Delaunay Triangulation with a hole in the domain

Hi everyone,

I did some temperature measurments on a rectangular plate with a hole in the middle. The matrix with the temperature measurements is therefore of the following form (The indices of the matrix elements are proportional to the spatial coordinates of the measurement positions). 'a' represents some temperature value. '0' means that no temperature was recorded at this spatial point:

• 0000000000000
• 00aaaaaaaaa00
• 00aaaaaaaaa00
• 00aaa000aaa00
• 00aa00000aa00
• 00aaa000aaa00
• 00aaaaaaaaa00
• 00aaaaaaaaa00
• 0000000000000

I would like to create a mesh of the 'a' entries omitting the '0' entries - using Delaunay triangulation - without the hole in the middle and the margins (the zero entries of the matrix). The mesh should represnt the shape of the plate, which should like this in the end:

Can someone pls suggest a solution or share his/her ideas with me, that would be nice. Thanks

Answer 1

[Bruno Luong]

Why reinvent the wheel? This FEX will do.

[Lockenlui]

Thanks for your suggestion. Okay, that is a mesh generator. But I don't understand yet, how I can solve my problem with this. My mesh 'nodes' are given by the 'measuremnt positions', these I can feed easily to the mesh generator. How can I teach the mesh generator not to mesh the hole?

[Bruno Luong]

Have you played with it?

[Lockenlui]

Yes, I also have to provide the boundary edges at the hole. But this is a never-ending task if I have to determine them manually, individually. Especially if for example the diameter of the hole changes.

[Bruno Luong]

Manually? Why? Make a program to do it for you.

[Lockenlui]

Yeah okay, but this is not a trivial task. I could identify all boundary nodes as those nodes, that have a '0' entry as a neighbouring element. Any clue how to proceed then?

I found a workaround: if coords is the (n,2)-coordinate matrix of the n measurement points, then:

shp = alphaShape(coords)
tri = alphaTriangulation(shp)

will give something link this:

[Bruno Luong]

Look at the code corresponds to

> tridemo(8)

that does much more than what you asked.