Convex Hull Area Calculator
Hull Area: - square units
Hull Perimeter: - units
Number of Hull Vertices: -
Understanding Convex Hulls
What is a Convex Hull?
A convex hull is the smallest convex polygon that contains all points in a given set.
Area = ½|Σ(x₁y₂ - x₂y₁)|
Perimeter = Σ√((x₂-x₁)² + (y₂-y₁)²)
where:
- (x₁,y₁), (x₂,y₂) are consecutive hull vertices
- Σ represents summation over all edges
- | | denotes absolute value
Algorithms and Properties
- Common Algorithms:
- Graham Scan (O(n log n))
- Jarvis March (O(nh))
- Quick Hull (O(n log n))
- Divide and Conquer (O(n log n))
- Properties:
- Convexity
- Minimal Enclosure
- Uniqueness
- Vertex Subset
- Applications:
- Computer Graphics
- Pattern Recognition
- Optimization
- Collision Detection
Advanced Concepts
Dynamic Updates
Online algorithms
3D Extension
Convex polyhedra
Approximation
ε-approximations
Parallel Methods
Distributed computing