Find a plane that is tangent to a part of the 3D model

Hello!

I have got a 3D model and I want to find a 2D plane that is tangent to the bottom of my 3D model. The bottom is made up of three sphere-like structures spliced together. I want to know how to find such a plane to make it tangent to the bottom? There should be three tangent points.

The following figure attaches my 3D model and schematic diagram

[Matt J]

What form does the input data take?

[Tingting]

I had stl format. Here is my model, thank you very much!

[Tingting]

Let me explain in detail. In my previous work, I have obtained the 3D model of the aortic root of the human body through automatic segmentation of the neural network. This plane is called the aortic annulus plane. My task is to search for this plane to obtain the aortic annulus (the circle obtained by three tangent points) diameter. Thank you for your attention!

Answer 1

[Matt J]

Obtain all the mesh vertices from your stl file in V. Then, compute the facet areas and normals of the convex hull with,

k=convhull(V);

dVa=V(k(:,2),:)-V(k(:,1),:);
dVb=V(k(:,3),:)-V(k(:,1),:);

C=cross(dVa,dVb);

Areas=vecnorm(C,2,2);   %facet areas
Normals=normalize(C,2,'norm'); %facet normals

From your diagram, your three spheres look to be within about 10 degrees of the direction vector d=[2 0 1]/sqrt(3), so,

 d=[2 0 1]'/sqrt(3);
 
 subset=find(acosd(abs(Normals*d))<30);
 
[~,i]=max(Areas(subset));

kp=k(subset(i),:);

Vp=V(kp,:); %The 3 annulus vertices

[Tingting]

Thank you for your reply!

Firstly, I showed the stl model, and it seems right, but the model is far away from (0,0,0)

data = stlread('label1.stl');

trimesh(data)

And Then I obtained all the mesh vertices from stl file,

V=data.Points;

I don't know if the mesh vertices I got is correct, but it seems to be correct. So how do I pan this model so that it is close to the origin in order to evaluate the direction of the direction vector d.

[Matt J]

There are panning and rotation tools in the figure menu bar, but I don't think you have to be terribly exact about d.

[Tingting]

Thanks Matt J, you are very patient. But when I run the code, Vp is none.

I think, is this unreasonable setting of d?.

Then I manually marked three points on the 3D model, as shown in the figure.

These three points establishes a plane, and the normal vector is found.

d= cross(p2 - p1, p3 - p1);

I got d=[390,-70,250]. And I approximate to [11,-2,7]

d=[11 -2 7]'/sqrt(174);

However, Vp is still empty. Excuse me, do you know the reason? Here is variables in the workspace.

[Matt J]

Here is variables in the workspace.

Could you attach V in a .mat file?

[Tingting]

Here is my .mat file, thank you for your help!

[Matt J]

Fixing this line seems to make it work,

 subset=find(acosd(abs(Normals*d))<30);

[Tingting]

Thank you very much! It really works!

[Tingting]

Excuse me, could you please share your code here, I don't know how to show mesh vertices .

[Matt J]

I just used scatter3. You could have used tetramesh() or plot3() or anything you like.

load meshvertices
XYZ=num2cell(V,1)';
scatter3(XYZ{:},'filled','MarkerEdgeColor','none','MarkerFaceAlpha',0.1)