Re: Joining points of ListPlot
- To: mathgroup at smc.vnet.net
- Subject: [mg117353] Re: Joining points of ListPlot
- From: DrMajorBob <btreat1 at austin.rr.com>
- Date: Wed, 16 Mar 2011 06:25:36 -0500 (EST)
If I change "mesh" to "mean", the bug goes away:
Clear[f]
f[{a_, b_}, {c_, d_}] := Boole[Abs[a - c] < .1] + Norm[{a, b} - {c, d}]
clusters =
FindClusters[curves, 2, DistanceFunction -> f,
Method -> "Agglomerate"];
Show[ListPlot@curves, Table[Graphics@Line@c, {c, clusters}]]
2 mean == .1
True
curves = Riffle[Table[{x, Sin[x]}, {x, 0., 2*Pi, .1}],
Table[{x, Cos[x]}, {x, .05, 2*Pi, .1}]];
mean = Mean@Abs@Differences@curves[[All, 1]]
ListPlot[curves]
0.05
Clear[f]
f[{a_, b_}, {c_, d_}] :=
Boole[Abs[a - c] < 2 mean] + Norm[{a, b} - {c, d}]
clusters =
FindClusters[curves, 2, DistanceFunction -> f,
Method -> "Agglomerate"];
Show[ListPlot@curves, Table[Graphics@Line@c, {c, clusters}]]
Bobby
On Tue, 15 Mar 2011 10:45:14 -0500, DrMajorBob <btreat1 at austin.rr.com>
wrote:
> This seems to do it perfectly in this case:
>
> curves = Riffle[Table[{x, Sin[x]}, {x, 0., 2*Pi, .1}],
> Table[{x, Cos[x]}, {x, .05, 2*Pi, .1}]];
> mesh = Max@Abs@Differences@curves[[All, 1]]
> ListPlot[curves]
>
> 0.05
>
> Clear[f]
> f[{a_, b_}, {c_, d_}] := Boole[Abs[a - c] < .1] + Norm[{a, b} - {c, d}]
> clusters =
> FindClusters[curves, 2, DistanceFunction -> f,
> Method -> "Agglomerate"];
> Show[ListPlot@curves, Table[Graphics@Line@c, {c, clusters}]]
>
> But here's a BUG:
>
> 2 mesh == .1
>
> True
>
> Clear[f]
> f[{a_, b_}, {c_, d_}] :=
> Boole[Abs[a - c] < 2 mesh] + Norm[{a, b} - {c, d}]
> clusters =
> FindClusters[curves, 2, DistanceFunction -> f,
> Method -> "Agglomerate"];
> Show[ListPlot@curves, Table[Graphics@Line@c, {c, clusters}]]
>
> (with VERY different clusters).
>
> Bobby
>
> On Tue, 15 Mar 2011 06:06:08 -0500, Daniel Lichtblau <danl at wolfram.com>
> wrote:
>
>> Antonio Mezzacapo wrote:
>>> Thank you for answering.
>>>
>>> I don't have any functional form of this points. I have only this
>>> array of
>>> points. Points on this array should be distributed *like* two crossing
>>> functions as Sin[x] and Cos[x], but I don't know the functional form of
>>> these functions.
>>>
>>> All that I have is an array of points!
>>> Because of the fact that these points distribute on the x-y cartesian
>>> plane
>>> like two crossing functions, I cannot use "joined->true" because it
>>> gives me
>>> strange results.
>>>
>>> Thank you
>>> Antonio
>>> [...]
>>
>> One approach is to use Nearest to find candidate neighbors, then apply a
>> slope test to remove some contenders. For this purpose i adapted some
>> code from a November thread.
>>
>> Our example:
>>
>> curves = Riffle[Table[{x, Sin[x]}, {x, 0., 2*Pi, .1}],
>> Table[{x, Cos[x]}, {x, .05, 2*Pi, .1}]];
>>
>> ListPlot[curves]
>>
>> Here is the code, with no attempt made to package it nicely. It gives an
>> imperfect rendering in this example. I think one could make more
>> judicious of Nearest and also improve on the slope test, in a way that
>> would give a more accurate picture of the two curves. But this is
>> certainly a reasonable start.
>>
>> Needs["GraphUtilities`"];
>>
>> curvesmodif = curves /. {x_, y_} :> {x, y};
>> nf = Nearest[curvesmodif];
>> neighbors =
>> Map[{#, Complement[nf[#, 4], {#}]} &,
>> curvesmodif] /. {x_Real, y_Real} :> {x, y};
>>
>> Do[{elem, trio} = neighbors[[i]];
>> slopes = Map[(elem[[2]] - #[[2]])/(elem[[1]] - #[[1]]) &, trio];
>> slopes = Join[slopes, {slopes[[1]]}];
>> slopediffs = Differences[slopes];
>> bestpair = Ordering[Abs[slopediffs], 1][[1]];
>> neighbors[[i]] =
>> Sort[{elem, trio[[Mod[bestpair, 3, 1]]],
>> trio[[Mod[bestpair + 1, 3, 1]]]}];
>> , {i, Length[neighbors]}]
>>
>> graph = Union[
>> Flatten[Map[{#[[1]] -> #[[2]], #[[2]] -> #[[3]], #[[2]] -> #[[1]], \
>> #[[3]] -> #[[1]]} &, neighbors]]];
>>
>> Do[elem = graph[[i]];
>> If[! MemberQ[graph, Reverse[elem]], graph[[i]] = Null];,
>> {i, Length[graph]}]
>> graph = graph /. Null :> Sequence[];
>>
>> pieces = WeakComponents[graph]
>>
>> plots = Map[ListPlot[#, Joined -> True] &, pieces];
>>
>>
>> Daniel Lichtblau
>> Wolfram Research
>>
>
>
--
DrMajorBob at yahoo.com