How to create a smoother heatmap

Question

I'd like to create a heat map to analyze the porosity of some specimens that I have 3D-printed. the X-Y coordinates are fixed since they are the positions in which the specimens are printed on the platform.

Heatmap:

Tbl = readtable('Data/heatmap/above.csv');
X = Tbl(:,1);
Y = Tbl(:,2);
porosity = Tbl(:,3);
hmap_above = heatmap(Tbl, 'X', 'Y', 'ColorVariable', 'porosity');

• The first question is: how can I sort the Y-axis of the plot? since it goes from the lower value (top) to the higher value (bottom) and I need it the other way around.

• The second question is: I only have around 22 data points and most of the chart is without color, so I'd like to get a smoother heatmap without the black parts.

The data set is quite simple and is shown below:

X	Y	porosity
74.4615	118.3773	0.039172163
84.8570	69.4699	0.046314637
95.2526	20.5625	0.041855213
105.6482	-28.3449	0.049796110
116.0438	-77.2522	0.045010692
25.5541	107.9817	0.038562053
35.9497	59.0743	0.041553065
46.3453	10.1669	0.036152061
56.7408	-38.7404	0.060719664
67.1364	-87.6478	0.037756115
-23.3533	97.5861	0.052840845
-12.9577	48.6787	0.045216851
-2.5621	-0.2286	0.033645353
7.8335	-49.1360	0.030670865
18.2290	-98.0434	0.024952472
-72.2607	87.1905	0.036199237
-61.8651	38.2831	0.026725885
-51.4695	-10.6242	0.029212058
-41.0739	-59.5316	0.028572611
-30.6783	-108.4390	0.036796151
-121.1681	76.7949	0.031688096
-110.7725	27.8876	0.034619855
-100.3769	-21.0198	0.039070101
-89.9813	-69.9272	NaN
-79.5857	-118.8346	NaN

Answer 1

If you want to assign color to the "black parts" you will have to interpolate the porosity over a finer grid than you currently have.

The best tool for 2D interpolation over a uniformly sampled grid is griddata

First you have to define the X-Y grid you want to interpolate over, and choose a suitable mesh density.

% this will be the number of points over each side of the grid
gridres = 100 ;
% create a uniform vector on X, from min to max value, made of "gridres" points
xs = linspace(min(X),max(X),gridres) ;
% create a uniform vector on Y, from min to max value, made of "gridres" points
ys = linspace(min(Y),max(Y),gridres) ;
% generate 2D grid coordinates from xs and ys
[xq,yq]=meshgrid(xs,ys) ;
% now interpolate the pososity over the new grid
InterpolatedPorosity = griddata(X,Y,porosity,xq,yq) ;

% Reverse the Y axis (flip the `yq` matrix upside down)
yq = flipud(yq) ;

Now my version of matlab does not have the heatmap function, so I'll just use pcolor for display.

% now display
hmap_above = pcolor(xq,yq,InterpolatedPorosity);
hmap_above.EdgeColor = [.5 .5 .5] ; % cosmetic adjustment
colorbar
colormap jet
title(['Gridres = ' num2str(gridres)])

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And here are the results with different grid resolutions (the value of the gridres variable at the beginning):

Now you could also ask MATLAB to further graphically smooth the domain by calling:

shading interp

Which in the 2 cases above would yield:

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Notes: As you can see on the gridres=100, you original data are so scattered that at some point interpolating on a denser grid is not going to produce any meaningful improvment. No need to go overkill on your mesh density if you do not have enough data to start with.

Also, the pcolor function uses the matrix input in the opposite way than heatmap. If you use heatmap, you have to flip the Y matrix upside down as shown in the code. But if you end up using pcolor, then you don't need to flip the Y matrix.

The fact that I did it in the code (to show you how to do) made the result display in the wrong orientation for a display with pcolor. Simply comment the yq = flipud(yq) ; statement if you stick with pcolor.

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Additionally, if you want to be able to follow the isolevels generated by the interpolation, you can use contour to add a layer of information: Right after the code above, the lines:

hold on
contour(xq,yq,InterpolatedPorosity,20,'LineColor','k')

will yield: