Making Graph from Delaunay Triangulation

Hi,

I have made a graph from Delaunay triangulation. But the graph seemed to be aligned differently. Why it is so? If I have to add numbers to nodes of Delaunay how can I do that? Weights for the graph is the euclidean distance between two nodes. Attaching code and figure below.

DT = delaunayTriangulation(pts); 
figure(2)
e=DT.edges;
 
pl=triplot(DT);



% Distances of the edges for weights
plist1 = pts(e(:,1),:);
plist2 = pts(e(:,2),:);
diffs = plist2-plist1;
 if diffs<0
     diffs=diffs*-1;
     
 end
dists = vecnorm(diffs');
disp(dists);
% create Graph
G = graph(e(:,1), e(:,2), dists);
figure(3)
p = plot(G,'EdgeLabel',G.Edges.Weight);

Answer 1

[Bruno Luong]

The plot of graph the graph is not supposed to respect the distance, only connectivity. Since it 's not always possible to project a graph to 2D screen while preserving the distance (weight). For example a graph the does not respect triangular inequality

G = graph([1 1 2],[2 3 3],[1 1 3]);
plot(G)

or a graph of a regular 3D tetrahedron

G=graph([1 1 1 2 2 3], [2 3 4 3 4 4], [1 1 1 1 1 1])

G = 
  graph with properties:

    Edges: [6×2 table]
    Nodes: [4×0 table]

h=plot(G)

h = 
  GraphPlot with properties:

     NodeColor: [0 0.4470 0.7410]
    MarkerSize: 4
        Marker: 'o'
     EdgeColor: [0 0.4470 0.7410]
     LineWidth: 0.5000
     LineStyle: '-'
     NodeLabel: {'1'  '2'  '3'  '4'}
     EdgeLabel: {}
         XData: [-1.1867 -0.7143 0.7143 1.1867]
         YData: [-0.7135 1.1881 -1.1881 0.7135]
         ZData: [0 0 0 0]

  Show all properties

However you can set the coordinates as you like:

set(h,'XData',[sqrt(3)/3,-sqrt(3)/6,-sqrt(3)/6,0]);
set(h,'YData',[0,1/2,-1/2,0]);
set(h,'ZData',[0,0,0,sqrt(6)/3]);
axis equal

In your case it will be coordinates of pts