On Tue, 5 May 2009, Zhichu Chen wrote:

On Tue, May 5, 2009 at 11:04 PM, Taco Hoekwater <t...@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.



third = third or {}

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

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

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"] 
      return false
  return true

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

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))
  return list

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")

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)
  for i,v in pairs(list) do
    third.toMP(v, "1cm")





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