Re: Using Nearest on a group of points
- To: mathgroup at smc.vnet.net
- Subject: [mg117623] Re: Using Nearest on a group of points
- From: Peter Pein <petsie at dordos.net>
- Date: Thu, 24 Mar 2011 06:32:42 -0500 (EST)
- References: <im9sk8$g5j$1@smc.vnet.net>
Am 22.03.2011 11:11, schrieb Martin VavpotiÄ?:
> Hello. I need some help with the function Nearest.
>
> I have a groups of points, each with two coordinates (x,y), describing
> a connected shape (the last point is a neighbor to the first one). The
> initial order of these points is completely scrambled but I need them
> to follow one another so their sequence describes a combined shape. I
> thought of using the Nearest function but there is a problem.
> Somewhere in the middle of my shape is a large gap where no points
> reside. I fear that if I use Nearest, the function will find the wrong
> point.
>
> What I need is for function Nearest to ignore points already sorted
> and search only for points that have not been used yet.
>
I've got two possible solutions; one is ugly and the other is probably slow:
get some "separated" random data:
In[1]:= pts = RandomSample[Union[RandomReal[{0, 1},
{5, 2}], RandomReal[{5, 6}, {5, 2}]], 10]
Out[1]=
{{5.05492,5.67991},{5.26878,5.95573},{0.845357,0.827223},{5.1551,5.96676},{5.27177,5.52867},{0.159596,0.353401},{0.317545,0.944187},{5.20924,5.85889},{0.68395,0.738788},{0.866587,0.699483}}
have a look at the mess:
In[2]:= ListPlot[pts, Joined -> True]
(* output deleted *)
use a brain twister using anonymous functions and a temporary variable:
(starting at the origin; could be any point in the plane)
In[3]:= sorted = Rest[First[NestWhile[
Block[{tmp}, {Join[#1[[1]],
tmp = Nearest[#1[[2]], #1[[1,-1]]]],
DeleteCases[#1[[2]], tmp[[1]]]}] & ,
{{{0, 0}}, pts}, #1[[2]] =!= {} & , 1]]]
Out[3]=
{{0.159596,0.353401},{0.317545,0.944187},{0.68395,0.738788},{0.845357,0.827223},{0.866587,0.699483},{5.05492,5.67991},{5.20924,5.85889},{5.26878,5.95573},{5.1551,5.96676},{5.27177,5.52867}}
and look at the result:
In[4]:= ListPlot[sorted, Joined -> True]
or apply a rule repeatedly:
In[5]:= sort2=Rest[First[{{{0.,0.}},pts}//.
{{s1___List,s2:{__Real}},remain:{r1___,rn:{__Real},r2___}}/;{rn}==Nearest[remain,s2]:>{{s1,s2,rn},{r1,r2}}]];
and the results are the same:
In[6]:= sorted === sort2
Out[6]= True
hth,
Peter