Fitting a straight line to a set of 3-D points

Hi there,

please can someone help me fit a straight line to my data? It's in 3-D I have done it in 2-D before but have no idea about 3-D

This is my code:

Many many thanks

lat_3d= [30.3894980000000;30.3824250000000;30.3886690000000;30.3878380000000;30.3953250000000;30.3874200000000;30.3807640000000;30.3924160000000;30.3874200000000;30.3811820000000;30.3919950000000;30.3928260000000;30.3903320000000;30.3836720000000;30.3774440000000];%new_3d_model_results(:,2);
lon_3d= [40.7508620000000;40.7486390000000;40.7489620000000;40.7476950000000;40.7515010000000;40.7486440000000;40.7461050000000;40.7486490000000;40.7486440000000;40.7451550000000;40.7514980000000;40.7521320000000;40.7502300000000;40.7495900000000;40.7410360000000];%new_3d_model_results(:,1);
depth_3d=[10.0097660000000;8.04296900000000;8.97460900000000;7.98085900000000;9.51289100000000;8.04296900000000;10.1132810000000;10.0304690000000;7.96015600000000;7.98085900000000;9.47148400000000;7.77382800000000;8.76757800000000;9.34726600000000;7.79453100000000]; %new_3d_model_results(:,3);

%% plot 3d 
scale = 111; % km/deg
figure 
%plot

% h=[30.3 30.45 40.7 40.8];
% lat_lon_proportions(h) % refernced at top of script 

% plot events 
hold on 
p10=plot3(lat_3d,lon_3d,depth_3d/scale,'o','MarkerFaceColor',light_p,'MarkerEdgeColor', 'k','MarkerSize',12); %QPS changed/ Initial Velocity Model
hold on 
grid on 
%axis equal
ax = gca;
ax.ZDir = 'reverse';
zVal = str2double(ax.ZTickLabel)*scale;
ax.ZTickLabel = num2str(zVal);
xlabel('Longitude (deg, E)');
ylabel('Latitude (deg, N)')
zlabel('Depth (km)')
zval = [2:2:20]';
ax.ZTick = zval/scale;
ax.ZTickLabel = num2str(zval);
hold on 

set(gca,'FontName','Helvetica','FontSize',20);
hold on 
xlim([30.3 30.45])
ylim([40.7 40.8])
hold on 
axis([30.3 30.45 40.7 40.8]);
view(-37.5, 4)

Answer 1

[Torsten]

What I would do is find the average P¯of your points and an eigenvector V of the covariance matrix for its largest eigenvalue. The line can then be represented as P ¯ +t*V .

[P_L]

could you pleasee provide more details on how to do this?

Many thanks

[Torsten]

https://math.stackexchange.com/questions/268528/fitting-a-3d-line-to-a-3d-line-point-cloud

Last answer.