Implementing a LineStyleFunction for line plots

Question

I have data in the form:

{{0, 3, 4}, {1, 3, -1}, {2, 4, -1}, ...}

and I would like to implement something similar to ColorFunction for the style of a line. Basically I would like to plot a standard line plot using the first two entries of each point {x, y, ..}, and then decide on the line style using the 3rd {.., .., z}.

Specifically I would like to plot dashed lines when the 3rd entry is positive and filled lines when negative, formed as one continuous curve.

EDIT: to clarify, there will be large regions where the 3rd entry is consistently positive or negative, so its purpose is to set the style for those regions. This method wouldn't really work for situations where the 3rd value oscillates between the two.

Many thanks, Hemmer

Answer 1

This is my interpretation of your question: the 3rd element of a point specifies the style of the line that connects that point with the next one.

data = Table[{i, RandomInteger[{1, 10}], RandomChoice[{-1, 1}]}, {i, 20}];
setsN = DeleteCases[Table[If[data[[i, 3]] < 0, data[[i ;; i + 1, {1, 2}]], {}], {i, 
    Length[data] - 1}], {}];
setsP = DeleteCases[Table[If[data[[i, 3]] > 0, data[[i ;; i + 1, {1, 2}]], {}], {i, 
    Length[data] - 1}], {}];
Show[
    ListLinePlot[setsN, PlotStyle -> {{Thick, Black}}],
    ListLinePlot[setsP, PlotStyle -> {{Thick, Black, Dashed}}]
]

Answer 2

Correction!

Sorry for misunderstanding. Here is a updated code

Options[plot] = Options[ListPlot];
plot[data_, options : OptionsPattern[ListPlot]] := Block[{line},
  line[{pt1_, pt2_}] := Module[
   {z},
   z = pt1[[3]];
   {
    If[z >= 0, Dashed, Thickness[0.0045]], 
    If[z >= 0, Orange, Cyan],
    Line[(#[[1 ;; 2]]) & /@ {pt1, pt2}]
   }
  ];
Show[ListPlot[data[[All, 1 ;; 2]], options],
     Graphics[line[#] & /@ Partition[data, 2, 1]]
    ]
]

Now we test it. We intentionally use PlotStyle -> None to hide the data points!

fun[x_] := Sin[13 x] + Cos[7 x];
data = Table[{i, a = fun[ i]; a, If[ a >= 0, 1, -1]}, {i, - Pi, Pi,2. Pi/120}];
plot[data, Frame -> True, Axes -> False, PlotStyle -> None]

Answer 3

It seems to me that using Graphics would be easier than messing with LinePlots.

We can define any number of styles with a function:

ClearAll[lineStyle];
lineStyle[z_] /; z < 0 := {Orange, Dashed};
lineStyle[z_] /; z > 0 := {Blue, Thick};
lineStyle[z_] := {Black};

Then create a function to plot data using this style:

ClearAll[styledPlot];
styledPlot[data_, o : OptionsPattern[]] := Graphics[Partition[data, 2, 1] /.
  {{x1_, y1_, z1_}, {x2_, y2_, z2_}} :> Append[lineStyle[z1], Line[{{x1, y1}, {x2, y2}}]], 
    Evaluate[FilterRules[{o}, Options[Graphics]]]]

In use:

styledPlot[
  Table[{i, RandomInteger[{1, 10}], RandomInteger[{-5, 5}]}, {i, 20}], 
  Frame -> True, PlotLabel -> "Styled"]

Answer 4

Using a minor modification of this answer to another question, Mesh, MeshFunctions, MeshStyle and MeshShading options can be used to specify the directives for different pieces of the lines in ListLinePlot.

Data:

 breaks = Join[{0}, Sort@RandomInteger[{2, 99}, 5], {100}];
 i = 2; arg3 = (j = i++; ConstantArray[(-1)^j, {#}]) & /@ Differences[breaks];
 data = {Range[100], RandomInteger[100, {100}], Flatten@arg3} // Transpose;

Calculate mesh points:

 meshpoints = Most@Accumulate[Length /@ Split[data, Last[#1] == Last[#2] &]];

... plot:

ListLinePlot[data[[All, ;; 2]], PlotStyle -> Blue,ImageSize -> 450, 
  Mesh -> {meshpoints},
  MeshStyle -> None, 
  MeshFunctions -> (#1 &), 
  MeshShading -> {Thick, Directive[Thick, Dashed]}]