Calculation of the surface area of a generic solid

Hello, everyone,

I am having problems calculating the surface of a generic 3d solid in stl format. How can I do this? (For the volume I am using these commands:

-mesh = generateMesh(model);

-mv = volume(mesh))

Answer 1

[Matt J]

One way might be to read the stl file into a triangulation object using stlread. With the triangulation object, you can use freeBoundary to obtain the surface facets of the mesh. It should then be a simple matter to compute the facet areas and add them up.

[Lorenzo Marta]

I have already tried to carry out this procedure:

• fv = stlread('myFile.stl');
• F= freeBoundary(fv);

But I get that F is a 0*0 double matrix

Do I have to do some triangulation between the 2?

[Matt J]

It might mean that your mesh is not solid, and therefore consists of triangles rather than tetrahedrons. If you have a triangulation of the surface already, you do not need to use freeBoundary. Just use the surface triangles tabulated in fv.

[Lorenzo Marta]

Yes, the available mesh may not be solid. But then I don't understand how to exploit the info in fv, since that file consists of 2 matrices, the first containing the coordinates of the points, the other one the connectivity list

[Matt J]

Each row of the connectivity list corresponds to one of the surface facets. It contains the row numbers where the vertices of the facet are to be found in TR.Points. So, for example if TR.T(m,:)=[3,5,7], then the vertices of the m-th facet are TR.Points([3,5,7], :).

[Lorenzo Marta]

OK, so I just loop over the rows of the connectivity matrix, referring to the 3 indicated vertices from which I calculate the area of the individual triangle?

[Matt J]

Yes.

[Matt J]

You could probably vectorize the area calculation as well. For example, if there are N facets and you organize the triangle vertices into three 3xN arrays A,B,C the total area could be computed with,

Area=sum( vecnorm( cross(B-A,C-A) ,2,1)  )/2;