How can I compare picture variables in metapost?

How can I compare picture variables in metapost?

[Zhichu Chen]

Hi all,

I want to draw some paths that won't intersect with each other
in metapost. Those paths are generated "randomly," e.g., draw
100 circles without any intersections. I use a very stupid
way like:
=============================================
% randomseed:= day + time*epsilon ;
save minL ; numeric minL ; minL = infinity ;
z[0] = origin;
for i=1 upto 99 :
  z[i] = (uniformdeviate 1 , uniformdeviate 1 ) ;
  for j=0 upto i-1 :
    if abs(z[i]-z[j])<minL : minL := abs(z[i]-z[j]) ; fi
  endfor
endfor
for i=0 upto 99 :
  draw fullcircle scaled 2cm shifted (z[i] scaled (2cm/minL))
    withcolor (i/100, (100-i)/100, abs(50-i)/100);
endfor
=============================================
The randomseed made me crazy, for one time it compiles
fine and sometimes it just flows out which I think may due
to the size of the picture becomes big enough.

I think a better way could be like this:
pick a random point, fill it with color, pick another point and
use "clip currentpicture to somepath" and determine whether
it is blank or not. But "if currentpicture=nullpicture" won't work,
so I'm stunned.

Thank you for your time.


-- 
Best Regards
Chen
----------------------------------------------------------------

          Zhi-chu Chen | Shanghai Synchrotron Radiation Facility
         No. 2019 | Jialuo Rd. | Jiading | Shanghai | P.R. China
             tel: 086 21 5955 3405 | zhichu.chen.googlepages.com
                                               | www.sinap.ac.cn
----------------------------------------------------------------
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___________________________________________________________________________________

Re: How can I compare picture variables in metapost?

[Taco Hoekwater]

Zhichu Chen wrote:
> Hi all,
> 
> I want to draw some paths that won't intersect with each other
> in metapost. Those paths are generated "randomly," e.g., draw
> 100 circles without any intersections. I use a very stupid
> way like:

I am probably missing something, because the fastest way to
draw  100 non-intersecting paths is just by having them in
a grid. You don't seem to want that, so: what do you want,
exactly? (be warned that "marble fill" is pretty hard).

Best wishes,
Taco
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___________________________________________________________________________________

Re: How can I compare picture variables in metapost?

[Zhichu Chen]

Hi Taco,

On Tue, May 5, 2009 at 8:51 PM, Taco Hoekwater <taco@elvenkind.com> wrote:
> Zhichu Chen wrote:
>>
>> Hi all,
>>
>> I want to draw some paths that won't intersect with each other
>> in metapost. Those paths are generated "randomly," e.g., draw
>> 100 circles without any intersections. I use a very stupid
>> way like:
>
> I am probably missing something, because the fastest way to
> draw  100 non-intersecting paths is just by having them in
> a grid. You don't seem to want that, so: what do you want,
> exactly? (be warned that "marble fill" is pretty hard).

Nice to have your attention.

Those paths are not meant to be somewhere and they appear
randomly. Like one path can have a neighbor very close to it
and another path may be not so close to any of the other
ones. Basically, they are not organized, they can't form a lattice.

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.

I don't think putting them in a grid is what I want. That'll just
make those objects look like they are sorted and kind of like
it's a fake picture which is generated intentionally.

I hope I haven't make you even more confused.

>
> Best wishes,
> Taco
> ___________________________________________________________________________________
> If your question is of interest to others as well, please add an entry to
> the Wiki!
>
> maillist : ntg-context@ntg.nl /
> http://www.ntg.nl/mailman/listinfo/ntg-context
> webpage  : http://www.pragma-ade.nl / http://tex.aanhet.net
> archive  : https://foundry.supelec.fr/projects/contextrev/
> wiki     : http://contextgarden.net
> ___________________________________________________________________________________
>



-- 
Best Regards
Chen
----------------------------------------------------------------

          Zhi-chu Chen | Shanghai Synchrotron Radiation Facility
         No. 2019 | Jialuo Rd. | Jiading | Shanghai | P.R. China
             tel: 086 21 5955 3405 | zhichu.chen.googlepages.com
                                               | www.sinap.ac.cn
----------------------------------------------------------------
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___________________________________________________________________________________

Re: How can I compare picture variables in metapost?

