Drawing polygons with holes using Gnuplot - gnuplot

Question

Is there a way using Gnuplot 5.0 to plot a polygon with a hole with filledcurves?
Here are my test data:
# Outer ring
0 -2
-2 0
0 2
2 0
0 -2
# Inner ring
-0.5 0.5
-0.5 -0.5
0.5 -0.5
0.5 0.5
-0.5 0.5
And here is the result:
I know I could re-order the vertices in order to hide the connecting line (in fact the polygon frontier) between the outer and inner ring. But I will deal with machine-generated data, and I would prefer minimize the amount of data preprocessing.
In some other drawing programs, we can draw holes inside polygons by changing the winding-rule to even-odd. But I didn't find such option in gnuplot.
Finally, I cannot just draw the "hole" in white, since in my application I have several shapes to draw, And I want to see other shapes behind the "hole".

Answer 1

Why not just plot the hole in white on top of the shape?
Separate your date into
# shape.txt
0 -2
-2 0
0 2
2 0
0 -2
and
# hole.txt
-0.5 0.5
-0.5 -0.5
0.5 -0.5
0.5 0.5
-0.5 0.5
and then use
plot "shape.txt" u 1:2 w filledcurves, 'hole.txt' u 1:2 w filledcurves lc 'white'

Answer 2

The following solution does what you already mentioned in your question: It reorders the points of the inner polygon in such a way, that the endpoint of the outer polygon and the starting point of the inner polygon have minimal distance (hence no line across the inner polygon). It does is automatically with gnuplot only, so this still might be an acceptable solution for you.
Assumptions:
the outer curve is closed (start point = end point)
the outer curve does not have duplicated points
Procedure:
go through the data and when the first x and y values are found again, the outer structure is finished and the inner structure starts (row index stored in idx0)
when the inner structure starts, it looks for the minimum distance to the start/end point of the outer structure (x0,y0) (row index stored in idx1)
the data is plotted into a datablock $Hollow: first the outer as is and then the inner starting from idx1 to end, and then the inner starting from (idx0+2) to idx1.
In the example below red lines are drawn first to illustrate the empty polygon in the center. Tested with gnuplot 5.0.0.
For multiple holes in a filled curve you might want to check gnuplot: How to draw a filled area with hole? with a rather general but pretty lengthy solution.
Code:
### draw hollow polygon
reset session
$Data <<EOD
# Outer ring
0 -2
-2 0
0 2
2 0
0 -2
# Inner ring
-0.5 0.5
-0.5 -0.5
0.5 -0.5
0.5 0.5
-0.5 0.5
EOD
Distance(x0,y0,x1,y1) = sqrt((x1-x0)**2 + (y1-y0)**2)
GetIdxs(colX,colY) = LastOuter==1 ? ( d1=Distance(x0,y0,column(colX),column(colY)), \
d0==d0 ? (d1<dmin ? (idx1=column(0), dmin=d1) : 0) : \
(idx1=column(0),dmin=d1), d0=d1, LastOuter) : \
column(0)==0 ? (d0=d1=dmin=NaN,x0=column(colX),y0=column(colY)) : \
column(colX)==x0 && column(colY)==y0 && LastOuter==0 ? \
(idx0=column(0),x0=column(colX),y0=column(colY),LastOuter=1 ) \
: LastOuter
set table $Dummy
plot LastOuter=0 $Data u 1:2:(GetIdxs(1,2)):(d1) w table
set table $Hollow
plot $Data u 1:2 every ::::idx0 w table
plot $Data u 1:2 every ::idx1 w table
plot $Data u 1:2 every ::idx0+2::idx1 w table
unset table
plot for [i=-5:5] -x+i/5.lw 2 lc "red" notitle, \
$Hollow u 1:2 w filledcurves lc 1
### end of code
Result:
Just for better understanding the content of $Dummy and $Hollow.
$Dummy
0 -2 -2 nan
-2 0 0 nan
0 2 0 nan
2 0 0 nan
0 -2 1 nan
-0.5 0.5 1 2.54951
-0.5 -0.5 1 1.58114
0.5 -0.5 1 1.58114
0.5 0.5 1 2.54951
-0.5 0.5 1 2.54951
$Hollow
0 -2
-2 0
0 2
2 0
0 -2
-0.5 -0.5
0.5 -0.5
0.5 0.5
-0.5 0.5
-0.5 -0.5

Answer 3

My other solution is based on reordering the inner curve in order to avoid the connection line from outer to inner curve crossing the open area. However, this was rather cumbersome with dummy and extra tables and with a lengthy, confusing expression.
Here is a another much simpler solution:
It is based on variable linecolors, i.e. invisible (fully-transparent) lines, when you switch from the outer curve to the inner curve. This should be fine unless you want to create a SVG or DXF and use the graph as pattern for a cutter.
Prerequisites:
outer and inner curves must be closed (first point = last point)
you have to make sure that outer and inner curves have opposite directions (CW=clockwise and CCW=counterclockwise), this was the case in your example. Otherwise the area will not be hollow but filled.
there should be no empty line between inner and outer curves, but two empty lines between the shapes.
You can easily tell gnuplot when the outer curve ends: when the first x,y-coordinates appears again. It doesn't matter where the inner curve starts as long as the direction is reversed to the outer one.
Just for illustration, I plotted sin(x) and made the 1st structure opaque and 2nd and 3rd structure in semitransparent color.
Script: (works for gnuplot>=5.0.3)
### plot areas with holes
reset session
$Data <<EOD
0 -2 0 # outer CW
-2 0 0
0 2 0
2 0 0
0 -2 0
-0.5 0.5 1 # inner CCW
-0.5 -0.5 1
0.5 -0.5 1
0.5 0.5 1
-0.5 0.5 1
-0.5 -1 0 # outer CCW
-0.1 -0.1 0
-1 0.5 0
-1.5 -1 0
-0.5 -1 0
-0.8 0.2 1 # inner CW
-0.2 -0.1 1
-0.6 -0.8 1
-1.2 -0.8 1
-0.8 0.2 1
0 -1 0 # outer CCW
1 -1 0
1.3 0 0
0.3 0 0
0 -1 0
1.1 -0.2 1 # inner CW
0.9 -0.8 1
0.2 -0.8 1
0.4 -0.2 1
1.1 -0.2 1
EOD
myColors = "0x00ff00 0x770000ff 0x77ff0000"
myColor(i) = i+1>words(myColors) ? 0x000000 : int(word(myColors,i+1))
myColorX(i) = (x0=x1, x1=$1, y0=y1, y1=$2, \
$0==0 ? (fx=x1,fy=y1) : x1==fx && y1==fy ? last=1 : 0, \
last ? 0xff123456 : myColor(i))
set key noautotitle
set multiplot layout 1,2
set title "fixed linecolor"
plot 2*sin(2*x) lw 2, \
for [i=0:2] $Data u 1:2:(myColor(i)) index i w filledcurves lc rgb var lw 2
set title "variable line color with fully transparent lines"
plot 2*sin(2*x) lw 2, \
for [i=0:2] x1=y1=(last=0,NaN) $Data u 1:2:(myColorX(i)) index i \
w filledcurves lc rgb var lw 2
unset multiplot
### end of script
Result: