Visualization of a set of data with a shape $ m \times n \times 3 $ with the last dimension interpreted as a color scale

Question

Actually, if the data is shaped as $ m \times n \times 2 $, functions like ListLinePlot just do the job. But now I want to add colors to the curves according to each 3rd data. But it has stuck me. Any ideas?

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A simpler version of the question should be this: Suppose I have an $ n \times 3 $ shaped data (below is not code but just what shows the spirit, and generation of test data is not difficult to implement by, say, RandomReal or RandomInteger):

data = {{x1, y1, z1}, {x2, y2, z2}, ..., {xn, yn, zn}};

Using Graphics3D[Line[data]] or ListPointPlot3D[data] can visualize it. But sometimes one has to work in just 2D, then how to encode the information carried by zi on the 2D curve sampled out by {xi, yi}?

Answer 1

Clear[colorDataListLinePlot]
Options[colorDataListLinePlot] = {
    "ColorScheme" -> "NeonColors"
    }~Join~Options[ListLinePlot];
colorDataListLinePlot[datum_, opts : OptionsPattern[]] := Module[{
   data = datum[[All, {1, 2}]], 
   colorfun = 
    Function[{x}, InterpolatingPolynomial[datum[[All, {1, 3}]], x]]
   }, ListLinePlot[data,
   ColorFunction -> 
    Function[{x, y}, 
     ColorData[OptionValue["ColorScheme"]][colorfun[x]]],
   FilterRules[{opts}, Options[ListLinePlot]]
   ]
  ]

The problem is that ColorFunction expects a continuous function and needs to be defined everywhere. I used InterpolatingPolynomial which does not give so nice results, but this might be because of the random nature of the data.

(*3 x 10 x 3 data structure with the "x"-component increasing*)
data = Table[{i, RandomReal[{-1, 1}], i}, {3}, {i, 10}];
Show@Table[
  colorDataListLinePlot[datum, "ColorScheme" -> "Rainbow", 
   PlotRange -> {{1, 10}, {-1, 1}}], {datum, data}]

Answer 2

VertexColors:

data = Table[{x, Sin[x], Cos[x]}, {x, 0, 2 Pi}];
{x, y, z} = Transpose[data];

Graphics[{
  Thick,
  Line[Transpose[{x, y}], VertexColors -> Hue /@ z]
  }]