Computational Geometry Algorithms

Graham's Scan is an algorithm that finds the convex hull of a set of points in $O(n log n)$ time.

The closest-pair algorithm is an algorithm that finds the closest pair of points in a set of points in $O(n log n)$ time.

The line-segment intersection algorithm is an algorithm that finds the intersection of two line segments in $O(1)$ time.

The shoelace formula is an algorithm that finds the area of a polygon in $O(n)$ time.

Cavalieri's principle is an algorithm that finds the volume of a tetrahedron in $O(1)$ time.

Dijkstra's algorithm is an algorithm that finds the shortest path between two points in a graph in $O(|V| + |E| log |V|)$ time.

Kruskal's algorithm is an algorithm that finds the minimum spanning tree of a graph in $O(|E| log |V|)$ time.

The Ford-Fulkerson algorithm is an algorithm that finds the maximum flow in a network in $O(|V| |E|^2)$ time.

The A* algorithm is an algorithm that finds the shortest path between two points in a Euclidean space in $O(|V| + |E| log |V|)$ time.

Quickhull is an algorithm that finds the convex hull of a set of points in three dimensions in $O(n log^2 n)$ time.

The closest-pair algorithm is an algorithm that finds the closest pair of points in a set of points in three dimensions in $O(n log n)$ time.

The plane-plane intersection algorithm is an algorithm that finds the intersection of two planes in $O(1)$ time.

Cavalieri's principle is an algorithm that finds the volume of a parallelepiped in $O(1)$ time.

The A* algorithm is an algorithm that finds the shortest path between two points on a surface in $O(|V| + |E| log |V|)$ time.

Quickhull is an algorithm that finds the convex hull of a set of points on a surface in $O(n log^2 n)$ time.