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

36 次查看（过去 30 天）
Alberto Acri
Alberto Acri 2023-9-29
编辑： Matt J 2023-9-30
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?

请先登录，再回答此问题。

采纳的回答

Bruno Luong
Bruno Luong 2023-9-29
Ran in:
load('V1_in.mat')
[~,~,V]=svd( V_1-mean(V_1));
N=V(:,3)
N = 3×1
0.2147 -0.1801 0.9599
  1 个评论
Bruno Luong
Bruno Luong 2023-9-29
Ran in:
% 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

请先登录，再进行评论。

更多回答（3 个）

Torsten
Torsten 2023-9-29
编辑：Torsten 2023-9-29
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).
Matthew Blomquist
Matthew Blomquist 2023-9-29
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!
Matt J
Matt J 2023-9-30
编辑：Matt J 2023-9-30
Use planarFit() from this FEX package,
https://www.mathworks.com/matlabcentral/fileexchange/87584-object-oriented-tools-for-fitting-conics-and-quadrics
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);
axis padded;
view(-70,15);drawnow

类别

在 Help Center 和 File Exchange 中查找有关 Data Distribution Plots 的更多信息

标签

产品


版本

R2021b

Community Treasure Hunt

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

Start Hunting!

Translated by