Konvexhülle

Konvexhülle refers to the smallest convex set that contains a given set of points or objects. Imagine stretching a rubber band around a collection of points on a flat surface. The area enclosed by the rubber band represents the konvexhülle of those points. Mathematically, a set is convex if for any two points within the set, the line segment connecting them is also entirely within the set.

In computational geometry, computing the konvexhülle is a fundamental problem. The konvexhülle of a finite set of points in a plane is a convex polygon. Its vertices are a subset of the original points. For a set of points in three-dimensional space, the konvexhülle is a convex polyhedron. Algorithms exist to efficiently compute the konvexhülle for various dimensions, such as the Graham scan or Monotone Chain algorithm in 2D, and the Gift Wrapping algorithm (also known as Jarvis March) which works in any dimension.

The concept of the konvexhülle has numerous applications. In pattern recognition and image processing, it can be used to characterize the shape of an object. In statistics, it's related to concepts like principal component analysis and outlier detection. It also finds use in collision detection for computer graphics and robotics, and in optimization problems. The complexity of computing the konvexhülle generally depends on the number of input points and the dimensionality of the space.