The purpose of this project is to completely reimplement the modules for creating Voronoi diagram(VD) and Delaunay triangulation(DT) in the Vector library of GRASS GIS using more efficient algorithms. The goal is to implement Guibas-Stolfi divide-and-conquer algorithm and Fortune's plane sweep algorithm with various improvements. All algorithms proposed in this project deal with vector representation of the map. The output is the vector map consisting of vertices and edges representing VD or DT. Since VD and DT can be used for solving many important geometrical problems such as finding convex hull and the nearest neighbour problem, the implementation of the fast algorithms has high importance.