How to calculate the volume of a facet using convhulln() function?

I am getting an error to calculate the volume of the square [0 0 0; 1 0 0; 1 1 0; 0 1 0], using convhulln, coming from qhullmx. Can you please help me on this? Thanks.

[John D'Errico]

What error? We cannot read your mind. If you are getting an error, then show the entire text of the error, complete with all information it generates.

Anyway, your subject talks about the volume of a facet, which makes no real sense anyway in context of the rest of your question.

Are you trying to compute the volume of that cube?

Finally, if you want help, it would be best if you tell us what version of MATLAB you are trying to do this under.

[Image Analyst]

What cube John? It looks just like a square in the z=0 plane. So it's not even really a 3-D volume. Even if it were tilted it would not enclose a 3D volume - it would still be a planar object - so using convhulln() is not appropriate.

Anyway, the answer is trivial = the volume is zero, and the surface area is 1 if you count one planar side of the square and 2 if you count the area "on top" of the square and "on bottom" of the square separately.

[John D'Errico]

oops. Not even a cube. Still asleep I guess. Yes, the enclosed volume is zero.

The issue is if the OP is looking to compute a 2-d "volume" of this object, in the plane of the square, thus the area. We don't really know what they are looking to get here.

Answer 1

[Image Analyst]

A facet does not have a volume. It will have an area. Perhaps you mean how to get the area. Try using polyarea() though be sure to have your vertices go in a sorted order around the perimeter or else you could get a negative area. (polyarea tells you that the area of a figure eight or bowtie is zero believe it or not.)

Answer 2

[Soumya Saxena]

I understand that you are getting an error with the "qhullmx" function while calling the "convhulln" function. You are defining 4 points in a 3D space as follows:

X= [0 0 0; 1 0 0; 1 1 0; 0 1 0]

However, all inputs have the 3rd dimension as 0. The z coordinate is 0. So,these become 4 points in the X-Y plane. This would represent a plane, not a 3D surface. If you put a non zero value in the in one of the 3rd dimension coordinates, the call should be error free. For example:

X= [0 0 0; 1 0 0; 1 1 0; 0 1 1]

convhulln(X)

The output should be:

2     3     1
4     2     1
3     4     1
4     3     2

Answer 3

[Abdul Suleman]

I thank Soumya Saxena and Image Analyst for their cooperative attitude. Indeed, I need to calculate the "area" of all facets of a given polytope. As far as I understand, polyarea() works for polygons only. Best, Abdul.