Mistake in delaunayTriangulation function

Hi

I have following X and Y points:

X = [ -0.05 -0.05 -0.05 -0.05 -0.016667 -0.016667 -0.016667 -0.016667 0.016667 0.016667 0.016667 0.016667 0.05 0.05 0.05 0.05];

Y = [ -0.025 -0.0083333 0.0083334 0.025 -0.025 -0.0083333 0.0083333 0.025 -0.025 -0.0083334 0.0083333 0.025 -0.025 -0.0083334 0.0083333 0.025];

I am using delaunay Triangulation as follows;

DT = delaunayTriangulation(X',Y')

and it gives points and connectivity list. However there should be 18 triangles but I have 20 triangles. When I checked it, I found that 2 lines are assumed as triangle and it is in Connectivity list.

You can check when you run my code:

DT.ConnectivityList

Connected points are 1-5-9 and 8-12-16 but they should not compose a triangle, they are actually on the same line.

How can I solve it?

Answer 1

[John D'Errico]

Those spurious triangles that got created have infinitesimal area.

In fact, IF I use the points you have supplied, I do get 18 triangles. But you have written out those numbers only to 5 significant digits, not the roughly 16 digits that MATLAB actually carries internally, so I cannot truly replicate what you did.

I've plotted the points you supplied. In fact, they form (roughly) a rectangular lattice.

To be honest, I'm not a big fan of using a delaunay triangulation on regular meshes, because it tends to produce a randomly oriented mesh. This is what I got from delaunayTriangulation.

The long, thin triangles that you got will typically be along the outside edge of that mesh. Here I've color coded the vertices from those two triangles with red * symbols.

plot(X,Y,'bo',X([1 5 9]),Y([1 5 9]),'r*',X([8 12 16]),Y([8 12 16]),'r*')

So, this really was not a "mistake", but just an artifact from bad data.