How can I colour my delaunay triangulation based on concentration of some property?

I have a delaunay triangulation and I would like to display the increasing concentration of a property through the cells of the triangulation using the increasing intensity of a specified colour.

Please can anyone help with how to do this?

Thank you,

[Mark]

Please can anyone help with this???

Answer 1

[Walter Roberson]

One way:

http://www.mathworks.com/help/matlab/math/interpolation-using-a-specific-delaunay-triangulation.html#btt8sdl

and http://www.mathworks.com/help/matlab/math/interpolating-scattered-data.html

Another way: http://www.mathworks.com/help/matlab/ref/triscatteredinterp.html

That is, use your triangulation to interpolate the value at a set of points.

Once you have the value, to express intensity of the color, use

target_color = [240, 18, 152];   %for example

cmap = linspace(0,1,256).' * target_color;   %matrix multiply

and define the intensity that is to map to the bottom and the intensity that is to map to the top:

minintens = -85.32;     %whatever appropriate
maxintens = 148139.2;   %whatever appropriate

and now that you have the map, graph the intensity such as with

   image(ArrayOfIntensities, [minintens, maxintens]);
   colormap(cmap);

[Mark]

Thanks a lot Walter, one question: What does ArrayOfIntensities represent?

[Walter Roberson]

ArrayOfIntensities would be the result of interpolating your data over a rectangular grid.

[Mark]

I have tried that, but I get the error: 'Error using image Incorrect number of arguments'. Plus I am working on a triangulated mesh constructed using delaunayTriangulation.

[Walter Roberson]

imagesc(ArrayOfIntensities, [minintens, maxintens]);

Yes you are working on a triangulated mesh, but you would interpolate the mesh over a grid.

I am checking into possibilities for triangular display.

[Walter Roberson]

Is your mesh over 2D or over 3D?

[Mark]

over 2D please...

[Mark]

I want to achieve something like what I have attached. They have used a triangulated mesh and simulate during run time the increased saturation within the triangulation from cell to cell.

[Walter Roberson]

For something like that I would interpolate the triangulation over a grid.

However, I need to know which delaunay triangulation method you used, delaunay() or delaunayTriangulation() or DelaunayTri(), and I need to know which MATLAB version you use; also I need to know whether the point is to get it working now or to have something that is going to continue to work in MATLAB (because the easiest approaches are marked as going away soon.) Also, is it important that you stay with the particular delaunay triangulation method you are using now? Is it important that you stick with explicit delaunay triangulation method ?

[Mark]

I used delaunayTriangulation() method, and I need it to work now to start with and then I can figure out later how to make it work for the longer term. Yes the delaunay triangulation method makes it easy for me to incorporate my fracture elements into the simulation domain. Plus my code is complete using the delaunayTriangulation() method, I just now need to visually display how the concentration of water propagates through by changing color intensity.

[Mark]

Hello Walter, any luck with how to do this?

Thank you,