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

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Abdul Suleman 2016-12-18

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回答： Abdul Suleman 2016-12-22

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.

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Image Analyst 2016-12-18

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 2016-12-18

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.

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Answer 1

Image Analyst 2016-12-22

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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.)

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Answer 2

Soumya Saxena 2016-12-21

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在 MATLAB Online 中打开

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:

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Answer 3

Abdul Suleman 2016-12-22

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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.