# Excluded volume¶

This module implements a method to place a number of spheres that have no overlap.

This example shows use of the excluded volume with the placement of 1000 particles at random positions with a diameter of `1` in a cubic box with each edge being `50`:

```local random = math.random
math.randomseed(os.time())

local edge = 50
local box = mdsim.box{length = {edge, edge, edge}}
local excluded = mdsim.positions.excluded_volume{box = box, cell_length = 1}

local obstacles = {}
local diameter = 1
local repeats = 50
for i = 1, 1000 do
for j = 1, repeats do
local r = {edge * random(), edge * random(), edge * random()}
if excluded:place_sphere(r, diameter) then
obstacles[i] = r
excluded:exclude_sphere(r, diameter)
break
end
end
if not obstacles[i] then
error(("cannot place obstacle %d after %d repeats"):format(i, repeats))
end
end

local particle = mdsim.particle{dimension = box.dimension, particles = #obstacles}
particle.data["position"] = obstacles
```

Note

If one uses the random number generator from Lua , this should be done in conjunction with LuaJIT, only. Standard Lua uses the OS-dependent `rand()` function.

class `halmd.mdsim.positions.``excluded_volume`(args)

Construct excluded volume instance

Parameters: args (table) – keyword arguments args.box (number) – instance of `halmd.mdsim.box` args.cell_length (number) – cell length for internal binning (must not be smaller than largest sphere diameter)
`exclude_sphere`(centre, diameter)

Place a single sphere at `centre` with a diameter of `diameter`

`exclude_spheres`(centres, diameters)

Place a set of spheres with their respective centres and diameters

`place_spheres`(centre, diameter)

Test if a sphere at `centre` with diameter `diameter` can be placed without overlap with any other previously set sphere