union/Intersection)

Visibility Graphs

Convex Hull Variations

Ham Sandwich Theorem & Cuts

📐 Geometric Algorithms Roadmap

Related Computer Science Domains

⚡ Solve Spatial Problems Efficiently