spatialgraph2D

Creates a graph object with 2D spatial locations associated with the nodes

This submission defines a graph class which allows 2D (x,y) location data to be attached to the nodes. It was designed with mosaic graphs in mind. By a mosaic graph, I mean a graph in which distinct edges may intersect one another only at the nodes. Currently, its main capability is decomposing a mosaic graph into its constituent polygons. As an example, given the graph,

s = [1 1 1 2 3 3 4 4 5 6 7 6 8 9 10 10 12 12 13 14 15 16 17 17 18 19 20 21 20 25];
t = [2 8 18 3 4 23 5 21 6 7 8 11 9 10 11 12 14 13 15 18 16 17 18 25 19 20 1 22 24 26];
G = graph(s,t);

we associate the nodes of G to the following x, y data,

x = [0.5 0 0 0 0.5 1 1.5 2 3 3 3 5.5 6 4 6 6 4 3 2 0.5 -1 -2 -1 1.5 4.5 4.5];
y = [0 0.5 1 1.5 2 2 1.5 1 1 1.5 2 1 0.5 0.5 0 -1 -1 -0.5 -1 -1 1 0.5 0.5 -0.5 -0.5 0];

We create a spatialgraph2D object as follows,

obj=spatialgraph2D(G,x,y);

Then, we can obtain a polyshape array of all the constituent polygons by doing,

pgon=polyshape(obj);

Or, obtain the node sequences demarcating each polygon with the syntax,

[~,nodeSequences]=polyshape(obj);

To visualize the decomposition, the class has several plotting methods. The following was used to generate the image thumbnail above.

mosaic(obj);