Here's a different variation. The idea is to generate a bunch of circles, and then to cull those that intersect. For the culling phase, I used a halfway implementation of Sweep & Prune which speeds things up a bit as far as collision detection goes for large n.
- Generate points randomly
- Sort their
x-coordinates
- Save pairs whose
x-coordinates overlap for further testing, discard the rest
- For saved pairs, determine whether
y-coordinates overlap as well
- If so, then they potentially collide, so do the actual collision test on them
- If they collide, then discard one of the pair
The macro is \circles{n}{rad}{width}{height} and \circles{500}{.1}{10}{5} gives:
\documentclass{article}
\usepackage{luacode}
\usepackage{tikz}
\usetikzlibrary{backgrounds}
\begin{luacode*}
local rand = math.random
local abs = math.abs
local pts = {}
local tstpairs = {}
-- generate the points
local function genpts(n,x,y)
for i = 1,n do
pts[i]={}
pts[i][1] = rand()*x
pts[i][2] = rand()*y
end
end
-- for sorted pairs, check if x-coords overlap
-- if so, store the pair in table tstpairs
local function getpairs(t,r)
for i = 1,#t do
tstpairs[i] = {}
for j = 1,#t-i do
if t[i+j][1]-t[i][1]<2*r then
tstpairs[i][#tstpairs[i]+1]=i+j
else
break
end
end
end
end
-- this is the actual collision test
-- it's less expensive to use x^2+y^2<d^2 than sqrt(x^2+y^2)<d
local function testcol(a,b,r)
local x = pts[b][1]-pts[a][1]
local y = pts[b][2]-pts[a][2]
if x*x+y*y<4*r*r then
return true
end
end
-- this is a bit of a mess, deleting pairs on the fly was causing some
-- problems, so I had to include some checks "if pts[k1]..." etc.
local function delpairs(r)
for k1,v1 in pairs(tstpairs) do
if pts[k1] then
for k2,v2 in pairs(v1) do
if pts[v2] then
if abs(pts[v2][2]-pts[k1][2])<2*r then
if testcol(k1,v2,r) then
pts[v2]=nil
end
end
end
end
end
end
end
-- quickSort helper
local function partition(array, p, r)
local x = array[r][1]
local i = p - 1
for j = p, r - 1 do
if array[j][1] <= x then
i = i + 1
local temp = array[i][1]
array[i][1] = array[j][1]
array[j][1] = temp
end
end
local temp = array[i + 1][1]
array[i + 1][1] = array[r][1]
array[r][1] = temp
return i + 1
end
-- quickSort to sort by x
-- taken from https://github.com/akosma/CodeaSort/blob/master/QuickSort.lua
local function quickSort(array, p, r)
p = p or 1
r = r or #array
if p < r then
q = partition(array, p, r)
quickSort(array, p, q - 1)
quickSort(array, q + 1, r)
end
end
-- draw output
local function showout(n,r,x,y)
tex.print("\\begin{tikzpicture}[radius="..r.."cm]")
tex.print("\\draw[red](0,0) rectangle ("..x..","..y..");")
for k,v in pairs(pts) do
tex.print("\\draw ("..pts[k][1]..","..pts[k][2]..") circle ;")
end
tex.print("\\end{tikzpicture}")
end
-- wrapper
function circles(n,r,x,y)
genpts(n,x,y)
quickSort(pts)
getpairs(pts,r)
delpairs(r)
showout(n,r,x,y)
end
\end{luacode*}
\def\circles#1#2#3#4{\directlua{circles(#1,#2,#3,#4)}}
\begin{document}
\circles{500}{.1}{10}{5}
\end{document}
