Geometry Algorithm Library Skill

Purpose

Implement computational geometry algorithms for competitive programming and algorithmic problems.

Capabilities

• Convex hull (Graham scan, Andrew's monotone chain)
• Line intersection algorithms
• Closest pair of points
• Point in polygon tests
• Voronoi diagram, Delaunay triangulation
• Polygon clipping

Target Processes

• computational-geometry

Algorithm Catalog

Convex Hull

• Graham scan O(n log n)
• Andrew's monotone chain O(n log n)
• Jarvis march O(nh)

Intersection Algorithms

• Line sweep for segment intersection
• Bentley-Ottmann algorithm
• Polygon intersection

Distance Problems

• Closest pair of points O(n log n)
• Farthest pair (rotating calipers)
• Point-polygon distance

Triangulation

• Ear clipping O(n^2)
• Delaunay triangulation
• Voronoi diagram

Input Schema

{
  "type": "object",
  "properties": {
    "algorithm": { "type": "string" },
    "variant": { "type": "string" },
    "language": {
      "type": "string",
      "enum": ["cpp", "python", "java"]
    },
    "includeVisualization": { "type": "boolean", "default": false }
  },
  "required": ["algorithm"]
}

Output Schema

{
  "type": "object",
  "properties": {
    "success": { "type": "boolean" },
    "code": { "type": "string" },
    "complexity": { "type": "object" },
    "usage": { "type": "string" }
  },
  "required": ["success", "code"]
}