Re: How can I compare picture variables in metapost?

[Aditya Mahajan <adityam@umich.edu>]

On Tue, 5 May 2009, Zhichu Chen wrote:

> On Tue, May 5, 2009 at 11:04 PM, Taco Hoekwater <taco@elvenkind.com> wrote:
>> Zhichu Chen wrote:
>>>
>>> What I want exactly is how to determine if there's anything on
>>> some region of the picture. I need this to test if the random
>>> point I picked is useful.
>>
>> That is easy to answer: you can't (well, not unless you invest a *lot*
>> of effort into creating a bitmap edge structure).
> Well, quick and pain.
>>
>> However what you can do is ask metapost to calculate intersectionpoints
>> with (the most likely ones of) the already existing objects. This may
>> be the easiest solution (even though it will be so slow that for large
>> numbers of items you may be forced to start a division tree).
>>
>> The core trick is that you randomly place a circle with random radius
>> inside an x-y field, and you keep those paths/pictures in an array. For
>> each newlyt generated circle, you look for an intersection with all the
>> already existing ones (and the rectangle borders) and keep trying
>> to re-place it until there are no more collisions.
>
> Seems that I don't have too many choices. Maybe using lua to do the
> math and throwing the result to metapost is faster? I think I can do
> this, but I don't know how. The documents are a little limited.

Here is an attempt with lua.

Aditya

\startluacode

third = third or {}

function third.generate (x,y,r)
   return { ["center"] = {math.random() * x, math.random()*y}
          , ["radius"] = math.random() * r }
end

function third.distance (p1, p2)
   return math.sqrt( (p1[1] - p2[1])^2 + (p1[2] - p2[2])^2 )
end

function third.feasible (c, list)
   if list then
   for i,v in pairs(list) do
     if third.distance (c["center"], v["center"]) < c["radius"] + v["radius"] then
       return false
     end
   end
   end
   return true
end

function third.add_circle (x,y,r,list)
   local c = {}
   repeat
     c = third.generate(x,y,r)
   until third.feasible(c,list)
   return c
end

function third.fill_circles(n,x,y,r)
   local list = {}
   for i=1,n do
     table.insert(list, third.add_circle(x,y,r, list))
   end
   return list
end

function third.toMP(c, scale)
   local tprint = function(s) tex.sprint(tex.ctxcatcodes,s) end
   local scaled = function(p) return ("(" .. p .. "*" .. scale .. ")") end
   tprint("draw fullcircle scaled " .. scaled(2*c["radius"]) ..
           " shifted (" .. scaled(c["center"][1]) .. "," ..
                           scaled(c["center"][2]) .. "); \n")
end


function third.show_circles(n,x,y,r)
   local tprint = function(s) tex.sprint(tex.ctxcatcodes,s) end
   local list = third.fill_circles(n,x,y,r)
   tprint("\\startMPcode")
   for i,v in pairs(list) do
     third.toMP(v, "1cm")
   end
   tprint("\\stopMPcode")
end

\stopluacode

\def\drawCircles{\ctxlua{third.show_circles(100,10,10,2)}}

\starttext
\drawCircles

\stoptext

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