Calculating volume of a tetramesh

Hi!

I am trying to calculate the volume of a complex 3D shape made with the function tetramesh. Does someone know if there is a function for that?

Thank you!

Answer 1

[Ameer Hamza]

As explained in Walter's answer here: https://www.mathworks.com/matlabcentral/answers/22394-how-to-get-the-volume-information-out-of-a-mesh#answer_29470 following two FEX packages will be helpful

https://www.mathworks.com/matlabcentral/fileexchange/15221-triangulationvolume

https://www.mathworks.com/matlabcentral/fileexchange/27830-mesh2tetra

Answer 2

[Ellen]

Thank you for your answer!

I tried the Mesh2Tetra on a 1x1x1 cube as follows:

A = importdata('cube.txt');
x = A(:,1);
y = A(:,2);
z = A(:,3);
k=boundary([x,y,z]);
Tc = Mesh2Tetra([x y z],k);

which gives me the correct results:

Swap Face orientation
Volume inside boundary mesh is : 1
.
Start Delaunay to Tetrahedrons
-Number of objects : 1
-Starting Volume : 1
-Processing object : 1
-Number of Faces : 12
-Object Volume : 1

However, it also gives me a lot of errors which makes me wonder what I did wrong:

Error using builtin
QH6154 qhull precision error: initial facet 1 is coplanar with the interior point
ERRONEOUS FACET:

While executing:  | qhull d Qt Qbb Qc
Options selected for Qhull 2010.1 2010/01/14:
  run-id 1670392318  delaunay  Qtriangulate  Qbbound-last  Qcoplanar-keep
  _pre-merge  _zero-centrum  Qinterior-keep  Pgood  _max-width  1
  Error-roundoff 2e-15  _one-merge 1.8e-14  Visible-distance 1.2e-14
  U-coplanar-distance 1.2e-14  Width-outside 2.4e-14  _wide-facet 7.3e-14

The input to qhull appears to be less than 4 dimensional, or a
computation has overflowed.

Qhull could not construct a clearly convex simplex from points:

The center point is coplanar with a facet, or a vertex is coplanar
with a neighboring facet.  The maximum round off error for
computing distances is 2e-15.  The center point, facets and distances
to the center point are as follows:


facet p4 p1 p2 p0 distance=    0
facet p6 p1 p2 p0 distance=    0
facet p6 p4 p2 p0 distance= -0.14
facet p6 p4 p1 p0 distance= -1.1e-16
facet p6 p4 p1 p2 distance= -5.6e-17

These points either have a maximum or minimum x-coordinate, or
they maximize the determinant for k coordinates.  Trial points
are first selected from points that maximize a coordinate.

The min and max coordinates for each dimension are:
  0:         0         1  difference=    1
  1:         0         1  difference=    1
  2:         0         1  difference=    1
  3:         0         1  difference=    1

If the input should be full dimensional, you have several options that
may determine an initial simplex:
  - use 'QJ'  to joggle the input and make it full dimensional
  - use 'QbB' to scale the points to the unit cube
  - use 'QR0' to randomly rotate the input for different maximum points
  - use 'Qs'  to search all points for the initial simplex
  - use 'En'  to specify a maximum roundoff error less than 2e-15.
  - trace execution with 'T3' to see the determinant for each point.

If the input is lower dimensional:
  - use 'QJ' to joggle the input and make it full dimensional
  - use 'Qbk:0Bk:0' to delete coordinate k from the input.  You should
    pick the coordinate with the least range.  The hull will have the
    correct topology.
  - determine the flat containing the points, rotate the points
    into a coordinate plane, and delete the other coordinates.
  - add one or more points to make the input full dimensional.


This is a Delaunay triangulation and the input is co-circular or co-spherical:
  - use 'Qz' to add a point "at infinity" (i.e., above the paraboloid)
  - or use 'QJ' to joggle the input and avoid co-circular data


Error in qhullmx

Error in delaunayn (line 101)
t = qhullmx(x', 'd ', opt);

Error in DelaunayInside3D (line 51)
    T2 = delaunayn(V2);

Error in Mesh2Tetra (line 119)
[T F]=DelaunayInside3D(V,F,struct('verbose',options.verbose));

Error in forumquestioncode (line 21)
Tc = Mesh2Tetra([x y z],k);

I also tried the triangulationVolume as follows:

A = importdata('cube.txt');
x = A(:,1);
y = A(:,2);
z = A(:,3);
tri = delaunay([x y z]);
[volume,area] = triangulationVolume(tri,x,y,z);

However this gives me an incorrect result: a volume of 0.3333 which should be 1.

Can someone help me with this?

[M.S. Khan]

attach file of your coordinates please. So we can try to calculate.