[Taco Hoekwater]

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).

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.

I can't come up with a solution that is both elegant and fast at the
moment, sorry.

Best wishes,
Taco
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___________________________________________________________________________________

Re: How can I compare picture variables in metapost?

[Zhichu Chen]

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.

>
> I can't come up with a solution that is both elegant and fast at the
> moment, sorry.
>
> Best wishes,
> Taco
> ___________________________________________________________________________________
> If your question is of interest to others as well, please add an entry to
> the Wiki!
>
> maillist : ntg-context@ntg.nl /
> http://www.ntg.nl/mailman/listinfo/ntg-context
> webpage  : http://www.pragma-ade.nl / http://tex.aanhet.net
> archive  : https://foundry.supelec.fr/projects/contextrev/
> wiki     : http://contextgarden.net
> ___________________________________________________________________________________
>



-- 
Best Regards
Chen
----------------------------------------------------------------

          Zhi-chu Chen | Shanghai Synchrotron Radiation Facility
         No. 2019 | Jialuo Rd. | Jiading | Shanghai | P.R. China
             tel: 086 21 5955 3405 | zhichu.chen.googlepages.com
                                               | www.sinap.ac.cn
----------------------------------------------------------------
___________________________________________________________________________________
If your question is of interest to others as well, please add an entry to the Wiki!

maillist : ntg-context@ntg.nl / http://www.ntg.nl/mailman/listinfo/ntg-context
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archive  : https://foundry.supelec.fr/projects/contextrev/
wiki     : http://contextgarden.net
___________________________________________________________________________________

Re: How can I compare picture variables in metapost?

[Taco Hoekwater]

Zhichu Chen wrote:
> 
> 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.

For circles, probably lua calculations will be faster because the
data manipulation will be a bit easier. But for non-circle paths,
you are better off with a metapost solution because of lua not
knowing about the actual paths.

Good luck,
Taco
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___________________________________________________________________________________

Re: How can I compare picture variables in metapost?

[Taco Hoekwater]

Taco Hoekwater wrote:
> Zhichu Chen wrote:
>>
>> 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.
> 
> For circles, probably lua calculations will be faster because the
> data manipulation will be a bit easier. But for non-circle paths,
> you are better off with a metapost solution because of lua not
> knowing about the actual paths.

linear search does seem to do that badly, here is a stub:

path p[];
path m;
pair n;

i := 0;
forever:
   exitif i > 99;
   m := fullcircle scaled (uniformdeviate 20)
	shifted (uniformdeviate 100, uniformdeviate 100);
   n := (-1,-1);
   if i<>0:
    for j = 0 upto (i-1):
     n := m intersectiontimes p[j];
     exitif (xpart n)>=0;
    endfor;
   fi
   if (xpart n)<0:
     p[i] := m ;
     i := i + 1;
     message(decimal(i));
   fi
endfor;

beginfig(1);
for i:=0 upto 99:
   fill p[i];
endfor;
currentpicture := currentpicture scaled 5;
endfig;
end.



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___________________________________________________________________________________

Re: How can I compare picture variables in metapost?

[Peter Rolf]

Taco Hoekwater schrieb:
> Taco Hoekwater wrote:
>> Zhichu Chen wrote:
>>>
>>> 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.
>>
>> For circles, probably lua calculations will be faster because the
>> data manipulation will be a bit easier. But for non-circle paths,
>> you are better off with a metapost solution because of lua not
>> knowing about the actual paths.
>
> linear search does seem to do that badly, here is a stub:
>
Mhh... isn't it easier to just test, if the distance (centerpoint to 
centerpoint) from the new circle
to all already found circles is greater (or equal) than the sum of the 
radii?
Anyhow an interesting and hard problem (I guess O(n!) ? ).

Best wishes,  Peter

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___________________________________________________________________________________

Re: How can I compare picture variables in metapost?

[Aditya Mahajan]

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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___________________________________________________________________________________

Re: How can I compare picture variables in metapost?

