Alpha shapes

Alpha shape of 2D/3D point set.

Description

Computes the basic Alpha shape of a 2D/3D point set by Delaunay triangulation.

OUTPUT:
- Area/Volume
- Triangulation of Alpha shape
- Boundary of Alpha shape
- Plot

• MATLAB release: MATLAB 7.11 (2010b)

[k Z]

Hi, nice code. Although the algorithm is useful when nonconvex data is used, I tested on convex data to check how robust it is. I try the sphere function. The volume of the sphere using alpha=Inf is not the same as the sphere volume, in this case the function convhulln computes more accurately the volume. It seems that summing the volume of all tetrahedron counts more that the overal volume, at least for this case. Check this please.

[Jonas Lundgren]

k Z, Thank you for the feedback. It seems to be a problem with DelaunayTri and nonunique data points. DelaunauyTri is also very slow for equally spaced data. I will switch to delaunayn and remove nonunique data points - when I have the time.

[Ajay]

Works well and easy to use, thanks much.

[HARI KRISHNAN]

thanks a lot

[Yuri Kotliarov]

It looks like the algorithm unequally connects point vertically and horizontally.
Try this data, for example:
n = 1000;
k = 10;
x = linspace(0,1,n)';
y(:,1) = k*x + randn(n,1) - k/2;
y(:,2) = -k*x + randn(n,1) + k/2;
xx = [x;x];
yy = y(:);
alphavol([xx yy], 0.5, 1);

[Jonas Lundgren]

Yuri, try the command "axis equal".

[ping]

 

[Borc]

 

[Borc]

Thanks for this nice code!
One Question:
There are some artefacts inside the volume (like rectangles). How could I avoid them?
As an example run the "3D Example - Ring" with the plotsettings 'FaceColor','r' and 'FaceAlpha',0.5 to see the artefacts inside the volume.
A solution would be very helpfully for me.
Thanks in advance

[Jonas Lundgren]

Borc, Yes I am aware of these artefacts in the 3D case. Thats why the code only delivers volume and not boundary faces. I will give this some thought.

[Jorge Leandro]

As I try to run one of your examples, Matlab (7.8.0 R2009) complains with the following message: "??? Error: File: alphavol.m Line: 78 Column: 3
Expression or statement is incorrect--possibly unbalanced (, {, or [."

Examining the referred line, I see:
[~,rcc] = circumcenters(TriRep(T,X));

It seems that Matlab cannot understand the tilde as an output value. I tried to change it to [cc rcc] = circumcenters... and now Matlab complains about line 194, which reads:
[~,p,r] = dmperm(C);
Again, the tilde seems to be the problem.
By the way, as far I as know, tilde is used as a negation operator in Matlab. What is its use here? Any clue on how to solve this problem?

Regards.

[Jonas Lundgren]

Jorge Leandro, tilde represents an unused argument. This notation was introduced in MATLAB 2009b. You can safely replace tilde by a dummy variable.

[Md Wahid]

hi, just a quick note. 'delaunay()' requires at least 2 inputs (x,y as a vector, probably couldnt take matrix). i was trying with the 2d example that provided in the code. changed in the 65th line as 'delaunay(X(:,1),X(:,2))'. now it works, the graph looks nice. thanks for the code. i didnt look inside or try with the theory yet, could be wrong! just to let you know...