Re: How can I compare picture variables in metapost?

[Aditya Mahajan <adityam@umich.edu>]

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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