Contour plot of concentration of chemical species

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SS 2019-11-10

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https://ww2.mathworks.cn/matlabcentral/answers/490281-contour-plot-of-concentration-of-chemical-species

评论： Star Strider 2019-11-14

Hi. I am releasing a chemical species CHX (N units) in a chamber. The size of the chamber is 100 X 100 X 100 cms^3. I want to plot the contour/surface plot of concentration of this chemical species in the chamber at different spatial locations.

I want to look at the concentration profiles overlapped or plotted on one plane, say X-Y plane (100 X 100 cm^2).

I am using a digital chemical analyzer which gives the X and Y vectors, X and Y which give the spatial location. Each and every (X,Y) corresponds to a spatial location at which the chemical species is present.

For example, if a given (X,Y) shows up "m" times it, means that there are "m" units of that species at that location. In my surface plot, at that particualr (X,Y), I want the value to be m/N (with some colormap). The same is with other (X,Y) locations.

Can someone help me with this?

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Answer 1

Star Strider 2019-11-10

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https://ww2.mathworks.cn/matlabcentral/answers/490281-contour-plot-of-concentration-of-chemical-species#answer_400739

在 MATLAB Online 中打开

Try this example:

xy = randi(9, 100, 2);                                      % Matrix Of ‘x’ and ‘y’ Positions
[Uxy,ia,ic] = unique(xy, 'rows');                           % Unique Rows
tally = accumarray(ic, 1);                                  % Tally Numbers Of Unique Row Repeats
Freq = [Uxy, tally];                                        % Concatenated Matrix
xv = min(xy(:,1)):max(xy(:,1));                             % ‘x’ Vector For Interpolation
yv = min(xy(:,2)):max(xy(:,2));                             % ‘y’ Vector For Interpolation
[X,Y] = ndgrid(xv,yv);                                      % Create Interpolation Grid
Z = griddata(Freq(:,1), Freq(:,2), Freq(:,3), X, Y);        % Interpolated Grid Of ‘tally’ Values
figure
contourf(X, Y, Z)                                           % Contour Plot
colorbar

Experiment to get the result you want.

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Star Strider 2019-11-11

在 MATLAB Online 中打开

My pleasure.

It might still be useful to have a representative sample of your data. Lacking that, this updated version of my previous code (most of it unchanged) to accomodate the new instrument results appears to me to do what you requested:

x = randi([-300 300], 1000, 1);                             % X: [-300 300]
y = randi([0 500], 1000, 1);                                % Y: [0 500]
xy = [x y];                                                 % Matrix Of ‘x’ and ‘y’ Positions
[Uxy,ia,ic] = unique(xy, 'rows');                           % Unique Rows
tally = accumarray(ic, 1);                                  % Tally Numbers Of Unique Row Repeats
Freq = [Uxy, tally/sum(tally)];                             % Concatenated Matrix (Normalised Concentrations)
xv = min(xy(:,1)):max(xy(:,1));                             % ‘x’ Vector For Interpolation
yv = min(xy(:,2)):max(xy(:,2));                             % ‘y’ Vector For Interpolation
[X,Y] = ndgrid(xv,yv);                                      % Create Interpolation Grid
Z = griddata(Freq(:,1), Freq(:,2), Freq(:,3), X, Y);        % Interpolated Grid Of ‘tally’ Values
xsf = [-300 1; 300 1] \ [0; 100];                           % X-Scale Relation
ysf = [   0 1; 500 1] \ [0; 100];                           % Y-Scale Relation
Xc = X*xsf(1) + xsf(2);                                     % Scale ‘X’ To Chamber Coordinates
Yc = Y*ysf(1) + ysf(2);                                     % Scale ‘Y’ To Chamber Coordinates
figure
contourf(Xc, Yc, Z)                                         % Contour Plot
hc = colorbar;
hc.Label.String = "[CHX]";

I created the original ‘x’ and ‘y’ vectors to match the ranges you mentioned, in order to test this. The ‘xsf’ and ‘ysf’ calculations map the [-300 300] X-coordinates and [0 500] Y-coordinates the instrument returns to the [0 100] dimensions of the chamber. (This is a simple linear regression using the \ operator.) I use them to calculate ‘Xc’ and ‘Yc’ (‘Xchamber’ and ‘Ychamber’ respectively), to use in the contourf call. I also added a title to the colorbar.

SS 2019-11-14

Hi Star Strider. I have a question. Is there any function which calculates the intensity at a grid cell based on the PDF (averaging of the Z data points in that cell) rather than interpolation scheme which griddats function does?

Star Strider 2019-11-14

I am not certain that I understand what you are asking. The griddata function is necessary to create the matrices to do the contour plot. There are several different interpolation methods available in griddata, so perhaps one of them (perhaps 'nearest') is what you are looking for. (To the best of my knowledge, you cannot define your own interpolation scheme to use with griddata or the other interpolation algorithms.)

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