Wall support

The structure of Voro++ makes it easy to handle complicated boundary conditions by adding in additional plane cuts due to walls. The code has built-in support for plane, cylindrical, and spherical walls, and extra ones can be easily coded as derived C++ classes.

1. cylinder.cc - this example creates a cylinder wall object, and imports a

test packing from "pack_cylinder". It outputs POV-Ray files for particles at cylinder_p.pov, and Voronoi cells at cylinder_v.pov. These can be rendered using the scene file cylinder.pov with the command:

povray +W600 +H800 +A0.3 +Ocylinder.png cylinder.pov

2. frustum.cc - this example creates a frustum by making use of a cone wall

object. It fills the frustum with 500 random points, and outputs the Voronoi cells in gnuplot format. Due to the conical wall being approximated with plane cuts, some inaccuracies can be seen.

3. tetrahedron.cc - this example creates a tetrahedron with four planes, and

randomly inserts particles into it, using the point_inside() function to determine whether the points are within the walls. It outputs the particles to tetrahedron_p.gnu, and the Voronoi cells to tetrahedron_v.gnu. These can be visualized in gnuplot using:

splot 'tetrahedron_p.gnu' with points, 'tetrahedron_v.gnu' with lines

Currently, the curved walls are made by a single approximating plane cut. This provides good results when particles are pressed against the walls, but is inaccurate it the particles are sparse. It would be possible to improve this by approximating the curved surface with a sequence of planes rather than just one.

The code currently only supports walls which lead to convex computational domains, since a non-convex domain would lead to non-convex cells. To correctly handle these cases, the easiest way would be to divide the domain into several convex sub-domains, carry out a calculation in each, and then glue the cells that cross the divisions. Native support for non-convex domains may be added in a later version.

4. torus.cc - this example shows how to create a custom wall object, derived

from the pure virtual "wall" class. A routine is written that can cut a Voronoi cell in response to a torus centered on the origin that is aligned with the xy plane. The program writes POV-Ray files of the particles and Voronoi cells, and these can be rendered using the following command:

povray +W800 +H600 +A0.3 +Otorus.png torus.pov