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



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

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

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

You are the mathematician, so you are *probably* right here :)

Best wishes,  Peter

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


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

Hi Taco,

On Tue, May 5, 2009 at 8:51 PM, Taco Hoekwater t...@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).

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


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

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.

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


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

Good luck,
Taco
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### Re: [NTG-context] How can I compare picture variables in metapost?


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

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 i0:
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: [NTG-context] How can I compare picture variables in metapost?


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

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

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

Best wishes,  Peter

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


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.

\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
then
return false
end
end
end
return true
end

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


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

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

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

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

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


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.

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.

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


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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