[Aditya Mahajan]

On Tue, 5 May 2009, Peter Rolf wrote:

> Taco Hoekwater schrieb:
>> Taco Hoekwater wrote:
>>> Zhichu Chen wrote:
>>>> 
>>>> 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.
>>> 
>>> For circles, probably lua calculations will be faster because the
>>> data manipulation will be a bit easier. But for non-circle paths,
>>> you are better off with a metapost solution because of lua not
>>> knowing about the actual paths.
>> 
>> linear search does seem to do that badly, here is a stub:
>> 
> Mhh... isn't it easier to just test, if the distance (centerpoint to 
> centerpoint) from the new circle
> to all already found circles is greater (or equal) than the sum of the radii?

Depends on what you mean by "does not intersect". Taco's solution only 
checks if the curves intersect or not. So, it is possible to have two 
concentric circles. If you check for distance you get circles which do not 
overlap.

Of course, in case of circles, non-overlap can also be tested 
mathmeaticically.

if |c_1 - c_2| < max(r_1, r_2) then
    |c_1 - c_2| < |r_1 - r_2|
else
    |c_1 - c_2| > r_1 + r_2
end

> Anyhow an interesting and hard problem (I guess O(n!) ? ).

I think it is O(n^3).You only have to check all combinations (which is 
O(n^2)) and do that for each point that you add add.

Aditya
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___________________________________________________________________________________

Re: How can I compare picture variables in metapost?

[Zhichu Chen]

Thank you all guys,

To Aditya: Clearly I over-emphasized the randomness. Actually, what I
meant is a little more complex: identical objects on random
coordinates and they don't intersect with each other. We can rotate
them but we can't re-size them and scale them. Your code is very
interesting. I'll see what I can do now.

Thank you again.


-- 
Best Regards
Chen
----------------------------------------------------------------

          Zhi-chu Chen | Shanghai Synchrotron Radiation Facility
         No. 2019 | Jialuo Rd. | Jiading | Shanghai | P.R. China
             tel: 086 21 5955 3405 | zhichu.chen.googlepages.com
                                               | www.sinap.ac.cn
----------------------------------------------------------------
___________________________________________________________________________________
If your question is of interest to others as well, please add an entry to the Wiki!

maillist : ntg-context@ntg.nl / http://www.ntg.nl/mailman/listinfo/ntg-context
webpage  : http://www.pragma-ade.nl / http://tex.aanhet.net
archive  : https://foundry.supelec.fr/projects/contextrev/
wiki     : http://contextgarden.net
___________________________________________________________________________________

Re: How can I compare picture variables in metapost?

[Aditya Mahajan]

On Wed, 6 May 2009, Zhichu Chen wrote:

> To Aditya: Clearly I over-emphasized the randomness. Actually, what I
> meant is a little more complex: identical objects on random
> coordinates and they don't intersect with each other. We can rotate
> them but we can't re-size them and scale them.

The difficult part in this case is recognizing that either the input is 
infeasible (you cannnot put 100 circles of radius 1 in a 10x10 square), or 
that a particular random sample is stuck and you need to restart.

> Your code is very
> interesting. I'll see what I can do now.

Both Taco's and my solutions can be adapted so that you do not randomize 
the radius. (Taco's solution will also work for arbitrary object that can 
then be rotated by a random amount).

Another option that you can consider (if you only want the result to look 
random), is to start with a uniform placement on a grid and then move 
objects around by a small amount randomly. This will give an appearance 
that they are placed at random.

Aditya
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___________________________________________________________________________________

Re: How can I compare picture variables in metapost?

[Aditya Mahajan]

On Tue, 5 May 2009, Aditya Mahajan wrote:

> Both Taco's and my solutions can be adapted so that you do not randomize the 
> radius. (Taco's solution will also work for arbitrary object that can then be 
> rotated by a random amount).

Here is another idea. Ask metapost to test for intersection, but code the 
rest of the logic in lua. Below is a proof of concept code for 
communicating with metapost.

