# calculate the normal for a plane passing through more than three points

11 visualizzazioni (ultimi 30 giorni)
Alberto Acri il 29 Set 2023
Modificato: Matt J il 30 Set 2023
Hi! I have a plane passing through three points (triangular plane) and from which I determine the normal.
P = [ 0.034488 0.036484 0.006912; ...
0.019104 0.055041 0.047894; ...
-0.008596 0.123650 0.033786];
N = cross(P(1,:) - P(2,:), P(3,:) - P(2,:));
N = N/norm(N);
Is it possible to do the same thing with a circular plane ('V1_in')?
• If it is not possible to do this, how can I create the matrix equal to 'P' using the 'V1_in' plane?
##### 0 CommentiMostra -2 commenti meno recentiNascondi -2 commenti meno recenti

Accedi per commentare.

### Risposta accettata

Bruno Luong il 29 Set 2023
[~,~,V]=svd( V_1-mean(V_1));
N=V(:,3)
N = 3×1
0.2147 -0.1801 0.9599
##### 1 CommentoMostra -1 commenti meno recentiNascondi -1 commenti meno recenti
Bruno Luong il 29 Set 2023
% Check againts other method for 3 points
P = [ 0.034488 0.036484 0.006912; ...
0.019104 0.055041 0.047894; ...
-0.008596 0.123650 0.033786];
N = cross(P(1,:) - P(2,:), P(3,:) - P(2,:));
N = N/norm(N)
N = 1×3
0.9037 0.3976 0.1592
[~,~,V]=svd( P-mean(P));
N=V(:,3)% opposite sign, which is arbitrary choice for a 2D plane
N = 3×1
-0.9037 -0.3976 -0.1592

Accedi per commentare.

### Più risposte (3)

Torsten il 29 Set 2023
Modificato: Torsten il 29 Set 2023
If the points in V1_in.mat all lie in a common plane, you can arbitrarily pick three points and define these points as P.
If the points are only "approximately" in a common plane, you have to determine this plane via regression (like @Bruno Luong did).
##### 0 CommentiMostra -2 commenti meno recentiNascondi -2 commenti meno recenti

Accedi per commentare.

Matthew Blomquist il 29 Set 2023
Hi Alberto,
If you think of the circular plane as a collection of points with coordinates (x, y, z), you can create a bunch of "triangular planes" by selecting any three coordinates to create a triangle. If all of the coordinates lie in the same plane, computing the normal of any triangular plane will be the same as computing the normal of the circular plane.
So, you can use the same code, but substitute three points from the circular plane (in V1_in) to your P matrix. Also, I often use the functions "patch" and "quiver3" to help visualize the normals.
Hope that helps!
##### 0 CommentiMostra -2 commenti meno recentiNascondi -2 commenti meno recenti

Accedi per commentare.

Matt J il 30 Set 2023
Modificato: Matt J il 30 Set 2023
Use planarFit() from this FEX package,
fitObj=planarFit(V_1')
fitObj =
planarFit with properties:
normal: [0.2147 -0.1801 0.9599]
distance: 82.5216
[hL,hD]=plot(fitObj); %Visualize the fit
legend([hL,hD],'Plane fit', 'XYZ samples', 'Location','northoutside','FontSize',15);
view(-70,15);drawnow
##### 0 CommentiMostra -2 commenti meno recentiNascondi -2 commenti meno recenti

Accedi per commentare.

### Categorie

Scopri di più su Scatter Plots in Help Center e File Exchange

R2021b

### Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by