Interpolating points in a 3D space with one line

Hello,

I have 5 points (black) in a 3D space. I would like to interpolate these points with a linear LINE and get the coefficients of this linear function.

I have just found how to interpolate these points with a surface so far by using the 'linearinterp' command in the curve fitting toolbox (see the attached figure).

Thanks for your help!

Answer 1

[Star Strider]

Try something like this —

rpm = rand(5,1);
dosage = rand(5,1)*0.1;
mass_of_leaves = rand(5,1);

B = [dosage mass_of_leaves ones(size(dosage))] \ rpm

B = 3×1

4.6860 0.3402 -0.0069

x = linspace(min(mass_of_leaves), max(mass_of_leaves), numel(mass_of_leaves));
y = linspace(min(dosage), max(dosage), numel(dosage));
z = [x(:) y(:) ones(size(x(:)))] * B;

figure
plot3(mass_of_leaves, dosage, rpm, 'p')
hold on
plot3(x, y, z, '-k')
hold off
grid on
xlabel('mass of leaves')
ylabel('dosage')
zlabel('rpm')

mdl = fitlm([mass_of_leaves dosage], rpm)

mdl = 
Linear regression model:
    y ~ 1 + x1 + x2

Estimated Coefficients:
                   Estimate        SE        tStat       pValue 
                   _________    ________    ________    ________

    (Intercept)    -0.006867    0.061301    -0.11202     0.92104
    x1               0.34018    0.086056       3.953    0.058441
    x2                 4.686     0.72903      6.4277    0.023359


Number of observations: 5, Error degrees of freedom: 2
Root Mean Squared Error: 0.0479
R-squared: 0.98,  Adjusted R-Squared: 0.96
F-statistic vs. constant model: 49.2, p-value = 0.0199

B = mdl.Coefficients.Estimate

B = 3×1

-0.0069 0.3402 4.6860

[ypred,yci] = predict(mdl, [x(:) y(:)]);

figure
plot3(mass_of_leaves, dosage, rpm, 'p')
hold on
plot3(x, y, ypred, '-k')
plot3(x, y, yci, '--k')
hold off
grid on
xlabel('mass of leaves')
ylabel('dosage')
zlabel('rpm')

.

[Annemarie]

Thanks a lot!

[Star Strider]

As always, my pleasure!

Answer 2

[Jonas]

have a look into the polyfitn() function on FEX

Answer 3

[Matt J]

You can use linear3dFit() from this FEX submission

https://www.mathworks.com/matlabcentral/fileexchange/87584-object-oriented-tools-for-fitting-conics-and-quadrics

Also, a 3D line is not given by a single equation, so it is not clear what you mean by "the coefficients".