function planefull(data)
% DRAWPLANE.M Draws a localized least-squares planar approximation for a set of points  
% Darren Pais, Caltech, July 23, 2005
% INPUT: a nx3 matrix where n is the number of points used - Minimum no of
% pts is 3 !
% OUTPUT: a mesh grid planar approximation of the points, RMS of residuals, plane dip angle 

% calculate centroid of give data
centroid=mean(data)

% translate points to form matrix M
M=[(data(:,1) - centroid(1) ) (data(:,2) - centroid(2) ) (data(:,3) - centroid(3) ) ] ;

% perform singular value decomposition (SVD) on matrix M=USV'
[U,S,V]= svd(M) ;

%find the smallest singular value of M and its position i
[small,i]=min(diag(S));

%find the singular vector corresponding to singular value small, this
%vector is the vector normal to the best plane. since the columns of S are
%orthonormal, the singular vector we find will correspond to the direction
%cosines of the normal to the plane.
dircos=V(:,i) 

% calculate 'D' in plane equation Ax+By+Cz = D
D=sum(centroid*dircos) ;

% form localized grid mesh bounds.
xmin=min( data(:,1)) ;
xmax=max( data(:,1)) ;
ymax=max( data(:,1)) ;
ymax=max( data(:,2)) ;
ymin=min( data(:,2)) ;


% this scaling is variable dependent on the data you input
x=xmin:1000:xmax ; y=ymin:1000:ymax ;

% draw plane
[X,Y]=meshgrid(x,y) ;
Z = (D-dircos(1,1)*X - dircos(2,1)*Y)/dircos(3,1) ;
hold on ;
mesh(X,Y,Z)

%determine plane dip angle i.e., the z-direction gradient of the plane
plane_dip_angle = acosd(dircos(3,1))


%determine the residuals, i.e., the distances of given data points to
%best-fit plane
[m,n] = size(data) ;
for i=1 : 1 : m
    distmat(i,1)= data(i,1)*dircos(1,1)+data(i,2)*dircos(2,1)+data(i,3)*dircos(3,1) - D ;
    distmat(i,1)=distmat(i,1)*-1 ;
end
       
%Calculate RMS value of the residuals
sum1=0 ;
for i=1 : 1 : m
    sum1=sum1+distmat(i)^2 ;
end

%Display RMS value 
RMS = ( sum1 / m )^.5


%Bar plot for data point vs. distance of point from plane.
figure ;
bar(distmat,1)
colormap summer
xlabel('Data Point Index') ;
ylabel('Distance in Meters') ;