geometry (version 0.3-5)

delaunayn: Delaunay triangulation in N-dimensions

Description

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.

Usage

delaunayn(p, options = "", full = FALSE)

Arguments

p

p is an n-by-dim matrix. The rows of p represent n points in dim-dimensional space.

options

String containing extra options for the underlying Qhull command.(See the Qhull documentation (../doc/html/qdelaun.html) for the available options.)

full

Return all information asscoiated with triangulation as a list. At present this is the triangulation (tri), a vector of facet areas (areas) and a list of neighbours of each facet (neighbours).

Value

• The return matrix has m rows and dim+1 columns. It contains for each row a set of indices to the points, which describes a simplex of dimension dim. The 3D simplex is a tetrahedron.

Details

If neither of the QJ or Qt options are supplied, the Qt option is passed to Qhull. The Qt option ensures all Delaunay regions are simplical (e.g., triangles in 2-d). See ../doc/html/qdelaun.html for more details. Contrary to the Qhull documentation, no degenerate (zero area) regions are returned with the Qt option since the R function removes them from the triangulation.

For slient operation, specify the option Pp.

References

Barber, C.B., Dobkin, D.P., and Huhdanpaa, H.T., The Quickhull algorithm for convex hulls, ACM Trans. on Mathematical Software, Dec 1996.

http://www.qhull.org

See Also

tri.mesh, convhulln, surf.tri, distmesh2d

Examples

# example delaunayn
d <- c(-1,1)
pc <- as.matrix(rbind(expand.grid(d,d,d),0))
tc <- delaunayn(pc)

# example tetramesh
library(rgl)
rgl.viewpoint(60)
rgl.light(120,60)
tetramesh(tc,pc, alpha=0.9)