Insets around a clock

Question

I have this code to generate a clock-like diagram:

Graphics[{Circle[{0, 0}, 2], Line[{{0, 0.8}, {0, 1.2}}], 
Arrow[Reverse@Table[{Cos[t], Sin[t]}, {t, -Pi, Pi/2, 0.1}]], 
Table[Line[{{2 Sin[θ],2 Cos[θ]}, {(2 - 0.2) Sin[θ], (2 -0.2 ) Cos[θ]}}], {θ, 0,2 π, π/9}],
 Text[Style[0, Large], {0, 0.6}]}]

It has 18 tick marks. I also have this code to generate 18 LinePlots:

AllData= Import["https://pastebin.com/raw/DsVfiMZN", "Table"];
datai=Table[data[20*i] =AllData[[All,2*i+1;;2*i+2]], {i, 0,17}];
ploti=Table[p[20*i]=ListLinePlot[data[20*i],PlotRange->{{0.5,7.5}, 
{0,0.6}},Axes->False,PlotStyle->{Black}],{i,0,17}];
GraphicsRow[ploti,ImageSize->1000]

Each one of the 18 plots is indexed as an angular position, so p[0] refers to 0 degrees, p[20], 20 degrees and so on. How can I place each plot around the clock at the correct tick marks? Something like this:

Somewhat related: (31257), (31347), (104639), (166247) – Mr.Wizard Nov 15 '19 at 12:07 — Mr.Wizard, Nov 15 '19 at 12:07

kglr · Accepted Answer · 2019-11-16T03:13:07.787

You can also arrange the lines on a circle like a pie chart:

ClearAll[llpOnCircle]
llpOnCircle[dt_, colors_, filling_: True, r1_: 1, r2_: 3/2, scale_: 1] := 
  MapIndexed[{Darker @ colors[[#2[[1]]]], 
     Line[(r1 + #[[2]] scale) {Cos[#[[1]]], Sin[#[[1]]]} & /@ #], 
     If[filling, {Opacity[.5], Lighter@colors[[#2[[1]]]] , 
       Polygon[Join[((r1 + #[[2]] scale) {Cos[#[[1]]], Sin[#[[1]]]} & /@ #), 
        (r2 {Cos[#[[1]]], Sin[#[[1]]]} & /@ Reverse[#])]]}, {}]} &, dt];

Examples:

We first pre-process the input data to partition and re-scale the columns:

columns = Range @ 36;
angles = Partition[Subdivide[0, 2 Pi, Length[columns]/2], 2, 1];
rescaled = AllData[[All, #]] & /@ Partition[columns, 2];
rescaled[[All, All, -1]] = Rescale[rescaled[[All, All, -1]]];
rescaled[[All, All, 1]] = MapIndexed[
   Rescale[#, MinMax[AllData[[All, 1]]], angles[[#2[[1]]]]] &, rescaled[[All, All, 1]]];

and combine the graphics primitives from OP's first code block

g1 = {Circle[{0, 0}, 2], Line[{{0, 0.8}, {0, 1.2}}], 
   Arrow[Reverse@Table[{Cos[t], Sin[t]}, {t, -Pi, Pi/2, 0.1}]], 
   Table[Line[{{2 Sin[θ], 2 Cos[θ]}, {(2 - 0.2) Sin[θ], (2 - 0.2) Cos[θ]}}], 
     {θ, 0, 2 π, π/9}], 
   Text[Style[0, Large], {0, 0.6}]};

with lines produces by llpOnCircle:

SeedRandom[777];
colors = RandomColor[18];
labels = RandomWord[18];
legend = SwatchLegend[colors, labels];


Legended[Graphics[{g1, llpOnCircle[rescaled, colors, True, 2.1, 2.6, .5]}, 
  ImageSize -> Large], legend]

Legended[Graphics[{g1, llpOnCircle[rescaled, colors, False, 2.1, 2.6, .5]}, 
  ImageSize -> Large], legend]

Change the fifth argument of llpOnCircle from 2.6 to 2 to get filling below the lines:

Legended[Graphics[{g1, llpOnCircle[rescaled, colors, True, 2.1, 2, .5]}, 
  ImageSize -> Large], legend]

Use colors = ColorData[97] /@ Range[Length@columns]; to get

Update: An alternative approach using SectorChart with a custom ChartElementFunction:

