`boundary`

Boundary of a set of 2-D or 3-D points, between the convex hull and a tight outline.

Category: Mathematics > Computational Geometry

Syntax

k = boundary(x, y)

Indices of the points on the boundary of 2-D points, with the default shrink factor 0.5.

k = boundary(x, y, s)

Uses the shrink factor s between 0 and 1.

k = boundary(P)

Points given as the rows of a matrix with two or three columns.

[k, v] = boundary(___)

Also returns the area (2-D) or volume (3-D) enclosed.

Description

boundary returns a polygon around the points that can be concave, unlike convhull. The shrink factor decides how closely the outline follows the points: with 0 the result equals the convex hull, and larger values let it enter concave notches.

The points are returned as indices into the input rather than coordinates, so [x(k) y(k)] gives the outline's vertices.

Input arguments

x, y: Column vectors of point coordinates.
s: Shrink factor. 0 gives the convex hull and 1 the most compact boundary.

Output arguments

k: Column vector of point indices. In 2-D it traces the polygon and the first index is repeated at the end.
v: Area or volume of the region.

Example

Concave outline versus convex hull

x = [0 2 2 1 1 0 0.5 1.5 0.5 0.5]';
y = [0 0 1 1 2 2 0.5 0.5 1.5 1.0]';
k0 = boundary(x, y, 0)'
[k1, v] = boundary(x, y, 1);
k1'
v

Output

k0 = 1×6

     1     2     3     5     6     1
ans = 1×9

     1     7     8     2     3     5     6    10     1
v = 2.2500

boundary