Voronoi tessellation can be used within a couple of different fields. Some of these fields include healthcare, construction and urban planning. Since Voronoi tessellations are used in multiple fields, it is motivated to know the strengths and weaknesses of the algorithms used to generate them, in terms of their efficiency.

The objectives of this thesis are to compare two CPU algorithm implementations for Voronoi tessellation in regards to execution time and see which of the two is the most efficient. The algorithms compared are The Bowyer-Watson algorithm and Fortunes algorithm.

The Fortunes algorithm used in the research is based upon a pre-existing Fortunes implementation while the Bowyer-Watson implementation was specifically made for this research. Their differences in efficiency were determined by measuring their execution times and comparing them. This was done in an iterative manner, where for each iteration, the amount of data to be computed was continuously increased.

The results show that Fortunes algorithm is more efficient on the CPU without using any acceleration techniques for any of the algorithms. It took 70 milliseconds for the Bowyer-Watson method to calculate 3000 input points while Fortunes method took 12 milliseconds under the same conditions.

As a conclusion, Fortunes algorithm was more efficient due to the Bowyer-Watson algorithm doing unnecessary calculations. These calculations include checking all the triangles for every new point added. A suggestion for improving the speed of this algorithm would be to use a nearest neighbour search technique when searching through triangles.