# Update of the ‘cgalMeshes’ package

**Saturn Elephant**, and kindly contributed to R-bloggers]. (You can report issue about the content on this page here)

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I made some progress on the **cgalMeshes** package, that I
introduced
here. The new version is not on CRAN yet.

In particular, one can know assign some properties to the meshes (the
`cgalMesh`

objects). One can assign some face properties:
colors and scalars, and some vertex properties: colors, scalars, and
normals. Actually a color can be any character string, but if you really
set some colors, and you write the mesh to a file, then you’ll retrieve
the colors in this file. Some of these properties are preserved by
certain operations on the mesh. For example, all properties are
preserved when one splits a mesh into connected components. This was my
original motivation by the way, more precisely I wanted to retrieve the
normals of the mesh in its connected components, because I had a mesh
made with the **rmarchingcubes** package and then it had
very good normals (the normals returned by the
**rmarchingcubes** package are obtained by an approximation
of the gradient of the function defining the isosurface). The union of
two meshes preserves the face properties of the two meshes. This is nice
when one does not want to lose the colors.

Here is a couple of new features. Let’s start by the new methods of the
`cgalMesh`

objects. The `$clip()`

method now
returns two meshes: the clipped mesh and the modified clipping mesh (it
is modified by a corefinement). These two meshes inherit the colors of
the original meshes. For example, here is the result one obtains by
clipping a cylinder to another cylinder, and then clipping the resulting
mesh by a third cylinder, with different colors for the three cylinders:

See this page by Paul Bourke for more fun with intersecting cylinders. I’ve tried to do something similar to the intersection of a bunch of random cylinders but my implementation is too time-consuming.

The `$fillBoundaryHole()`

method allows to fill the holes of
a mesh. There’s one option, `fair`

, allowing to request a
smooth hole filling or a flat hole filling. Here is an example of a
sphere with a hole, filled with the option `fair=TRUE`

and
`fair=FALSE`

:

Also some subdivision and deformation methods are available now. Below is a coarse mesh of a Hopf torus and the mesh obtained after two iterations of the Loop subdivision:

Now let’s see some new functions of the package. The
`algebraicMesh()`

function allows to construct a mesh of an
algebraic surface, that is to say an isosurface of the form
\(P(x, y, z) = 0\) where
\(P\) is a polynomial. Of course it is
possible to make an isosurface
\(f(x, y, z) = 0\) where
\(f\) is arbitrary with
**CGAL** but I don’t know an efficient way to pass a
function from R to C++. Here is the Barth decic obtained with this
function:

The algorithm used by **CGAL** is not the marching cubes
algorithm. Actually, so far, I didn’t observe any advantage of this
algorithm as compared to the marching cubes algorithm (if you know such
an advantage, please leave an
answer here).

There is now the `convexHull()`

function in the package, and
also `convexHullsIntersection`

to (fastly) compute a mesh of
the intersection of some convex hulls. I used it to get the intersection
of the
compound of five tetrahedra:

The `sphericalTriangle()`

function allows to get a mesh of a
spherical triangle. Here is a spherical icosahedron:

Hopefully the package will pass the CRAN checks.

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