Java Implementation

Now, we will go over the process of implementing the Bowyer-Watson algorithm in Java. We make implementation a step-by-step process.

1. Initializing the Algorithm

We begin by specifying a class named BowyerWatson with our algorithm as a member. The class will consist of the methods for point addition, triangle construction, and the Bowyer-Watson algorithm implementation.

2. Adding Points

The implementation of this by our members should enable the addition of data points to the triangulation. To realize our goal we will define the method addPoint(Point p) Points can be represented as items of a Point class that store x and y coordinates.

3. Constructing Initial Triangulation

Firstly, to use the Bowyer-Watson algorithm, we need to create a triangulation from the data provided. We can simply pick a large triangle that approximates this area. This is the base of our further triangulation.

4. Applying Bowyer-Watson Algorithm

The central implementation plan entails the use of Bowyer-Watson algorithm method. The method constructs the triangulation point by point at every step and also adjusts it as the triangulation should follow the Delaunay property.

5. Handling Edge Cases

In addition to that we need to make sure that we take care of boundary cases like points lying on the boundary or duplicate points.

6. Visualization (Optional)

In addition to this, alternative methods of displaying the triangulation can be developed by making use of Java’s graphics capabilities.

To gain some practical programming experience related to computational geometry topics, we will apply the Bowyer-Watson algorithm that will be able to facilitate the process to some extent.