Drawing a simple polygon using Gnuplot with "angle signs" - gnuplot

Question

Disclaimer: I am new to Gnuplot, and I need to plot some "simple" things for my studies.
I want to plot a part of a polygon with some names and vectors added.
The picutre below was created with Euklid Dynageo, and I am now trying to create this with Gnuplot.
The biggest problem I am facing right now is the labeling u,v,w and adding the angles to the plot. I think I would use vectors and lines.
Do you now a 'simple' way to create this plot?

Answer 1

If you really need to use Gnuplot for this, you have to make it all manually by placing various objects, labels and arrows (keep in mind that complex plots will be cumbersome). A minimal example for two arrows and alpha_1, similar like in your example, could like like this:
# two arrows:
set arrow 1 from 0,0 to sqrt(2)/2,sqrt(2)/2
set arrow 2 from 0,0 to 1,0
# the alpha_1 symbol:
set label 1 '{/Symbol a}_1' at 0.2,0.1 front
# the filled yellow arc (from 0 to 45deg):
set style fill solid 1.0 border
set object 1 circle at 0,0 radius 0.2 arc[0:45] fc rgb "yellow"
# proper ratio, range, and plot 'something':
set xrange[-0.1:1.1]
set yrange[-0.1:1.1]
set size ratio 1
plot 1/0
Lookup the manual for possible object properties.

