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

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?

Answer 1

[Akira Agata]

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).

[Hongshun Chen]

What if the plane is parallel to the z. Singularity will come out when calculating the plane normal.

Answer 2

[KSSV]

[num,txt,raw] = xlsread('Step_scan01_ex.xls') ;

x = num(:,1) ; y = num(:,3) ; z = num(:,3) ; 

x0 = min(x) ; x1 = max(x) ; nx = 500 ;
y0 = min(y) ; y1 = max(y) ; ny = 500 ;
xx = linspace(x0,x1,nx) ;
yy = linspace(y0,y1,ny) ;
[X,Y] = meshgrid(xx,yy) ;
Z = griddata(x,y,z,X,Y)  ;
surf(X,Y,Z)
shading interp