Re: [NTG-context] How can I compare picture variables in metapost?

6 May 2009


      On Tue, 5 May 2009, Zhichu Chen wrote:
...
On Tue, May 5, 2009 at 11:04 PM, Taco Hoekwater  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

Re: [NTG-context] How can I compare picture variables in metapost?

Aditya Mahajan