How to produce better DensityPlot for data which has a very asymmetric grid?

Question

I have a data file (can be downloaded here). Each line of the data has three numbers corresponding to x,y,z, the data can be formed by

data = ReadList["test.dat",{number,number,number}];

If I plot this data with ListPointPlot3D@data, I got

You can see that it is extremely dense in the y axis, and sparse on x axis.

But if I plot the data with ListDensityPlot@data, I got

Though this plot capture the shape, but it is misleading. It plots many segments of horizontal lines instead of a continuous line with varying line width ( the line width indicate the weight). It makes people feel the following way

Interpolation order doesn't solve this.

For example,

f = Interpolation[data, InterpolationOrder -> 4];
DensityPlot[f[x, y], {x, 1, 41}, {y, -5, 19.52`}, PlotPoints -> 150, 
 PlotRange -> All]

still gives the same result.

Of course, one simple way to improve this is to increase x grid. But x grid has a much more computational cost than y grid.

So how to get better interpolation of such kind of DensityPlot dataset with very asymmetry grid? The Plot should be showing continuous lines with varying line width like this

Answer 1

So you want continuous lines in your density plot, but you have very sparse data. So here's an upsampling-based method.

First some trivial upsampling based on neighbor-distance:

subdata = Pick[data, GreaterThan[.1] /@ Rescale@data[[All, 3]]];

upsampled =
  DeleteDuplicates[#, Norm[#[[;; 2]] - #2[[;; 2]]] < .1 &] &@
   Join[
    Flatten[
     Table[
      If[1 < Norm[subdata[[i, ;; 2]] - subdata[[j, ;; 2]]] < 1.5,
       Mean@subdata[[{i, j}]],
       Nothing
       ],
      {i, Length@subdata},
      {j, Length@subdata}
      ],
     1
     ],
    subdata
    ];
upsampled[[All, ;; 2]] // Point // Graphics

Then make a background grid where the true interpolation will live:

gridspacings =
  MapThread[
   Append[
     MinMax[#],
     Min@{
       Min@
        Select[GreaterThan[10^-3]]@
         Differences@Sort[#2],
       .1
       }
     ] &, {
    Transpose@data[[All, ;; 2]],
    Transpose@upsampled[[All, ;; 2]]
    }];
background =
  Flatten[
   Table[{x, y},
    Evaluate@{x, Sequence @@ gridspacings[[1]]},
    Evaluate@{y, Sequence @@ gridspacings[[2]]}
    ],
   1
   ];

Next let grid points have the value of the nearest point in the original sample and use a 1/r^n-type decay to assign the real value at a grid point:

nf = Nearest[Thread[upsampled[[All, ;; 2]] -> upsampled]];
bgn = nf[background, 1][[All, 1]];
mtBg =
  Compile[
   {{bg, _Real, 2}, {nb, _Real, 
     2}, {maxnorm, _Real}, {minRad, _Real}, {scl, _Real}, {pow, \
_Real}},
   MapThread[
    Append[#,
      If[Norm[# - #2[[;; 2]]] < maxnorm,
       #2[[3]]/(scl*Max@{Norm[# - #2[[;; 2]]], minRad})^pow,
       0.
       ]
      ] &,
    {
     bg,
     nb
     }
    ]
   ];
updata = mtBg[background, bgn, 100, .5, 1., 2];

This can be trivially interpolated and DensityPlot-ted:

itf = Interpolation[updata];
DensityPlot[itf[x, y], {x, 1, 41}, {y, -5, 19.5}]

You can kinda tune the look of that by the parameters in mtBg.

Here's another version:

itf2 = Interpolation[mtBg[background, bgn, .8, .1, .1, 1]];
DensityPlot[itf2[x, y], {x, 1, 41}, {y, -5, 19.5}, PlotRange -> All ]

---

Original

It seems to be a bit better if you do some clipping first:

data = Import["https://pastebin.com/raw/TZwajVgT", "TSV"];

Pick[data, GreaterThan[0] /@ Rescale@data[[All, 3]]] //
 
 ListDensityPlot[#,
   Background -> ColorData["DarkRainbow"][0],
   ColorFunction -> ColorData["DarkRainbow"]
   ] &

Alternatively you can build it from the ground up:

With[{cd = ColorData["DarkRainbow"]},
 Graphics[
  {
   PointSize[Large],
   Point[data[[All, ;; 2]],
    VertexColors ->
     Map[Directive[Opacity[#], cd[1 - #]] &, Rescale@data[[All, 3]]]
    ]
   },
  Background -> cd[0]
  ]
 ]

Note that that's pretty much the same as this:

With[{cd = ColorData["DarkRainbow"]},
 ListPointPlot3D[data,
  ColorFunction -> Function@Directive[Opacity[#3], cd[1 - #3]],
  Background -> cd[0],
  ViewPoint -> Above,
  Boxed -> False
  ]
 ]