Delaunay triangulation in N dimensions
The Delaunay triangulation is a tessellation of the convex hull of the points such that no N-sphere defined by the N- triangles contains any other points from the set.
delaunayn(p, options = NULL, output.options = NULL, full = FALSE)
p |
An M-by-N matrix whose rows represent M points in N-dimensional space. |
options |
String containing extra control options for the underlying Qhull command; see the Qhull documentation (../doc/qhull/html/qdelaun.html) for the available options. The If |
output.options |
String containing Qhull options to control
output. Currently |
full |
Deprecated and will be removed in a future release.
Adds options |
If output.options is NULL (the default),
return the Delaunay triangulation as a matrix with M rows
and N+1 columns in which each row contains a set of
indices to the input points p. Thus each row describes a
simplex of dimension N, e.g. a triangle in 2D or a
tetrahedron in 3D.
If the output.options argument is TRUE or is a
string containing Fn or Fa, return a list with
class delaunayn comprising the named elements:
triThe Delaunay triangulation described above
areasIf TRUE or if Fa is specified, an
M-dimensional vector containing the generalised area of
each simplex (e.g. in 2D the areas of triangles; in 3D the volumes
of tetrahedra). See ../doc/qhull/html/qh-optf.html#Fa.
neighboursIf TRUE or if Fn is specified,
a list of neighbours of each simplex.
See ../doc/qhull/html/qh-optf.html#Fn
This function interfaces the Qhull library and is a port from Octave (http://www.octave.org) to R. Qhull computes convex hulls, Delaunay triangulations, halfspace intersections about a point, Voronoi diagrams, furthest-site Delaunay triangulations, and furthest-site Voronoi diagrams. It runs in 2D, 3D, 4D, and higher dimensions. It implements the Quickhull algorithm for computing the convex hull. Qhull handles round-off errors from floating point arithmetic. It computes volumes, surface areas, and approximations to the convex hull. See the Qhull documentation included in this distribution (the doc directory ../doc/qhull/index.html).
Qhull does not support constrained Delaunay triangulations, triangulation of non-convex surfaces, mesh generation of non-convex objects, or medium-sized inputs in 9D and higher. A rudimentary algorithm for mesh generation in non-convex regions using Delaunay triangulation is implemented in distmesh2d (currently only 2D).
Raoul Grasman and Robert B. Gramacy; based on the corresponding Octave sources of Kai Habel.
Barber, C.B., Dobkin, D.P., and Huhdanpaa, H.T., “The Quickhull algorithm for convex hulls,” ACM Trans. on Mathematical Software, Dec 1996.
# example delaunayn d <- c(-1,1) pc <- as.matrix(rbind(expand.grid(d,d,d),0)) tc <- delaunayn(pc) # example tetramesh ## Not run: rgl::rgl.viewpoint(60) rgl::rgl.light(120,60) tetramesh(tc,pc, alpha=0.9) ## End(Not run) tc1 <- delaunayn(pc, output.options="Fa") ## sum of generalised areas is total volume of cube sum(tc1$areas)
Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.