plot magnitude data at location (x,y,z)

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Jorge 2024-8-22

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https://ww2.mathworks.cn/matlabcentral/answers/2147234-plot-magnitude-data-at-location-x-y-z

评论： Star Strider 2024-8-23

I can't figure out how to plot magnitudes of a variable at different (x,y,z) locations. In effect, I need to plot a 4D plot, (x,y,z,value). I thought I'd be able to do a 3D plot and set the 4D as color scale or something like that, but I can't figure how to do that.

Perhaps I'm over thinking this....but, I'd appreciate any help.

Thanks!

Jorge

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Answer 1

Star Strider 2024-8-22

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https://ww2.mathworks.cn/matlabcentral/answers/2147234-plot-magnitude-data-at-location-x-y-z#answer_1503679

在 MATLAB Online 中打开

data.mat

@Jorge —

Try this —

LD = load('data')

LD = struct with fields:

data: [201x4 double]

x = LD.data(:,1);

y = LD.data(:,2);

z = LD.data(:,3);

c = LD.data(:,4);

figure

stem3(x, y, z)

hold on

scatter3(x, y, z, 100, c, 'filled')

hold off

CL = clim;

colormap(turbo)

xlabel('X')

ylabel('Y')

zlabel('Z')

view(130,30)

Zfcn = scatteredInterpolant(x, y, z, 'natural','none'); % Create Surface Matrix

Warning: Duplicate data points have been detected and removed - corresponding values have been averaged.

Cfcn = scatteredInterpolant(x, y, c, 'natural','none'); % Create Colour MAtrix

Warning: Duplicate data points have been detected and removed - corresponding values have been averaged.

N = numel(x);

xv = linspace(min(x), max(x), N);

yv = linspace(min(y), max(y), N);

[Xm,Ym] = ndgrid(xv, yv);

Zm = Zfcn(Xm, Ym);

Cm = Cfcn(Xm, Ym);

figure

surfc(Xm, Ym, Zm, Cm, 'EdgeColor','interp')

clim(CL)

colormap(turbo)

xlabel('X')

ylabel('Y')

zlabel('Z')

view(130,30)

The only change from my previous answer was using your data. Some parts do not interpolate well and leave gaps, however that appears to be inhereint in your data, at least as far as scatteredInterpolant interprets them.

.

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Star Strider 2024-8-23

编辑：Star Strider 2024-8-23

在 MATLAB Online 中打开

data.mat

The scatteredInterpolant function replaces the mean of the duplicated values with the duplicate values and deletes the others. Note that ‘data’ appears as a structure loading it into a avariable, and simply a matrix otherwsie. I don’t know what ‘val’ is, since ‘data’ is a matrix and not a table, so I assume the fourth column is the fourth dimension that is to be used to assign the colours.

In this instance, with the duplicated values, it takes the mean of each duplicate and plots it as the mean of the values. Here, there are four distinct ‘layers’, and each layer must be rencered separately.

This is what I get with the new ‘data.mat’ file —

load('data')

whos( '-file','data')

Name Size Bytes Class Attributes data 560x4 17920 double

LD = load('data')

LD = struct with fields:

data: [560x4 double]

x = LD.data(:,1);

y = LD.data(:,2);

z = LD.data(:,3);

c = LD.data(:,4);

figure

stem3(x, y, z)

hold on

scatter3(x, y, z, 100, c, 'filled')

hold off

CL = clim;

colormap(turbo)

xlabel('X')

ylabel('Y')

zlabel('Z')

view(-45,30)

[Uz,ixs,ixv] = unique(z);

L = accumarray(ixv, (1:numel(ixv)).', [], @(v) {[x(v) y(v) z(v) c(v)]})

L = 5x1 cell array

{112x4 double} {112x4 double} {112x4 double} {112x4 double} {112x4 double}

figure

hold on

for k = 1:numel(L)

x = L{k}(:,1);

y = L{k}(:,2);

z = L{k}(:,3);

c = L{k}(:,4);

Zfcn = scatteredInterpolant(x, y, z, 'natural','none'); % Create Surface Matrix

Cfcn = scatteredInterpolant(x, y, c, 'natural','none'); % Create Colour MAtrix

N = numel(x);

xv = linspace(min(x), max(x), N);

yv = linspace(min(y), max(y), N);

[Xm,Ym] = ndgrid(xv, yv);

Zm = Zfcn(Xm, Ym);

Cm = Cfcn(Xm, Ym);

surf(Xm, Ym, Zm, Cm, 'EdgeColor','interp')

clim(CL)

colormap(turbo)

end

hold off

xlabel('X')

ylabel('Y')

zlabel('Z')

view(-45,30)

grid on

figure

hold on

for k = 1:numel(L)

x = L{k}(:,1);

y = L{k}(:,2);

z = L{k}(:,3);

c = L{k}(:,4);

Zfcn = scatteredInterpolant(x, y, z, 'natural','none'); % Create Surface Matrix

Cfcn = scatteredInterpolant(x, y, c, 'natural','none'); % Create Colour MAtrix

N = numel(x);

xv = linspace(min(x), max(x), N);

yv = linspace(min(y), max(y), N);

