GNUPlot: Generate `surf`-like plot from `scatter` base

Question

firstly, I'm very new to GNUPlot, so please forgive me if I might sound silly or say stupid things.

I have to visualise some 3D data. I firstly wanted to have something that just worked correctly.

Here it is an example:

It's a scatter plot, meaning that I have the list of all (x, y, z) values, which come from a given computation.

I was now wondering if there is a way to convert this plot into a surf-like one, but without having to create a grid-mesh, because actually, real plots are made up of many of these zones, contingent in space, but not necessarily in memory (i.e. there's not order in listing all points, as well as each patch has its own setup). In which case, creating a grid is not possible..

Here is the script I built up to now:

# Main window settings
MAINFONT    = ""
WINDOWTITLE = "BRM (mesher)"
WSIZEW = 3040 # base: 1980
WSIZEH = 2080 # base: 1080
set term wxt \
   size WSIZEW, WSIZEH \
   position 50, 50 \
   font MAINFONT title WINDOWTITLE


#
# commands taken from GNU demo folder
#

# unset hidden3d
# set parametric
set view 45, 45
set border linestyle 102 linewidth 2


# draws a grid in the XY plane (at the base)
# set style line 102 lc rgb "#d6d7d9" lt 0 lw 1
set grid back ls 102


#
# setting styles
#

LINETYP = 8
LINEWDT = 2
POINTTY = 7
POINTIN = 0
POINTSZ = 1

#                              "#AARRGGBB"
set style line 1 linecolor rgb "#B5000000" \
   linetype LINETYP linewidth LINEWDT \
   pointtype POINTTY pointinterval POINTIN pointsize POINTSZ

set style line 2 linecolor rgb "#B5EEEEEE" \
   linetype LINETYP linewidth LINEWDT \
   pointtype POINTTY pointinterval POINTIN pointsize POINTSZ
set style data points


# #
# # LEGEND (related)
# #
# LEGENDTITLE = "brm"
# set key nobox \
#    title LEGENDTITLE

#
# Annotation: title and labels
#
FIGURETITLE = "Bispectrum (MESHER)"
XLABEL = "f_1"
YLABEL = "f_2"
set title FIGURETITLE
set xlabel XLABEL
set ylabel YLABEL

# ??
set ticslevel 0.1


#
# RANGES
#
_xrange  = 0
_yrange  = 0

_xrangev_min = -0.58
_xrangev_max =  0.58
if (_xrange == 0) \
   set autoscale x; \
else \
   set xrange [_xrangev_min : _xrangev_max]

_yrangev_min = -0.58
_yrangev_max =  0.58
if (_yrange == 0) \
   set autoscale y; \
else \
   set yrange [_yrangev_min : _yrangev_max]


# by default, always autoscale Z axis
set autoscale z

#
# PALETTE (???)
#
set palette defined


#
# DATA file - ACTUAL PLOTTING (end of script)
#
DATAFILE = "brm_gnu.dat"
splot DATAFILE linestyle 1

set terminal png transparent \
   size WSIZEW, WSIZEH \
   truecolor enhanced
set out 'brm_gnu.png'
splot DATAFILE linestyle 2

Data in file brm_gnu.dat is layed down like this:

