Difference between convhull() and convhulln()?

In MATLAB's function libraries, there are 2 functions that achieve descriptively the same purpose: 1) convhull() 2) convhulln()

I notice that these 2, when applied to the same set of input, gives me slightly different answers for volume (negligible error, but I am confused why there is a difference since I thought the algorithm gives an EXACT volume). And for some sets of vertices, convhulln() outputs an error while convhull() works.

Can someone explain to me the difference between the two?

Answer 1

[Walter Roberson]

convhulln can operate in higher dimensional spaces.

Negligible error would be due to floating point roundoff, probably.

Answer 2

[Image Analyst]

convhull() operates on 2D data - points in an infinitely thin plane. How are you computing the volume from that? It won't have a volume. Or a volume of zero.

convhulln operates on higher dimensional data. In 3D it would be like putting a tight balloon around your points. It would return the points that are "pointy" in your balloon envelope. How do you compute the volume from that?

[david dang]

I've been computing the volume with convhull() just fine http://www.mathworks.com/help/matlab/ref/convhull.html It has a volume output. It works in 3-D

Answer 3

[John D'Errico]

Welcome to the wonderful, wacky world of floating point arithmetic.

There is no such thing as an "exact" computation when done in floating point arithmetic by two distinct code sequences. That you get subtly (though negligibly) different results when two different computations are applied is no surprise at all. Many such mathematically, theoretically identical operations, when implemented in floating point arithmetic, will fail to yield numerically identical results.

Answer 4

[Witek Jachimczyk]

Pls. have a look at this page:

https://www.mathworks.com/help/matlab/math/computing-the-convex-hull.html

This is the relevant passage:

"MATLAB provides the convhulln function to support the computation of convex hulls and hypervolumes in higher dimensions. Though convhulln supports N-D, problems in more than 10 dimensions present challenges due to the rapidly growing memory requirements.

The convhull function is superior to convhulln in 2-D and 3-D as it is more robust and gives better performance."

HTH,

Witek