geometry (version 0.3-6)

convhulln: Compute smallest convex hull that encloses a set of points

Description

Returns an index matrix to the points of simplices (“triangles”) that form the smallest convex simplicial complex of a set of input points in N-dimensional space. This function interfaces the Qhull library.

Usage

convhulln(p, options = "Tv")

Arguments

p

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 details below and Qhull documentation at http://www.qhull.org/html/qconvex.htm#synopsis.

Value

An m-by-dim index matrix of which each row defines a dim-dimensional “triangle”. The indices refer to the rows in p. If the option FA is provided, then the output is a list with entries hull containing the matrix mentioned above, and area and vol with the generalised area and volume of the hull described by the matrix. When applying convhulln to a 3D object, these have the conventional meanings: vol is the volume of enclosed by the hull and area is the total area of the facets comprising the hull's surface. However, in 2D the facets of the hull are the lines of the perimeter. Thus area is the length of the perimeter and vol is the area enclosed.

Details

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

convex.hull, delaunayn, surf.tri, distmesh2d

Examples

# NOT RUN {
# example convhulln
# ==> see also surf.tri to avoid unwanted messages printed to the console by qhull
ps <- matrix(rnorm(3000), ncol=3)  # generate points on a sphere
ps <- sqrt(3)*ps/drop(sqrt((ps^2) %*% rep(1, 3)))
ts.surf <- t(convhulln(ps))  # see the qhull documentations for the options
# }
# NOT RUN {
rgl.triangles(ps[ts.surf,1],ps[ts.surf,2],ps[ts.surf,3],col="blue",alpha=.2)
for(i in 1:(8*360)) rgl.viewpoint(i/8)
# }