Creating custom schematics with mathematica

Question

I want to produce the following schematic

A starting code

Clear["Global`*"];
a1 = Graphics[{Arrowheads[0.025], Arrow[{{0, 0}, {2, 0}}]}];
a2 = Graphics[{Dashed, Line[{{0, 0}, {-2, 0}}]}];
a3 = Graphics[{Arrowheads[0.025], Arrow[{{0, 0}, {0, 2}}]}];
a4 = Graphics[{Arrowheads[0.025], Arrow[{{0, 0}, {-1.5, -1}}]}];
a5 = Graphics[{Dashed, Line[{{0, 0}, {1.5, 1}}]}];
p1 = ListPlot[{{-1.1, -0.72}}, 
     PlotStyle -> {GrayLevel[0.4], PointSize[0.045]}];
p2 = ListPlot[{{ 1.1, 0.72}}, 
     PlotStyle -> {GrayLevel[0.4], PointSize[0.045]}]; 
Show[{a1, a2, a3, a4, a5, p1, p2}, ImageSize -> 550]

I can also easily insert all the text. My problem is how to insert the twisted arrow around the z axis. Any ideas?

@Kuba A good starting example would be nice. In particular, how to draw the arrows at the end of the axes and also the curved arrow around the z-axis. — Vaggelis_Z, Sep 05 '16 at 09:45
I think this is too broad. Please start by learning how to build graphics from primitives, then ask specific questions about the points where you get stuck. See here for axes with arrows: http://mathematica.stackexchange.com/a/11606/12 http://mathematica.stackexchange.com/q/2785/12 — Szabolcs, Sep 05 '16 at 09:47
The curved arrow will need to be done from scratch. Use a Table to create the set of coordinates manually, and put them in Arrow. — Szabolcs, Sep 05 '16 at 09:49
I think broad guidelines would be in order, so you know that you are on the right track: 1. build everything from graphics primitives and put them in a Graphics3D. The axes need to be done manually too if we want arrowheads, use Arrow. Use Dashed or Dotted directives for those appearances. For lines, Line. For text, Text. Use Background -> White in Text to make it obscure the line behind like with $r_1$. Use Sphere[] for the balls, $P_1, P_2$. The curved arrow will be a single Arrow primitive. Use the Arrowheads directive to control the arrow size. — Szabolcs, Sep 05 '16 at 10:03
" My problem is the arrows." Use Arrow instead of Line, and use the Arrowheads directive to specify their size. Instead of ListPlot, use Point and the PointSize directive. Normally one would put everything in a single Graphics instead of combining multiple ones with Show. Since this is really 3D, you can consider Graphics3D instead. — Szabolcs, Sep 05 '16 at 14:06
ellipse = Graphics[Rotate[Circle[{0, 0}, {2, 1}, {135*Degree, 405*Degree}], 0*Degree]]; arrow = Graphics[{Arrowheads[Medium], Arrow[{{2*Cos[45*Degree], Sin[45*Degree]}, {2*Cos[45*Degree] - 0.12, Sin[45*Degree] + 0.07}}]}]; plot = Show[ellipse, arrow] The values of 0.12 and 0.07 are a result of trial and error; this can be made automatic using a tangent but I don't have the time now. I'll look at this again later. — corey979, Sep 05 '16 at 14:24
@corey979 It seems to work. But how can I adjust the size of the twisted arrow? — Vaggelis_Z, Sep 05 '16 at 14:27

score 6 · Accepted Answer · answered Sep 05 '16 at 15:53

I've created this:

TwistArrow[pos_List, ab_List] := 
 Module[{ellipse, arrow, pos1 = pos[[1]], pos2 = pos[[2]], 
   a = ab[[1]], b = ab[[2]]},
  ellipse = 
   Graphics[
    Rotate[Circle[pos, {a, b}, {135 Degree, 405 Degree}], 0 Degree]]; 
  arrow = Graphics[{Arrowheads[0.015], 
     Arrow[{{a Cos[45 Degree] + pos1, 
        b Sin[45 Degree] + pos2}, {a Cos[45*Degree] + pos1 - 0.06, 
        b Sin[45*Degree] + pos2 + 0.035}}]}]; 
  plot = Show[ellipse, arrow]
  ]

which gives (plot1 is the figure Showed in the question)

Show[plot1,TwistArrow[{0, 1}, 0.1 {2, 1}]]

pos_List={0,1} is the location of the center of the ellipse, and ab_List=0.1 {2,1} are the major and minor axis of the ellipse (or semi-axis?). The other parameters, i.e. all angles, size of the arrow (Arrowheads[0.015]) and the positioning (-0.06 and +0.035) were chosen for this particular problem. One can put them all as arguments of the function, but I think it's easiest to just fiddle with the parameters to find the right ones.

It works like a charm! Many thanks. – Vaggelis_Z Sep 05 '16 at 16:08 — Vaggelis_Z, Sep 05 '16 at 16:08

score 3 · Answer 2 · answered Sep 05 '16 at 15:11

3

Have a look at SciDraw at http://scidraw.nd.edu/. Lots of support for many kinds of figures.

answered Sep 05 '16 at 15:11

Keith

49
1
3

Looks interesting. – Daniel Lichtblau Sep 05 '16 at 16:18
@DanielLichtblau It's one of the largest and most carefully designed free packages that I am aware of. The biggest strength is creating multipanel figures. Drawbacks are performance and the fact that it is quite different from standard Mathematica, so it takes a while to learn. – Szabolcs Sep 06 '16 at 10:26

Creating custom schematics with mathematica

2 Answers2