Plane Fitting a 3D Scatter Plot

Question

Sarah 2019-3-7

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/448708-plane-fitting-a-3d-scatter-plot

评论： Star Strider 2019-12-1

I have a 3D scatter plot that I want to have a planar fit. How do you do this?

x = [14.9 1.7 0.0 10.9 0.0];
y = [11.3 9.1 23.7 12.8 2.9];
z = [5.32787E-17 2.93234E-16 2.09997E-16 5.45E-17 4.55E-16];
scatter3(x,y,z)

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Answer 1

Star Strider 2019-3-7

1
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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/448708-plane-fitting-a-3d-scatter-plot#answer_364205

在 MATLAB Online 中打开

A simple linear regression is straightforward:

x = [14.9 1.7 0.0 10.9 0.0];
y = [11.3 9.1 23.7 12.8 2.9];
z = [5.32787E-17 2.93234E-16 2.09997E-16 5.45E-17 4.55E-16];
B = [x(:) y(:) ones(size(x(:)))] \ z(:);
xv = linspace(min(x), max(x), 10)';
yv = linspace(min(y), max(y), 10)';
[X,Y] = meshgrid(xv, yv);
Z = reshape([X(:), Y(:), ones(size(X(:)))] * B, numel(xv), []);
scatter3(x,y,z, 'filled')
hold on
mesh(X, Y, Z, 'FaceAlpha', 0.5)
hold off
view(-120, 35)
title(sprintf('Z = %+.3E\\cdotX %+.3E\\cdotY %+.3E', B)) 

producing:

Plane Fitting a 3D Scatter Plot - 2019 03 06.png

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Star Strider 2019-3-7

在 MATLAB Online 中打开

Try this:

x = [14.9 1.7 0.0 10.9 0.0];
y = [11.3 9.1 23.7 12.8 2.9];
z = [5.32787E-17 2.93234E-16 2.09997E-16 5.45E-17 4.55E-16];
B = [x(:) y(:) ones(size(x(:)))] \ z(:);
xv = linspace(min(x), max(x), 50)';
yv = linspace(min(y), max(y), 50)';
[X,Y] = meshgrid(xv, yv);
Z = reshape([X(:), Y(:), ones(size(X(:)))] * B, numel(xv), []);
Ze = [x(:) y(:) ones(size(x(:)))] * B;                                      % Calculate Surface At Each Data Triplet
Err = Ze - z(:);                                                            % Calculate Errors
SStot = sum((z - mean(z)).^2);                                              % Total Sum-Of-Squares
SSres = sum(Err.^2);                                                        % Residual Sum-Of-Squares
Rsq = 1 - SSres/SStot;                                                      % Coefficient Of Determination
figure
surf(X, Y, Z, 'FaceAlpha', 0.5, 'EdgeColor','none')
hold on
plot3([x; x], [y; y], [z(:) Ze]', '-r', 'LineWidth',1)                      % Plot Errors (Red Lines From Surface To Data)
scatter3(x,y,z, 'filled')
hold off
view(-120, 35)
xlabel('X')
ylabel('Y')
zlabel('Z')
% title(sprintf('Z = %+.3E\\cdotX %+.3E\\cdotY %+.3E', B)) 
title('Z = -2.0998\times10^{-17}X - 1.135\times10^{-17}Y + 4.644\times10^{-16}')
text(10, 20, 3.5E-16, sprintf('R^2 = %0.3f', Rsq))

I tweaked my previous code slightly to incorporate the additions you requested. I also manually entered the title string, with the same data as previously. The first one still works, this one is easier to read.

Experiment to get the result you want.

The updated plot:

Plane Fitting a 3D Scatter Plot (2) - 2019 03 06.png

Damla Yüksel 2019-12-1

Hello, in the following line, matlab returns an error:

"Error using plot3

Vectors must be the same length.

Error in (line 33)

plot3([x; x], [y; y], [z(:) Ze]', '-r','LineWidth',1) % Plot Errors (Red Lines From Surface To Data)"

What should I do for this error?

Star Strider 2019-12-1

You should make the vectors the same length!

It is best for you to post this as a new Question, supplying ‘x’, ‘y’, ‘z’ and ‘Ze’.

Your Comment does not relate to the substance of this thread, so I will delete it (and my Comment here) in a few yours.

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Answer 2

KSSV 2019-3-7

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/448708-plane-fitting-a-3d-scatter-plot#answer_364201

在 MATLAB Online 中打开

x = [14.9 1.7 0.0 10.9 0.0];
y = [11.3 9.1 23.7 12.8 2.9];
z = [5.32787E-17 2.93234E-16 2.09997E-16 5.45E-17 4.55E-16];
nx = 10 ; ny = 10 ;
xi = linspace(min(x),max(x),nx) ; 
yi = linspace(min(y),max(y),ny) ; 
[X,Y] = meshgrid(xi,yi) ;
F = scatteredInterpolant(x',y',z') ; 
Z = F(X,Y) ;
scatter3(x,y,z)
hold on
surf(X,Y,Z)

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Plane Fitting a 3D Scatter Plot

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