MATLAB Examples

# Voronoi vertices of a 3D gridded point set inside a cube

## Initial data

Set the random number generator.

```rng(1); ```

Set the point set the Voronoi vertices of which are calculated.

```d=[-1 1]; [x,y,z]=meshgrid(d,d,d); points=[x(:),y(:),z(:);zeros(1,3)]; ```

Perform random permutation to points to avoid infinite loops in convhull_nd.

```points=points+0.001*rand(size(points)); ```

## Processing

Find the vertices of the Voronoi diagram of the point set.

```V=voronoi_nd(points); ```

## Plots

Plot the initial point set and the Voronoi vertices defined by .

```figure('Name','Cube 3D mesh','NumberTitle','off') scatter3(points(:,1),points(:,2),points(:,3),... 'marker','o','MarkerEdgeColor',[0 0 1],'LineWidth',2) hold on scatter3(V(:,1),V(:,2),V(:,3),... 'marker','o','MarkerEdgeColor',[1 0.5 0],'LineWidth',2) xlabel('x','FontSize',13); ylabel('y','FontSize',13); zlabel('z','FontSize',13); title('Cube 3D mesh','FontSize',13) axis([-1.5 1.5 -1.5 1.5 -1.5 1.5]) ```

## 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/