The R geometry package: Mesh generation and surface tessellation (original) (raw)

The R geometry package: Mesh generation and surface tessellation

The geometry package provides R with several geometry functions available in Octave, Matlab and SciPy. In particular, it provides an interface to the qhull library (which also underlies the corresponding Matlab and Octave functions). Currently only part of the qhull library is accessible and the interface for Delaunay triangulation differs from more modern versions of Matlab.

The geometry package also implements a simple technique to refine a given mesh and generate high quality meshes and surface triangulations. A description of the technique and a number of examples can be found at the site of its inventors Per-Olof Persson and Gilbert Strang.

Downloads

Original qhull sources are included in the distribution. The distribution is subject to this license. The non-qhull sources are subject to the GPL version 2 or higher.

Bugs and other issues

Please look at geometry’s Github tracker to view known bugs and to report bugs and feature requests.

Contribute

If you have ideas for functions, or functions you made and think would be of value to include in the geometry package (take into account that the package is called geometry and restricts itself to functions directly related to computational geometry), you can e-mail me david.c.sterratt@ed.ac.uk.

Tips and wrinkles

Obtaining volume and area of convex hulls

In older versions of the package, to obtain the volume and area of a convex hull, the procedure outlined in the next section had to be followed. Now it is possible to recover the area as follows:

> ps <-matrix(rnorm(30),,3)
> convhulln(ps, "FA")
> x
$hull
     [,1] [,2] [,3]
[1,]    6    9   10
[2,]    6    2    9
[3,]    7    6   10
[4,]    7    6    2
[5,]    1    9   10
[6,]    1    2    9
[7,]    1    7   10
[8,]    1    7    2

$area
[1] 32.55313

$vol
[1] 11.3083

Using the Qhull options

Qhull provides many options. For instance you may request the volume of a convex hull and its surface area by specifying the FSoption. Currently the output cannot be accessed directly. However, Qhull has the option TO filename which can be used to write the output to a file which can then be parsed into R again. For instance, if you want to compute the volume of a convex hull of a set of points, if you have a matrix with 3 columns,

> ps <-matrix(rnorm(30),,3)

say, that might be something like:

> x <- convhulln(ps,"FS TO 'bla.txt'"); # use of the 'TO filename' option

This command created the text file bla.txt that contains the requested output (i.e. the output specified by the Qhull options). For the Qhull option FS this is the following: [from the doc] “The first line consists of the number of integers (“0”). The second line consists of the number of reals (“2”), followed by the total facet area, and the total volume. Later versions of Qhull may produce additional integers or reals.” You can then parse the text in the file according to your needs; in your case it will be something like:

> qh.outp <- scan("bla.txt")
> volume <- qh.outp[4]