Answer 2

gnuplot is a very versatile plotting tool, but certainly not optimized for such tasks. For this type of drawing maybe Inkscape or others tools might be better choices, especially for interactive drawing by clicking, dragging and snapping.
And as #JackGlasshard already mentioned, of course you can do such graphs with gnuplot which will be rather time consuming if you do it manually.
Alternatively, you can facilitate the work if you use a "template".
Creating such a template probably only makes sense if you need to create more than one drawing.
Just for fun and feasibility, I tried to create such a template for general use to make such graphs easier.
For the input data you need 3 datablocks (without headers)
$Points: # no., x, y, label, xoff, yoff, pt, ps, color
you define: point number, x-coordinate, y-coordinate, point label, x-offset, y-offset, pointtype, pointsize, point color
$Vectors: # p1, p2, label, arrow, lw, dt, xoff, yoff, color
you define: first point number, second point number, label, arrowsstyle (-1=backhead, 0=nohead, 1=head, 2=heads), linewidth, dashtype, x-offset, y-offset, vector color
$Angles: # p1, p2, p3, r, label, aoff, roff, color
you define: 1st point number, 2nd point number (=angle center point), 3rd point number, radius, label, angular label offset, radial label offset, color
Now, you only have to change the data part of the script for your custom graph. In case you want to insert "invisible" vector starting or end points, simply set pointsize to 0 in $Points. The plotting of the variable arrowheads is a bit cumbersome because of the issue mentioned in this question.
For sure, more features and more flexibility can be added to the template. No warranty that the script is free of bugs. There is certainly room for improvements.
Update: (linewidth and dashtype added)
Since there is no variable linewidth (lw var) and no variable dashtype (dt var)
you have to plot each line separately in a for loop and every ::n::n.
Furthermore, I noticed that the order of variable pointsize (ps var) and and variable pointtype (pt var) apparently has changed from gnuplot 5.2 to 5.4. Not sure whether this intentional or a "bug".
The version below has the order for gnuplot 5.4.
Script:
### drawing sketch with points, vectors and angles
reset session
# no., x, y, label, xoff, yoff, pt, ps, color
$Points <<EOD
1 1 1 "" 0 0 5 1 0xff0000
2 10 2 V_{i-1} 0 0 5 1 0xff0000
3 15 10 V_i 0 0 5 1 0xff0000
4 4 12 X -1.5 0 5 1 0xff0000
5 14 16 V_{i+1} 0 0 5 1 0xff0000
6 5 20 "" 0 0 5 1 0xff0000
EOD
# p1, p2, label, arrow, lw, dt, xoff, yoff, color
# arrows: -1=backhead, 0=nohead, 1=head, 2=heads
$Vectors <<EOD
1 2 "" 0 1.0 1 0 0 0xff0000
2 3 "" 0 2.0 1 0 0 0x000000
3 5 "" 0 1.5 3 0 0 0x000000
4 2 w 1 1.0 1 1.0 0 0x000000
4 3 v 1 1.0 1 0 0.7 0x0000ff
4 5 u 1 1.0 1 0 0.7 0x000000
5 6 "" 0 1.0 1 0 0 0x000000
EOD
# p1, p2, p3, r, label, aoff, roff, color
# p2=angle center point
$Angles <<EOD
2 4 3 4.0 α_{i-1} 7.0 0.5 0xffcccc
3 4 5 4.5 α_i 3.0 0.7 0xffffcc
EOD
### end of data input
### start of template
# point/vector coordinates
px(n,m) = real(word($Points[int(word($Vectors[n],m))],2)) # x coordinate of point n
py(n,m) = real(word($Points[int(word($Vectors[n],m))],3)) # y coordinate of point n
vxd(n) = px(n,2)-px(n,1) # vector delta x
vyd(n) = py(n,2)-py(n,1) # vector delta y
vxc(n) = (px(n,2)+px(n,1))/2. # vector center x
vyc(n) = (py(n,2)+py(n,1))/2. # vector center y
lw(n) = real(word($Vectors[n],5))
dt(n) = int(word($Vectors[n],6))
# angles
as(n) = int(column(5)+2) # arrow style
ax(n) = real(word($Points[int(word($Angles[int(column(0)+1)],n))],2)) # angle center x
ay(n) = real(word($Points[int(word($Angles[int(column(0)+1)],n))],3)) # angle center y
set angle degrees
Angle(x0,y0,x1,y1) = (_dx=x1-x0, _dy=y1-y0, _L=sqrt(_dx**2 + _dy**2), _L==0 ? NaN : \
(_dy>=0 ? acos(_dx/_L) : -acos(_dx/_L) ))
a1(m) = Angle(ax(2),ay(2),ax(1),ay(1)) # starting angle
a2(m) = Angle(ax(2),ay(2),ax(3),ay(3)) # end angle
set style arrow 1 backhead filled # -1
set style arrow 2 nohead filled # 0
set style arrow 3 head filled # 1
set style arrow 4 heads filled # 2
set size ratio -1 # ensure same x- and y-ratio
set key noautotitle
set xrange [0:22]
set yrange [0:22]
set mxtics 5
set mytics 5
set grid x,y,mx,my
set style fill solid 0.5 border lc "black"
plot $Angles u (ax(2)):(ay(2)):4:(a1(0)):(a2(0)):8 w circles lc rgb var, \
'' u (ax(2)+($4*0.5+$7)*cos(0.5*(a1(0)+a2(0))+$6)): \
(ay(2)+($4*0.5+$7)*sin(0.5*(a1(0)+a2(0))+$6)):5 w labels font "Times New Roman,13" center, \
for [i=1:|$Vectors|] $Vectors \
u (px(i,1)):(py(i,1)):(vxd(i)):($4==-1?vyd(i):NaN):9 every ::i-1::i-1 w vectors lc rgb var lw lw(i) dt dt(i) filled backhead, \
for [i=1:|$Vectors|] '' \
u (px(i,1)):(py(i,1)):(vxd(i)):($4== 0?vyd(i):NaN):9 every ::i-1::i-1 w vectors lc rgb var lw lw(i) dt dt(i) filled nohead, \
for [i=1:|$Vectors|] '' \
u (px(i,1)):(py(i,1)):(vxd(i)):($4== 1?vyd(i):NaN):9 every ::i-1::i-1 w vectors lc rgb var lw lw(i) dt dt(i) filled head, \
for [i=1:|$Vectors|] '' \
u (px(i,1)):(py(i,1)):(vxd(i)):($4== 2?vyd(i):NaN):9 every ::i-1::i-1 w vectors lc rgb var lw lw(i) dt dt(i) filled heads, \
for [i=1:|$Vectors|] '' \
u (vxc(i)+$7):(vyc(i)+$8):3:9 every ::i-1::i-1 w labels font ",12" tc rgb var, \
$Points u 2:3:7:8:9 w p ps var pt var lc rgb var, \
'' u ($2+$5):($3+$6):4:9 w labels tc rgb var font ",12" left offset 1,0
### end of script
Result: