`convhulln`

Convex hull of points in n dimensions, as facets of point indices.

Category: Mathematics > Computational Geometry

Syntax

H = convhulln(P)

Returns the facets of the hull of the points in the rows of P.

[H, V] = convhulln(P)

Also returns the volume enclosed by the hull.

Description

Unlike convhull, which returns an ordered boundary loop in 2-D, convhulln returns an unordered list of facets, one per row. This general form is the same in any dimension. The point set must span the full dimension: coplanar points in 3-D, for instance, have no volume and raise an error.

Input arguments

P: Matrix with one point per row and one column per dimension.

Output arguments

H: One row per facet, listing the indices of the points on it: 2 columns in 2-D, 3 in 3-D.
V: Volume of the hull (area in 2-D).

Example

Faces and volume of a tetrahedron

P = [0 0 0; 1 0 0; 0 1 0; 0 0 1];
[H, V] = convhulln(P)

Output

H = 4×3

     2     3     1
     3     4     1
     4     2     1
     4     3     2
V = 0.1667

convhulln