MATLAB: Plane Fitting a 3D Scatter Plot

3d plotscurve fittingMATLABplotplotting

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)

Best Answer

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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s=10;b=8/3; r=28;h=0.003; a=28
x=0;y=1; z=0; f=zeros(1,3); f=[x y z]; 
k=1;
for t=0:h:100 
    k1_x=a*(y(k)-x(k));
    k2_x=a*(y(k)-x(k))+(k1_x*h*0.5);
    k3_x=a*(y(k)-x(k))+(k2_x*h*0.5);
    k4_x=a*(y(k)-x(k))+(k3_x*h);
    x(k+1)=x(k)+(k1_x+2*k2_x+2*k3_x+k4_x)*h/6; 
    k1_y=x(k)*(r-z(k))-y(k);
    k2_y=(x(k)*(r-z(k))-y(k))+k1_y*h*0.5;
    k3_y=(x(k)*(r-z(k))-y(k))+k2_y*h*0.5;
    k4_y=(x(k)*(r-z(k))-y(k))+k3_y*h*0.5;
    y(k+1)=y(k)+(k1_y+(2*k2_y)+(2*k3_y)+(k4_y))*h/6; 
    k1_z=x(k)*y(k)-b*z(k);
    k2_z=(x(k)*y(k)-b*z(k))+k1_z*h*0.5;
    k3_z=(x(k)*y(k)-b*z(k))+k2_z*h*0.5;
    k4_z=(x(k)*y(k)-b*z(k))+k3_z*h*0.5;
    z(k+1)=z(k)+(k1_z+(2*k2_z)+(2*k3_z)+(k4_z))*h/6; 
    k=k+1;
end
    plot3(x,y,z); grid on; xlabel('x'); ylabel('y');
    zlabel('z'); title('Lorenz attractor');

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this problem was solved now..

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MATLAB: How can i call array elements in a plot3 function

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