Re: Joining points of ListPlot

*To*: mathgroup at smc.vnet.net*Subject*: [mg117333] Re: Joining points of ListPlot*From*: Daniel Lichtblau <danl at wolfram.com>*Date*: Tue, 15 Mar 2011 06:06:08 -0500 (EST)

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