What are the different parallel algorithms for computational geometry?

There are several parallel algorithms for computational geometry that aim to solve various geometric problems efficiently. Some of the commonly used parallel algorithms in computational geometry include:

1. Parallel Convex Hull: The convex hull is a fundamental problem in computational geometry. The parallel convex hull algorithms aim to compute the convex hull of a set of points in parallel. Some popular parallel convex hull algorithms include the Kirkpatrick-Seidel algorithm, the Chan algorithm, and the Akl-Toussaint heuristic.

2. Parallel Line Segment Intersection: Line segment intersection is another important problem in computational geometry. Parallel algorithms for line segment intersection aim to find all the intersections among a set of line segments efficiently. The Bentley-Ottmann algorithm is a well-known parallel algorithm for line segment intersection.

3. Parallel Triangulation: Triangulation is a common operation in computational geometry, used for various purposes such as mesh generation and surface reconstruction. Parallel triangulation algorithms aim to divide a given set of points into triangles efficiently. Some popular parallel triangulation algorithms include the Delaunay triangulation and the Ear Clipping algorithm.

4. Parallel Voronoi Diagram: Voronoi diagrams are widely used in computational geometry for proximity analysis and spatial partitioning. Parallel Voronoi diagram algorithms aim to compute the Voronoi diagram of a set of points in parallel. The Fortune's algorithm and the incremental algorithm are commonly used parallel algorithms for Voronoi diagram computation.

5. Parallel Range Searching: Range searching involves finding all the points within a given range or query region efficiently. Parallel range searching algorithms aim to perform this operation in parallel. Some popular parallel range searching algorithms include the Kd-tree and the R-tree.

These are just a few examples of parallel algorithms for computational geometry. The choice of algorithm depends on the specific problem and the available parallel computing resources.