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

Description

Returns information about the smallest convex complex of a set of input points in $N$ -dimensional space (the convex hull of the points). By default, indices to points forming the facets of the hull are returned; optionally normals to the facets and the generalised surface area and volume can be returned. This function interfaces the Qhull library.

Usage

convhulln(
  p,
  options = "Tv",
  output.options = NULL,
  return.non.triangulated.facets = FALSE
)

Value

By default (return.non.triangulated.facets is

FALSE), return an $M$ -by- $N$ matrix in which each row contains the indices of the points in p forming an

$N - 1$ -dimensional facet. e.g In 3 dimensions, there are 3 indices in each row describing the vertices of 2-dimensional triangles.

If return.non.triangulated.facets is TRUE then the number of columns equals the maximum number of vertices in a facet, and each row defines a polygon corresponding to a facet of the convex hull with its vertices followed by NAs until the end of the row.

If the output.options or options argument contains

FA or n, return a list with class convhulln

comprising the named elements:

p: The points passed to convnhulln
hull: The convex hull, represented as a matrix indexing p, as described above
area: If FA is specified, the generalised area of the hull. This is the surface area of a 3D hull or the length of the perimeter of a 2D hull. See ../doc/qhull/html/qh-optf.html#FA.
vol: If FA is specified, the generalised volume of the hull. This is volume of a 3D hull or the area of a 2D hull. See ../doc/qhull/html/qh-optf.html#FA.
normals: If n is specified, this is a matrix hyperplane normals with offsets. See ../doc/qhull/html/qh-opto.html#n.

Arguments

p: An $M$ -by- $N$ matrix. The rows of p represent $M$ points in $N$ -dimensional space.
options: String containing extra options for the underlying Qhull command; see details below and Qhull documentation at ../doc/qhull/html/qconvex.html#synopsis.
output.options: String containing Qhull options to generate extra output. Currently n (normals) and FA (generalised areas and volumes) are supported; see ‘Value’ for details. If output.options is TRUE, select all supported options.
return.non.triangulated.facets: logical defining whether the output facets should be triangulated; FALSE by default.

Author

Raoul Grasman, Robert B. Gramacy, Pavlo Mozharovskyi and David Sterratt david.c.sterratt@ed.ac.uk

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

Examples

Run this code

## Points in a sphere
ps <- matrix(rnorm(3000), ncol=3)
ps <- sqrt(3)*ps/drop(sqrt((ps^2) %*% rep(1, 3)))
ts.surf <- t(convhulln(ps))  # see the qhull documentations for the options
if (FALSE) {
rgl::triangles3d(ps[ts.surf,1],ps[ts.surf,2],ps[ts.surf,3],col="blue",alpha=.2)
for(i in 1:(8*360)) rgl::view3d(i/8)
}

## Square
pq <- rbox(0, C=0.5, D=2)
# Return indices only
convhulln(pq)
# Return convhulln object with normals, generalised area and volume
ch <- convhulln(pq, output.options=TRUE)
plot(ch)

## Cube
pc <- rbox(0, C=0.5, D=3)
# Return indices of triangles on surface
convhulln(pc)
# Return indices of squares on surface
convhulln(pc, return.non.triangulated.facets=TRUE)

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