convexHull

Class: delaunayTriangulation

Convex hull

Syntax

K = convexHull(DT) [K,v] = convexHull(DT)

K = convexHull(DT) returns the vertices of the convex hull.

[K,v] = convexHull(DT) also returns the area or volume bounded by the convex hull.

`DT`	A Delaunay triangulation, see `delaunayTriangulation`.

K

Convex hull vertices, returned as a matrix of vertex IDs. The shape of K depends on whether your triangulation is 2-D or 3-D:

When DT is 2-D, K is a column vector containing the sequence of vertex IDs around the convex hull.
When DT is 3-D, K is a triangulation connectivity list containing the triangles on the convex hull.

v

Area or volume bounded by the convex hull, returned as a scalar value.

A row number of the matrix, DT.Points. Use this ID to refer a specific vertex in the triangulation.

Create a Delaunay triangulation from a set of random points.

x = gallery('uniformdata',[10,1],0);
y = gallery('uniformdata',[10,1],1);
DT = delaunayTriangulation(x,y);

Calculate the convex hull.

k = convexHull(DT)

Plot the points and highlight the convex hull in red.

figure
plot(DT.Points(:,1),DT.Points(:,2), '.','markersize',10);
hold on
plot(DT.Points(k,1),DT.Points(k,2),'r')
hold off

Use convexHull to calculate the convex hull of a set of random points within a unit cube.

Create a Delaunay triangulation from a set of random points.

P = gallery('uniformdata',[25,3],1);
DT = delaunayTriangulation(P);

Calculate the convex hull and the volume bounded by the convex hull.

[K,v] = convexHull(DT);

Examine the volume.

v =

    0.3561

Plot the convex hull.

trisurf(K,DT.Points(:,1),DT.Points(:,2),DT.Points(:,3),...
       'FaceColor','cyan')