Mesh Grid of a 3d array

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SA 2021-6-21

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/861915-mesh-grid-of-a-3d-array

评论： SA 2021-6-22

I want to plot the error when I compare a numerical approximation and an exact solution. I want to use the matlab mesh function (mesh(X,Y,Z)) to visualise the error approximation. With the mesh function the Z component has to be a matrix. My numerical approximation and exact solution are all vectors but they were 3d arrays convected to vectors. How do I use the mesh function to plot the error given that the Z component has to be a matrix? I tried the code below but I am not sure if it's right. Any help will be greatly appreciated. In the code xx (numerical approximation) and yy(exact solution) are vectors of dimension xd^3 and zz is the difference between xx and yy.

xd = nthroot(length(zz),3);
yd = xd;
u = zeros(xd,yd,1);
v = zeros(xd,yd,1);
xstart = -3.0;
xend = 3.0;
h = (xend-xstart)/(xd-1);
x = zeros(xd,1);
y = zeros(xd,1);
for i = 1:xd
    x(i) = xstart + (i-1)*h;
    y(i) = xstart + (i-1)*h;
end
    
err = 0.0;
for i = 1:xd
    for j = 1:yd
        u(j,i,1) = xx((j-1)*xd+i);
        v(j,i,1) = yy((j-1)*xd+i);
        if abs(u(j,i,1)-v(j,i,1)) > err %error
            err=abs(u(j,i,1)-v(j,i,1));
        end
    end
end
mesh(x,y,u-v);     
xlabel('x');
ylabel('y');
zlabel('maxerror');

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Answer 1

Joel Lynch 2021-6-22

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https://ww2.mathworks.cn/matlabcentral/answers/861915-mesh-grid-of-a-3d-array#answer_730170

编辑：Joel Lynch 2021-6-22

在 MATLAB Online 中打开

So this may be due to confusion about how mesh() works. Mesh produces a 2D surface in a 3D volume, with the Z-axis being the value of the matrix at each X/Y point. If your solution's are truly 3D (a value defined at each X/Y/Z point), mesh cannot really plot any more than one 2D slice at a time (at least cleanly). A good alternative would be to represent error as color in a 3D plot, using slice, but you won't be able to see every point at once.

You could also present the data a few other ways: 1. animated or subplotted 2D frames, plotting 1 2D "slice" at a time, 2. A single Mesh() showing the average or maximum error along the Z axis at each X/Y, and 3. Using something like histogram(err(:)) to see the breakdown of all the errors.

Also, you can greatly simplify the creation of x/y vectors by using linspace:

x = linspace( xstart, xend, nthroot(numel(zz),3) ); y = x;

and you can vectorize (compute all at once) the error generation by:

err = abs(u-v)

The if branch is useless, as error will always be >=0.

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Joel Lynch 2021-6-22

在 MATLAB Online 中打开

Okay, how does this look? - I used the reshape command to convert error to a 3D matrix, then plotted with slice.

% Load Data
load analytical_soln.txt
exact_solution = importdata('analytical_soln.txt');
load recovered_potential.txt
computed_solution = importdata('recovered_potential.txt');
% Compute Error
error = abs(exact_solution-computed_solution);
% Get number of elements from cubed-root of the number of elements in error
xd =  nthroot(numel(error),3);
% Create x/y/z vectors, and X/Y/Z Meshgrid
x = linspace( -3, 3, xd ); y = x; z = x;
[X,Y,Z] = meshgrid(x,y,z);
% Reshape error to 3D matrix
error = reshape(error,[xd,xd,xd]);
% 3D Slice plot
xslice = [0, 3];
yslice = [0, 3];
zslice = [-3, 0];
slice(X,Y,Z,error,xslice,yslice,zslice);     
xlabel('x');
ylabel('y');
zlabel('z');
colorbar
title('3D Error Plot with slice')