MATLAB Examples

# Convex hull of a large point set

## Introduction

In this example the convex hull of a relatively large point set is calculated. For this purpose, the initial point set is divided into smaller point sets. The convex hull of each point set is calculated, and finally the convex hull of all the resulting convex hulls is calculated.

## Initial data

Set the random number generator.

```rng(1); ```

Set the number of points.

```np=1e6; ```

Set the points the convex hull of which is to be calculated.

```points=rand(np,3); ```

## Processing

Set the number of the subsets into which the initial point set is divided.

```ni=10; ```

Calculate the convex hull of each point subset and assemble the resulting convex hulls.

```chull=[]; for i=1:ni fp=1+np/ni*(i-1); lp=np/ni*i; rp=(fp:lp)'; chulli=convhull_nd(points(rp,:),10); chull=[chull;unique(chulli(:))]; end ```

Drop out duplicate points in the convex hull assembly.

```chull=unique(chull); ```

Find the convex hull of the convex hull assembly.

```chullfinal=convhull_nd(points(chull,:)); ```

## Contact author

```(c) 2014 by George Papazafeiropoulos
First Lieutenant, Infrastructure Engineer, Hellenic Air Force
Civil Engineer, M.Sc., Ph.D. candidate, NTUA```

Website: http://users.ntua.gr/gpapazaf/