I want to be able to generate a set of polygons where I can extract all nodes for every polygon. For example:

Polygon 1 - (0, 0),(0,2),(2,0) Polygon 2 - (0, 2),(2,2),(2,0) Polygon 3 - (0, 2),(5,5),(8,5),(8,0),(2,0) And so on...

I’m not interested in available tools since this is just a part of a project. I want to be able to insert random points to generate this random dataset with polygons and its nodes coordinates.

Where do I start? Is there an algorithm I can implement in a programming language? BTW: the data is supposed to be used in a PostgreSQL database as geometries. The language I want to use is Java.

## Answer

The Tinfour project has a Java class called the BoundedVoronoiDiagram that may be useful to you as a source of ideas, see Tinfour.org. There an example application called ExampleVoronoi that I used (slightly modified) to produce the following picture from 10 vertices:

Adding the following code to the end of the demo produces a list of polygons and their vertices. The code identifies polygons as either open (unbounded) or closed (bounded and finite):

List<ThiessenPolygon> polygons = diagram.getPolygons(); for (ThiessenPolygon p : polygons) { Vertex v = p.getVertex(); // defining vertex for polygon String openString = p.isOpen() ? "open " : "closed"; double area = p.getArea(); System.out.format("Vertex %2d, polygon is %s, area=%5.2f%n", v.getIndex(), openString, area); List<IQuadEdge> edges = p.getEdges(); for (IQuadEdge e : edges) { Vertex a = e.getA(); // first point in edge System.out.format(" %12.6f, %12.6f%n", a.getX(), a.getY()); } }

For example:

Vertex 9, polygon is closed, area= 0.09 0.358217, 0.496937 0.625090, 0.764692 0.454992, 0.887576 0.181977, 0.854051