## random_points.cc – The Voronoi diagram for random points in a cube

This example code demonstrates a basic use of the `container`

class, that is used to hold a particle system prior to the computation of
Voronoi cells. In lines 11 to 14 of the code, the boundaries of the container
are defined, and the total volume is stored in the variable `cvol`

.
For computational efficiency, the container is divided up into a rectangular
grid of regions, each of which store the particles in their part of the
container. Line 17 of the code creates six blocks in each coordinate, making
216 in total.

On line 31 the container object is created. The first six arguments are the coordinate boundaries. The next three set the computational grid size. The following three set whether each direction is periodic or not; for this example we use non-periodic boundary conditions. The final entry allocates initial space for eight particles per region, although a precise value of this is typically not necessary, as the code can dynamically allocate more.

In lines 36 to 41, twenty particles are added to the container at random
positions using the `put()`

routine. This function computes which region
the particle is in, and adds its position and a numerical ID (passed in the
variable `i`

) to that region.

On line 44, the `sum_cell_volumes()`

routine is called, that
calculates all of the Voronoi cells, and sums their volumes. Since the cells
should exactly partition the container, this should exactly match the value
of the container volume stored`cvol`

. The output of the code is:

`Container volume : 8`

Voronoi volume : 8

Difference : -1.77636e-15

Voronoi volume : 8

Difference : -1.77636e-15

The difference on the order of 10^{-15} is due to rounding error, as
the double-precision floating point numbers used in the calculation typically store
around this much accuracy.

In the remaining part of the code, the particle positions and their Voronoi cells are outputted to files that can be read by Gnuplot, using the command:

`splot "random_points_p.gnu" u 2:3:4, "random_points_v.gnu" with lines`

## Code listing

1: // Voronoi calculation example code 2: // 3: // Author : Chris H. Rycroft (LBL / UC Berkeley) 4: // Email : chr@alum.mit.edu 5: // Date : August 30th 2011 6: 7: #include "voro++.hh" 8: using namespace voro; 9: 10: // Set up constants for the container geometry 11: const double x_min=-1,x_max=1; 12: const double y_min=-1,y_max=1; 13: const double z_min=-1,z_max=1; 14: const double cvol=(x_max-x_min)*(y_max-y_min)*(x_max-x_min); 15: 16: // Set up the number of blocks that the container is divided into 17: const int n_x=6,n_y=6,n_z=6; 18: 19: // Set the number of particles that are going to be randomly introduced 20: const int particles=20; 21: 22: // This function returns a random double between 0 and 1 23: double rnd() {return double(rand())/RAND_MAX;} 24: 25: int main() { 26: int i; 27: double x,y,z; 28: 29: // Create a container with the geometry given above, and make it 30: // non-periodic in each of the three coordinates. Allocate space for 31: // eight particles within each computational block 32: container con(x_min,x_max,y_min,y_max,z_min,z_max,n_x,n_y,n_z, 33: false,false,false,8); 34: 35: // Randomly add particles into the container 36: for(i=0;i<particles;i++) { 37: x=x_min+rnd()*(x_max-x_min); 38: y=y_min+rnd()*(y_max-y_min); 39: z=z_min+rnd()*(z_max-z_min); 40: con.put(i,x,y,z); 41: } 42: 43: // Sum up the volumes, and check that this matches the container volume 44: double vvol=con.sum_cell_volumes(); 45: printf("Container volume : %g\n" 46: "Voronoi volume : %g\n" 47: "Difference : %g\n",cvol,vvol,vvol-cvol); 48: 49: // Output the particle positions in gnuplot format 50: con.draw_particles("random_points_p.gnu"); 51: 52: // Output the Voronoi cells in gnuplot format 53: con.draw_cells_gnuplot("random_points_v.gnu"); 54: }