Re: How can I compare picture variables in metapost?

[Peter Rolf <indiego@gmx.net>]

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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