How to display non-rectangular and ungridded data as a map with gnuplot?

Let's asume the following 100 points with x,y,z values.

Data: (tbTriangulationTest.dat)

-7.6392 -11.107 84.8488
0.903339 9.3734 8.46736
-14.1859 20.7705 -294.647
1.70653 0.400903 0.684154
-7.15958 4.18987 -29.9977
-7.4528 4.57573 -34.102
-6.92655 12.5265 -86.7655
7.19843 12.2755 88.364
7.6977 4.97676 38.3096
7.7979 -12.6609 -98.7287
-7.05982 7.2656 -51.2938
-6.24214 -5.79787 36.1911
5.07354 -5.66814 -28.7575
2.14596 -24.9946 -53.6374
14.466 4.81118 69.5987
15.4306 -2.16115 -33.3478
11.1028 -1.0111 -11.2261
-11.4716 2.55607 -29.3223
-0.256364 14.5526 -3.73077
-6.83535 2.39029 -16.3385
3.19476 6.24488 19.9509
-7.72445 0.172802 -1.3348
-4.39985 7.86195 -34.5914
2.31929 13.8717 32.1724
2.4772 10.766 26.6694
-3.84819 0.687076 -2.644
-3.38394 2.43134 -8.22753
-14.4258 -0.320421 4.62232
0.359401 16.5257 5.93933
-0.11949 -6.9755 0.833503
0.0203191 14.5566 0.295777
5.26722 -10.3545 -54.5394
1.76742 3.98467 7.04257
-1.86885 13.3988 -25.0403
-1.07509 -7.08523 7.61723
7.47418 -7.07921 -52.9113
-0.109939 5.9067 -0.649376
-6.54697 2.69141 -17.6206
1.93999 6.87386 13.3352
9.99989 -5.95029 -59.5023
-8.83706 6.71112 -59.3066
6.74163 -1.71645 -11.5717
-4.12996 2.70168 -11.1578
6.29323 4.01845 25.289
18.2854 1.91548 35.0253
9.09857 12.9239 117.589
-9.01182 -11.5522 104.106
11.3029 -10.4565 -118.19
-24.4571 1.79031 -43.7857
19.34 -12.7014 -245.644
-10.2519 4.79582 -49.1662
6.24068 1.32636 8.27735
-15.0611 21.314 -321.012
12.2994 -22.9166 -281.861
4.53579 -3.02911 -13.7394
-2.30123 10.4506 -24.0492
-3.25415 -1.33511 4.34464
-0.235662 -7.96686 1.87749
21.0184 6.90852 145.206
0.643772 4.77797 3.07592
-13.3988 -7.69317 103.08
-2.49046 2.3838 -5.93674
-4.37109 -13.7552 60.1251
-3.29135 -4.70658 15.491
-5.11691 -18.2533 93.4004
12.3443 -11.7966 -145.621
13.0676 15.3554 200.659
17.5267 -15.0171 -263.202
2.71931 -3.37602 -9.18042
0.998506 -4.7515 -4.74441
-5.89248 3.18231 -18.7517
0.137122 -0.471599 -0.0646664
7.8984 20.8154 164.409
7.78891 -15.5838 -121.381
-9.83 -1.36857 13.453
9.36609 0.0750601 0.70302
-13.0303 -0.141129 1.83895
16.3977 -5.6081 -91.9598
2.33021 1.19008 2.77313
11.5595 -5.43006 -62.7686
-0.801337 14.7878 -11.85
5.32441 -5.41455 -28.8293
23.4373 14.0071 328.288
-17.7308 1.2621 -22.378
-0.820822 -7.65832 6.28611
-2.78152 15.6323 -43.4815
-0.294363 -2.24102 0.659673
20.2027 -4.30447 -86.962
-3.97186 9.53271 -37.8626
14.0495 -5.68544 -79.8777
1.8913 11.6477 22.0292
6.6496 0.813952 5.41246
8.37437 -6.54425 -54.804
4.78983 -9.09723 -43.5742
14.9403 -3.81761 -57.0361
-1.81065 -8.15522 14.7663
-11.7699 5.49208 -64.641
-8.61747 10.5284 -90.728
0.0274375 -7.02236 -0.192676
0.125369 5.45746 0.684198

Now, I want to plot a height map of this data. With the following code I get the result below.

Code:

reset session

set term wxt size 630,630
FILE = "tbTriangulationTest.dat"

set view map
set palette rgb 33,13,10
set xrange [-30:25]
set yrange [-30:25]
set xtic 5
set ytic 5

set dgrid3d 100,100 gauss 5

splot FILE w pm3d

Result:

This graph looks nice, however, to my opinion it does not necessarily give a realistic impression of the data since areas on the outside will be colored where there is actually no data at all. Well, that's a consequence of the rectangular gridding. Furthermore, depending on the interpolation method there might be artifacts.

So, my question:

Is there maybe a better way in gnuplot to display non-rectangular and ungridded data as a map?

Gnuplot version 6 now offers a solution based on the convex hull + masked surface approach I suggested initially. The convex hull part could have been done already in a script, but it seemed like a generally useful thing to build in. The use of a polygon as a mask is new. Here is the relevant section from the user manual.

Masking

The plotting style with mask is used to define a masking region that can be applied to pm3d surfaces or to images specified later in the same plot or splot command. Input data is interpreted as a stream of [x,y] or [x,y,z] coordinates defining the vertices of one or more polygons. As in plotting style with polygons, polygons are separated by a blank line. If the mask is part of a 3D (splot) command then a column of z values is required on input but is currently not used for anything. If a mask definition is present in the plot command, then any subsequent image or pm3d surface in the same command can be masked by adding the keyword mask. If no mask has been defined, this keyword is ignored.

set table $HULL
plot $POINTS using 1:2 convexhull
unset table

set dgrid3d 100,100 gauss 5
set multiplot layout 1,2
splot $POINTS using 1:2:3 with pm3d, \
      $POINTS using 1:2:(0) nogrid with points
splot $HULL using 1:2:(0) with mask, \
      $POINTS using 1:2:3 mask with pm3d
unset multiplot

This example illustrates using the convex hull circumscribing a set of points to mask the corresponding region of a pm3d surface. The splot command for the first panel renders the unmasked surface and the set of points, plotted in that order. The splot command for the second panel renders the masked surface. Note that definition of the mask must come first (plot style with mask), followed by the pm3d surface it applies to (plot style with pm3d modified by the mask keyword). A more complete version of this example is in the online demo collection mask_pm3d.dem