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

In geometry: Mesh Generation and Surface Tessellation

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
)

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.

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.

Note

This function was originally a port of the Octave convhulln function written by Kai Habel.

See further notes in delaunayn.

Author(s)

Raoul Grasman, Robert B. Gramacy, Pavlo Mozharovskyi and David Sterratt [e-mail]

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

intersectn, delaunayn, surf.tri, convex.hull

Examples

## 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
## Not run: 
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)

## End(Not run)

## 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)

geometry documentation built on Sept. 11, 2024, 9 p.m.