MATLAB: How to create a linear line of best fit for a set of 3-dimensional coordinates

line of best fitlinear regressionMATLAB

I have 3 sets of data containing 10 numbers each. example >> x=[-77.0675, -75.3709, -73.4958, -70.8106, -68.0568, -65.7213, -63.6809, -61.8022, -60.7548, -59.0176]; >> y=[-174.3252, -176.0859, -178.0156, -180.2053, -182.2752, -184.0714, -186.6690, -189.5100, -191.8722, -194.4930]; >> z=[738.9531, 736.8734, 735.4359, 735.1597, 735.2994, 735.8879, 736.5197, 737.7522, 738.6343, 739.2247]; I can 3d plot this data with the plot3 command, but am unable to create a linear line of best fit for the 3 data sets. Does anybody know how to do this?

Best Answer

You could do something like the code below, although I doubt that is what you want (the trend looks like a parabola to me), nor can I guarantee this will yield the best linear fit in 3D.

x=[ -77.0675,  -75.3709,  -73.4958,  -70.8106,  -68.0568, ...
    -65.7213,  -63.6809,  -61.8022,  -60.7548,  -59.0176];
y=[-174.3252, -176.0859, -178.0156, -180.2053, -182.2752, ....
   -184.0714, -186.6690, -189.5100, -191.8722, -194.4930];
z=[ 738.9531,  736.8734,  735.4359,  735.1597,  735.2994, ...
    735.8879,  736.5197,  737.7522,  738.6343,  739.2247];
xyz=[x(:),y(:),z(:)];
r=mean(xyz);
xyz=bsxfun(@minus,xyz,r);
[~,~,V]=svd(xyz,0);
x_fit=@(z_fit) r(1)+(z_fit-r(3))/V(3,1)*V(1,1);
y_fit=@(z_fit) r(2)+(z_fit-r(3))/V(3,1)*V(2,1);
figure(1),clf(1)
plot3(x,y,z,'b')
hold on
plot3(x_fit(z),y_fit(z),z,'r')

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MATLAB: Can I find 2 points along a 3-dimensional linear line of best fit

You can write a function that finds the point on the line that is closest to your data line, but this doesn't. It finds two points on the line that are closest to you data points, not the line Matlab draws between those points.

Next time, post your code as text and use the {}Code button to format it. You should make it easy for people to copy and paste your code to Matlab.

x=[ -77.0675,  -75.3709,  -73.4958,  -70.8106,  -68.0568, ...
    -65.7213,  -63.6809,  -61.8022,  -60.7548,  -59.0176];
y=[-174.3252, -176.0859, -178.0156, -180.2053, -182.2752, ....
   -184.0714, -186.6690, -189.5100, -191.8722, -194.4930];
z=[ 738.9531,  736.8734,  735.4359,  735.1597,  735.2994, ...
    735.8879,  736.5197,  737.7522,  738.6343,  739.2247];
xyz=[x(:),y(:),z(:)];
r=mean(xyz);
xyz=bsxfun(@minus,xyz,r);
[~,~,V]=svd(xyz,0);
x_fit=@(z_fit) r(1)+(z_fit-r(3))/V(3,1)*V(1,1);
y_fit=@(z_fit) r(2)+(z_fit-r(3))/V(3,1)*V(2,1);
figure(1),clf(1)
plot3(x,y,z,'b')
hold on
plot3(x_fit(z),y_fit(z),z,'r')
%create a new z vector for more fine-grained matching
extra_factor=10;N_new=extra_factor*numel(z);
z2=linspace(min(z),max(z),N_new);
%implicit expansion (>=R2016b):
%dist_to_data=sqrt((x_fit(z2)'-x).^2+(y_fit(z2)'-y).^2+(z2'-z).^2);
dist_to_data=sqrt(...
    bsxfun(@minus,x_fit(z2)',x).^2+...
    bsxfun(@minus,y_fit(z2)',y).^2+...
    bsxfun(@minus,       z2',z).^2);
dist_to_data=min(dist_to_data,[],2);
%filter the first derivative and find the zero crossing to find the closest
%point to the data
filtered_dist=movmean(diff(dist_to_data),extra_factor);
%zero cross index finder (by Star Strider, matlabcentral/answers/267222 )
zci = @(v) find(v(:).*circshift(v(:), [-1 0]) <= 0);
zero_cross_index=zci(filtered_dist);
%select the candidates and sort them based on distance to data
z_close=z2(zero_cross_index);
[~,order]=sort(dist_to_data(zero_cross_index));
z_close=z_close(order);
%plot only the two points closest to the data
plot3(x_fit(z_close(1)),y_fit(z_close(1)),z_close(1),'kx')
plot3(x_fit(z_close(2)),y_fit(z_close(2)),z_close(2),'ko')

MATLAB: How to convert a char into double

Note that there are not only numbers in that string, it also contains 'S' characters apparently at random, e,g.:

>> f(8480:8500)
ans =
3 -118 S 623 1623 -71
%      ^ not digit character!

One simple and efficient solution is to remove those 'S' characters before using sscanf:

v = sscanf(strrep(f,'S',''),'%d');

This correctly returns all 4297 numbers in the string, and can be easily adapted (e.g. using regexprep to remove specific types of characters, e.g. if it is possible that other alphabetic characters might occur in the string).

The simplest and most efficient solution by far is this:

v = sscanf(f,'%d%*[S ]');

Nothing will beat that simple command in terms of simplicity or speed.

Best Answer

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MATLAB: Can I find 2 points along a 3-dimensional linear line of best fit

MATLAB: How to convert a char into double

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