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 -0.906500000000000      -3.700000000000063E-002  1.327938872744156E-008
 -0.906500000000000      -1.850000000000063E-002  8.877473815630514E-009
 -0.906500000000000      -6.314393452555578E-016  4.255507953928457E-009
 -0.906500000000000       1.849999999999937E-002  1.044166431933323E-008
 -0.906500000000000       3.699999999999937E-002  1.743614564704666E-008
 -0.906500000000000       5.549999999999937E-002  2.412148830393200E-008
 -0.906500000000000       7.399999999999937E-002  3.209052259334402E-008
 -0.906500000000000       9.249999999999937E-002  4.040794806557133E-008
 -0.906500000000000       0.110999999999999       5.083090912922838E-008
 -0.906500000000000       0.129499999999999       6.275741062996620E-008
 -0.906500000000000       0.147999999999999       7.854088457460013E-008
 -0.906500000000000       0.166499999999999       9.845150853016995E-008
 -0.906500000000000       0.184999999999999       1.265800089781315E-007
 -0.906500000000000       0.203499999999999       1.653939929314344E-007
 -0.906500000000000       0.221999999999999       2.196862110699713E-007
 -0.906500000000000       0.240499999999999       2.602144086867102E-007
 -0.906500000000000       0.258999999999999       9.884958131045721E-008
 -0.906500000000000       0.277499999999999      -2.035802542405856E-007
 -0.906500000000000       0.295999999999999      -2.545269003492000E-007
 -0.906500000000000       0.314499999999999      -2.259593091092582E-007
 -0.906500000000000       0.332999999999999      -1.963318006679911E-007
 -0.906500000000000       0.351499999999999      -1.737574136603818E-007
 -0.906500000000000       0.369999999999999      -1.579312255221945E-007
 -0.906500000000000       0.388499999999999      -1.466792948328887E-007
 -0.906500000000000       0.406999999999999      -1.392395360328343E-007
 -0.906500000000000       0.425499999999999      -1.344964799883919E-007
 -0.906500000000000       0.443999999999999      -1.323297848028745E-007
 -0.906500000000000       0.462499999999999      -1.322469414183294E-007
 -0.906500000000000       0.480999999999999      -1.345321624991211E-007
 -0.906500000000000       0.499499999999999      -1.390900220084392E-007
 -0.906500000000000       0.517999999999999      -1.466735981468943E-007
 -0.906500000000000       0.536499999999999      -1.576717543811861E-007
 -0.906500000000000       0.554999999999999      -1.737028723144627E-007
 -0.906500000000000       0.573499999999999      -1.958655577255762E-007
 -0.906500000000000       0.591999999999999      -2.258266556659192E-007
 -0.906500000000000       0.610499999999999      -2.536813208860895E-007
 -0.906500000000000       0.628999999999999      -2.033996127677433E-007
 -0.906500000000000       0.647499999999999       9.839891803808796E-008
 -0.906500000000000       0.665999999999999       2.598892689170532E-007
 -0.906500000000000       0.684499999999999       2.183239868389179E-007
 -0.906500000000000       0.702999999999999       1.651091175348573E-007
 -0.906500000000000       0.721499999999999       1.255105409220265E-007
 -0.906500000000000       0.739999999999999       9.821654436346623E-008
 -0.906500000000000       0.758499999999999       7.762178553728138E-008
 -0.906500000000000       0.776999999999999       6.254401541217292E-008
 -0.906500000000000       0.795499999999999       4.997354948465678E-008
 -0.906500000000000       0.813999999999999       4.020011324238698E-008
 -0.906500000000000       0.832499999999999       3.124110268472883E-008
 -0.906500000000000       0.850999999999999       2.390820741791080E-008
 -0.906500000000000       0.869499999999999       1.655039280302377E-008
 -0.906500000000000       0.887999999999999       1.021290092645050E-008
 -0.906500000000000       0.906499999999999       9.561331090630669E-009
 -0.906500000000000       0.924999999999999       9.044608397277014E-009

Thanks :)

PS: ANY suggestion/comment/critics not strictly related to the question, but that would improve my knowledge, is well accepted!

EDIT 1: Here is an example of how I'd like the plot to look like instead:

Answer 1

You don't show nearly enough data to get a feel for what the full data set looks like. In the hope that it helps, here is an example of using set dgrid3d on a small number of points to produce a plot sort of like the one you show:

$DATA << EOD
-5.0 -5.0 0
-5.0  5.0 0
 5.0  5.0 0
 5.0 -5.0 0
 0.0  0.0 0
-3.0 -2.0 8.e10
-1.0  2.0 6.e10
-2.0 -1.0 9.e10
 2.0  2.0 5.e10
 0.0 -3.0 8.e10
 3.0  0.0 7.e10
EOD

set grid x y z
set grid vertical
set xyplane at 0

set dgrid3d 100,100 gauss kdensity 0.6, 0.6

splot $DATA with pm3d

Examples using amended data

Probably the best answer is to change your data format slightly so that each X value has its own block in the file. I.e. put a blank line between the section with X=-0.925 and the section with X=-0.888 and so on. That make the plot command very simple. However it seems there are some glitches in your data, maybe due to inconsistent sampling?

set hidden3d offset 0   # remove hidden lines
splot "DATA" with lines title "blank line between x slices"

A different way is to use dgrid3d as shown before. You must tailor the dgrid3d parameters and weighting scheme to your data. I cannot do that for you, you have to think about how you want each data point to contribute to the surface: How big is the neighborhood it affects? Is it a requirement that the surface pass exactly through each point? How smooth should the surface be? Etc...

Anyhow, here is a simple example using your amended data. The sample data pretty much consists of 100 samples for each x and 3 for each y so that's what we set as a grid. We ask for a spline fit through the points.

set dgrid3d 100,3 spline
set hidden3d
plot "DATA" with lines