\startluacode
   circle = circle or {}

   function circle.path(x,y,r, name)
     local path = "path " .. name .. "; \n" ..
                   name .. "= fullcircle scaled " .. 2*r ..
                  " shifted (" .. x .. "," .. y ..") ; \n"
     return path
   end

   function circle.intersect(x1,y1,r1,x2,y2,r2)
     local mpx = metapost.format("metafun")
     local c = circle.path(x1,y1,r1, "c")
     local d = circle.path(x2,y2,r2, "d")
     local intersect = "pair n; n := c intersectiontimes d ; \n"
     local message   = "if (xpart n) < 0 : \n" ..
                       "   message(\"**false**\") ; \n" ..
                       "else : \n" ..
                       "   message(\"**true**\") ; \n" ..
                       " endif \n"
     local file = c .. d .. intersect .. message
     -- print(file)
     local result = mpx:execute(file)
     local log    = result.log
     if result.status < 2 then
       print("Metapost run successful *****************")
       circle.show_result(x1,y1,r1,x2,y2,r2,circle.parse(log))
     else
       print("Metapost run unsuccessful *****************")
     end
     print(log)
   end

   function circle.parse(log)
     local space = lpeg.S(" \t\n")
     local yes   = lpeg.C("**true**")
     local no    = lpeg.C("**false**")
     local result = (yes + no) / circle.result
     local parser = space^0 * result * space^0
     return parser:match(log)
   end

   function circle.result(str)
     return str == "**true**"
   end

   function circle.show_result(x1,y1,r1,x2,y2,r2,flag)
     local tprint = function(s) tex.sprint(tex.ctxcatcodes,s) end
     local result = "Circles  (" .. x1 .. "," .. y1 .. "):" .. r1 ..
                       " and  (" .. x2 .. "," .. y2 .. "):" .. r2 .. " "
     if flag then
       result = result .. " intersect. "
     else
       result = result .. " do not intersect. "
     end
     tprint (result)
   end


\stopluacode

\starttext
\startluacode
   circle.intersect(1,1,1,2,2,1.5)
   circle.intersect(1,1,1,3,3,0.5)
\stopluacode
\stoptext





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___________________________________________________________________________________

Re: How can I compare picture variables in metapost?

[Peter Rolf]

Aditya Mahajan schrieb:
> On Tue, 5 May 2009, Peter Rolf wrote:
>
>> Taco Hoekwater schrieb:
>>> Taco Hoekwater wrote:
>>>> Zhichu Chen wrote:
>>>>>
>>>>> 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.
>>>>
>>>> For circles, probably lua calculations will be faster because the
>>>> data manipulation will be a bit easier. But for non-circle paths,
>>>> you are better off with a metapost solution because of lua not
>>>> knowing about the actual paths.
>>>
>>> linear search does seem to do that badly, here is a stub:
>>>
>> Mhh... isn't it easier to just test, if the distance (centerpoint to 
>> centerpoint) from the new circle
>> to all already found circles is greater (or equal) than the sum of 
>> the radii?
>
> Depends on what you mean by "does not intersect". Taco's solution only 
> checks if the curves intersect or not. So, it is possible to have two 
> concentric circles. If you check for distance you get circles which do 
> not overlap.
>
aye

> Of course, in case of circles, non-overlap can also be tested 
> mathmeaticically.
>
> if |c_1 - c_2| < max(r_1, r_2) then
>    |c_1 - c_2| < |r_1 - r_2|
> else
>    |c_1 - c_2| > r_1 + r_2
> end
>
>> Anyhow an interesting and hard problem (I guess O(n!) ? ).
>
> I think it is O(n^3).You only have to check all combinations (which is 
> O(n^2)) and do that for each point that you add add.
You are the mathematician, so you are *probably* right here :)

Best wishes,  Peter
>
> Aditya
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If your question is of interest to others as well, please add an entry to the Wiki!

maillist : ntg-context@ntg.nl / http://www.ntg.nl/mailman/listinfo/ntg-context
webpage  : http://www.pragma-ade.nl / http://tex.aanhet.net
archive  : https://foundry.supelec.fr/projects/contextrev/
wiki     : http://contextgarden.net
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