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convexHull - Class: DelaunayTri

Convex hull

Syntax

K = convexHull(DT) [K AV] = convexHull(DT)

Description

K = convexHull(DT) returns the indices into the array of points DT.X that correspond to the vertices of the convex hull.

[K AV] = convexHull(DT) returns the convex hull and the area or volume bounded by the convex hull.

Inputs

`DT`	Delaunay triangulation.

Outputs

`K`	If the points lie in 2-D space, `K` is a column vector of length `numf`. Otherwise `K` is a matrix of size `numf`-by-`ndim`, `numf` being the number of facets in the convex hull, and `ndim` the dimension of the space where the points reside.
`AV`	The area or volume of the convex hull.

Definitions

The convex hull of a set of points X is the smallest convex polygon (or polyhedron in higher dimensions) containing all of the points of X.

Examples

Example 1

Compute the convex hull of a set of random points located within a unit square in 2-D space.

x = rand(10,1);
y = rand(10,1);
dt = DelaunayTri(x,y);
k = convexHull(dt);
plot(x,y, '.', 'markersize',10); 
hold on;
plot(x(k), y(k), 'r'); 
hold off;

Example 2

Compute the convex hull of a set of random points located within a unit cube in 3-D space and the volume bounded by the convex hull.

X = rand(25,3);
dt = DelaunayTri(X);
[ch v] = convexHull(dt);
trisurf(ch, X(:,1),X(:,2),X(:,3), 'FaceColor', 'cyan')