visualization gnuplot spherical-coordinate

Drawing rectangles in spherical coordinates in gnuplot

I have the following dataset: which is a spherical partition using the Leopardi et al, 2006 algorithm. Each grid cell is a rectangle in spherical coordinates, defined by a top left corner (theta0,phi0) and a bottom right corner, (theta1,phi1). I made the plot above by generating a lot of points for each rectangle and using splot to plot all the points. But what I really want is to plot each rectangle with a different solid color.

The example at link is close to what I want to do, using the

set obj 1 rect

command. What I'd like to do is something like:

set obj 1 rect from spherical THETA0,PHI0,R to spherical THETA1,PHI1,R

and then repeat this for lots of different rectangles. But of course this won't work since there is no "spherical" option in the gnuplot coordinates. There is a "polar" option but it only works with 2D polar coordinates, or 3D cylindrical coordinates.

Does anyone know of a way to plot colored rectangles defined in spherical coordinates with gnuplot?

Solution

To my knowledge there is no simple drawing of a rectangle in spherical coordinates, please correct me if I'm wrong. You don't show your script how you actually created your graph, except you wrote that you've created a lot of of points for plotting the spherical rectangles. I guess that's what you have to do. However, you can "simply" let gnuplot do it with a "user-friendly" input.

A few comments without going too much into the detail:

there is the option set mapping spherical (check help mapping)
define parametric functions in the range [t=0:1] which describe the outline of a rectangle
define a dummy array A in order to plot the rectangles in a loop defined by your input datablock $Data
in each iteration of the loop use a function call tmp=init(i) to get the parameters from your datablock $Data into the variables x0,y0,dx,dy
the script uses the file world.dat located in the gnuplot directory

There is certainly room for improvements.

Script: (requires gnuplot>=5.2.0, because of using arrays)

### plotting spherical rectangles
reset session

set view equal xyz
set view 60,100,1.97
set isosamples 19,25
set mapping spherical
set xyplane relative 0
set angles degrees
unset key
unset border
unset tics
set parametric
set hidden3d offset 0
set urange [-90:90]
set vrange [0:360]

# LAT0  LON0  LAT1  LON1  color
$Data <<EOD             
  63     0    35    22    0xff0000
  10    -5   -10    10    0x00cc00
  52   -40     8   -25    0x0000ff
EOD

R = 6371         # earth radius
N = 32           # choose a number divisible by 4
array A[N+1]     # dummy array

rectX(i,t) = t<0.25 ? 4*dx*t : t<0.5 ? dx            : t<0.75 ? 4*dx*(0.75-t) : 0
rectY(i,t) = t<0.25 ? 0      : t<0.5 ? 4*dy*(t-0.25) : t<0.75 ? dy            : 4*dy*(1-t)
init(i)    = (x0=real(word($Data[i],2)),    y0=real(word($Data[i],1)), \
              dx=real(word($Data[i],4))-x0, dy=real(word($Data[i],3))-y0)
lon(i)     = rectX(i,column(0)/N) + x0
lat(i)     = rectY(i,column(0)/N) + y0
color(i)   = int(word($Data[i],5))

splot R*cos(u)*cos(v), R*cos(u)*sin(v), R*sin(u) w l lc rgb "grey" , \
      'world.dat' u 1:2:(R) w l lc "black", \
      for [i=1:|$Data|] tmp=init(i) A u (lon(i)):(lat(i)): \
          (R):(color(i)) w l lw 2 lc rgb var
### end of script

Result: