Is there a better alternative to the convexhull function to produce 3D triangulation?

I have scanned a cube of known dimensions using Microsoft Kinect. I need to calculate the volume of the cube and compare it against the theoretical volume to determine accuracy. I have used convexhull to calculate the triangles and a function called faceNormal by David Legland to calculate normals. However, I notice that the mesh generated does not reflect the real shape because some faces of the cube are really not flat. If I use other software such as Geomagic the same point cloud looks much better after mesh generation. I have calculated the volume of the cube: 1. Reconstructed with Matlab = 0.936 litres 2. Reconstructed with Geomagic = 0.783 litres 3. Theoretical volume = 0.696 litres

In average the volume reconstructed with Matlab is 34% higher that the theoretical volume which is not great. I would like to know other alternatives to the convexhull function to calculate 3D triangulation.

Answer 1

[Matt J]

CONVHULL or CONVHULLN will calculate the volume directly from the input vertices, and return it as the 2nd output argument.

[Johanna Acosta]

Many thanksd for your answer. Based on your suggestion, I used CONVHULLN but the volume I get is still a 37% higher than the theoretical volume. As the object I scanned is not convex, is there any other function to calculate triagulation for non convex shapes?

[Matt J]

In your original post, you said you were scanning a cube (which would be convex). What is the shape then?

[Matt J]

You can apply CONVHULLN to the Delaunay triangulation of a nonconvex shape

      DT=DelaunayTri(V);   %The rows of V are the vertices

      T=DT.Triangulation;
      N=size(T,1);

      vols=zeros(1,N);

      for ii=1:N

       [~,vols(ii)]=convhulln(V(T(ii,:),:));

      end

      volume = sum(vols),

Answer 2

[Sean de Wolski]

Perhaps:

doc isosurface

But this will be much slower than convhulln