MATLAB: Plane fit (z=ax+by+c) to 3D point data

least squrareMATLABplane fitting

Hi,

I have step plot (attached) and I want to fit a plane on the lower terrace of it. Excel file of point cloud is attached as well. Data represent in file is N-by-3 numeric data and each column corresponds to x, y and z. Could anyone please help me out how to fit the plane to the lower terrace?

Best Answer

Assuming that your data is N-by-3 numeric array, say yourData, and each column corresponds to x, y and z, the following code can generate a, b and c for fitting plane (z = ax + by + c).

% Assuming that yourData is N-by-3 numeric array
B = [ones(N,1), yourData(:,1:2)] \ yourData(:,3);

Where a = B(2), b = B(3) and c = B(1).

Related Solutions

MATLAB: Contour plot for given x,y,z


[num,txt,raw] = xlsread('Book1.xlsx') ; 
x = num(:,1) ; 
y = num(:,2) ; 
z = num(:,3) ; 
figure(1)
scatter(x,y,20,z,'filled') ; colorbar
%% Method 1 / Griddata
nx = 500 ; ny = 500 ;
[X,Y] = meshgrid(linspace(min(x),max(x),nx),linspace(min(y),max(y),ny)) ;
Z =griddata(x,y,z,X,Y) ;
figure(2)
contour(X,Y,Z) ;
figure(3)
pcolor(X,Y,Z)
shading interp 
%% Method 2 simple reshaping 
x = unique(x) ; nx = length(x) ;
y = unique(y) ; ny = length(y) ;
Z = reshape(z,ny,nx) ;
figure(4)
contour(x,y,Z)

MATLAB: How to fit Plane (z=ax+by+c) to 3D point cloud data

Try this:

arr = xlsread('Step_scan01_ex.xls');
x=arr(:,1);
y=arr(:,2);
z=arr(:,3);
DM = [x, y, ones(size(z))];                             % Design Matrix
B = DM\z;                                               % Estimate Parameters
[X,Y] = meshgrid(linspace(min(x),max(x),50), linspace(min(y),max(y),50));
Z = B(1)*X + B(2)*Y + B(3)*ones(size(X));
figure(1)
plot3(arr(:,1),arr(:,2),arr(:,3),'.')
hold on
meshc(X, Y, Z)
hold off
grid on
xlabel('x(mm)'); ylabel('y(mm)'); zlabel('z(mm)');
title('Masked plot');
grid on
text(-20, 50, 450, sprintf('Z = %.3f\\cdotX %+.3f\\cdotY %+3.0f', B))

Best Answer

Related Solutions

MATLAB: Contour plot for given x,y,z

MATLAB: How to fit Plane (z=ax+by+c) to 3D point cloud data

Related Question