[Xm,Ym] = ndgrid(xv, yv);

Zm = Zfcn(Xm, Ym);

Cm = Cfcn(Xm, Ym);

surf(Xm, Ym, Zm, Cm, 'EdgeColor','interp')

clim(CL)

colormap(turbo)

end

hold off

xlabel('X')

ylabel('Y')

zlabel('Z')

view(-45,30)

grid on

daspect(gca, [2.5 1 5])

I doubt that a volumetric version of this is possible, since that is not how the data are arranged. Plotting four distinct layers is likely the best possible outcome. It is possible to ‘squash’ it a bit in the z-direction, however that does not appear to accomplish much. Experiment with the daspect call to change the aspect ratios of the axes. (Assigning them as [1 1 1] is the same as axis('equal').)

EDIT — (23 Aug 2024 at 12:01)

Changed explicit loop to accumarray call to produce ‘L’.

.

Jorge 2024-8-23

在 MATLAB Online 中打开

if you have the time to explain it to me, let me try to break it down so you can understand what I don't understand. If you want to move on, that's fine too, no worries.

1) why do you need to do unique z, when every row in the matrix is 'unique"?

2) wht is this exactly doing:

Zfcn = scatteredInterpolant(x, y, z, 'natural','none');

why do we need to interpolate the z values when I have them --they are fixed coordinates?

3) In my mind, I figured all we had to do was somehow create a 3d grid or mesh, and then map the value on column for to the respective location in the grid.

For example, if I had only a 2D data (x,y, value).

I could use meshgrid to create the cartesian grid, and then I would have to figure out how to map each value v to its respectdive (x,y) coordinate. Perhaps that is the crux of the thing....I don't understand how what you did does that (in this case in 3D, but I don't understand it for the 2D case either).

I'm going to continue playing with what you did above until I figure it out.

thank you.

Star Strider 2024-8-23

The values may be ‘unique’ in some sense, however the matrix itself is scattered. You can see that by displaying it. That is the first thing I did, because if it was truly gridded, I would have only needed to use the reshape function to create matrices from the various vectors, once I got them separated by rows according to the ‘z’ values. (That would also have required the unique funciton in order to determine the rows at which ‘z’ changed value.)

The unique call is used to provide a vector ‘ixv’ that returns the positions of every row corresponding to specific values of ‘z’ (since it defines the layers), and sorts them (although the sorting is not specifically necessary and can be suppressed by using the 'stable' argument to unique). My code then uses that vector to separate out the corresponding values of the original matrix into five equal-size cell arrays corresponding to each specific ‘z’ value, using accumarray to do this. (The accumarray function is more efficient than the loop I used originally, so I replaced it.) The cell arrays do not have to be the same size, however they are in these data.

It is necessary to interpolate the ‘z’ values in order to create the surfaces. The scattteredInterpolant function creates the interpolation function ‘Zfcn’ that then uses the ‘Xm’ and ‘Ym’ matrices created from the ‘xv’ and ‘yv’ vectors to interpolate the surface that then exists as ‘Zm’ (the surface values) and ‘Cm’ (the surface colours). Interpolating to a finer grid (the result of the ndgrid call) produces more detail.

If you only have a 2D data, you cannot create a surface from it, since it lacks the third dimension. The data already have to exist in 3D in order to create a surface plot. With 2D data, you can createa line plot and then interpolate it as a line in 2D in order to add more data points and perhaps smooth it a bit (using 'pchip', 'spline' or 'makima' interpolation methods), however that is all you can do.

See the documentation for the various functions for details.

Jorge 2024-8-23

thanks for taking the time to explain!

Star Strider 2024-8-23

As always, my pleasure!

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Answer 2

Aquatris 2024-8-22

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编辑：Aquatris 2024-8-22

在 MATLAB Online 中打开

Here is one way where you use colors to indicate the magnitude;

% random data

x = [0:pi/50:10*pi nan]; % nan is added to remove connection between first and last data point

y = sin(x);

z = cos(x);

m = x; % magnitude you want as colors, i set it to x cause it looks nice :D

colormap(winter)

patch(x,y,z,m,'Facecolor','none','EdgeColor','interp')

colorbar

view(3)

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Jorge 2024-8-22

data.mat

Thank you for you input. That does give me something I can use, but I'm left wondering if there is yet a better way to display the data. Here's a sample of data I collected in the lab. The data has the coordinates of the x,y,z fixture, and the values measured. The format is [x,y,z,value]. if you think of a better, please let me know. I appreciate the help. Thank you.

Aquatris 2024-8-23

编辑：Aquatris 2024-8-23

在 MATLAB Online 中打开

data.mat

Here is similar scatter3 way with your code:

load('data.mat')

x = data(:,1);

y = data(:,2);

z = data(:,3);

m = data(:,4);

scatter3(x,y,z,100,m,'filled')

colorbar

view(-15,10)

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plot magnitude data at location (x,y,z)

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