ClearAll[cEF]
cEF = {Line[MapThread[# {Cos@#2, Sin@#2} &, {#[[2, 1]] + #3[[1]], 
       Subdivide[#[[1, 1]], #[[1, 2]], Length[#3[[1]]] - 1]}]]} &;

yvals = rescaled[[All, All, -1]]; 
SectorChart[{1, Max@yvals} -> # & /@ yvals, SectorOrigin -> {Automatic, 3}, 
 Epilog -> Inset[Graphics @ g1, {0, 0}, Automatic, Scaled[1/2]], 
 ImageSize -> 600, ChartStyle -> (ColorData[97] /@ Range[18]), 
 ChartElementFunction -> cEF, 
 ChartLabels -> Placed[MapIndexed[Style[#, 14, ColorData[97][#2[[1]]]] &, labels], 
   "RadialOutside"]]

You can control the radial width of the sectors using a combination of values in the second part of the SectorOrigin option setting and in the last argument of Inset. You can use the option SectorSpacing to separate sectors:

SectorChart[{1, Max@yvals} -> # & /@ yvals, 
 SectorSpacing -> {.5, 0}, 
 SectorOrigin -> {Automatic, 4}, 
 Epilog -> Inset[Graphics@g1, {0, 0}, Automatic, Scaled[4/5]], 
 ImageSize -> 600, 
 ChartStyle -> (ColorData[97] /@ Range[18]), 
 ChartElementFunction -> cEF]

To add edges for a more clear separation of sectors, replace cEF with cEF2 where

ClearAll[cEF2]
cEF2 = {Line[MapThread[1.02 # {Cos@#2, Sin@#2} &, {#[[2, 1]] + #3[[1]], 
       Subdivide[#[[1, 1]], #[[1, 2]], Length[#3[[1]]] - 1]}]], 
    FaceForm[], 
    ChartElementData["Sector"][{#[[1]], {.95 #[[2, 1]], 1.02 #[[2, 2]]}}, ##2]} &;

Update 2: Play with options settings for SectorOrigin to control the starting positions and orientation of sectors. For example:

Row[SectorChart[{1, Max@yvals} -> # & /@ yvals, 
    SectorOrigin -> #, 
    Epilog -> Inset[Graphics@g1, {0, 0}, Automatic, Scaled[1/2]], 
    ImageSize -> 400, ChartStyle -> (ColorData[97] /@ Range[18]), 
    ChartElementFunction -> cEF2, 
    PlotLabel -> Row[{"SectorOrigin -> ", #}]] & /@ 
  {{{Pi/2, "Clockwise"}, 1.5}, {{Pi/2, "Counterclockwise"}, 2}}]

Nice, but there is something strange with the insets. They are in the wrong positions. If you look at the one at the position zero, it seems to be replaced by the one at 80 degrees. How can I remove all the filling? — Rodrigo, Nov 15 '19 at 02:55
@Rodrigo, updated with a version that makes filling optional. Re positions you can control the starting position and direction in the pre-processing stage using, for example, angles = Reverse @Partition[Subdivide[0, 2 Pi, Length[columns]/2], 2, 1] to get the parts oriented clockwise; and angles = RotateRight[#, 5] &@Reverse@Partition[Subdivide[0, 2 Pi, Length[columns]/2], 2, 1] to have the fifth part positioned at 0 and the parts oriented clockwise. — kglr, Nov 15 '19 at 03:30
Now it looks correct. Even with filling set as false, the lines still keep the random color. Can that be turn off as well? — Rodrigo, Nov 15 '19 at 03:38
@Rodrigo, you can use colors = Table[Black, 18] to make all lines Black. — kglr, Nov 15 '19 at 03:42
With the second example, using cEF2, the insets are still in the wrong position. Also, if I turn off the legends, the insets move outwards. — Rodrigo, Nov 15 '19 at 17:29
Great. Just one more thing. In update 2, what attribute changes the height of the insets? I mean the width of the outer circular crown. I would like to make it just a bit narrower. — Rodrigo, Nov 16 '19 at 01:47
@Rodrigo, you can play with combinations of the second part of SectorOrigin and the last argument of Inset. For example, try SectorOrigin -> {{Pi/2, "Counterclockwise"}, 10} and Epilog -> Inset[Graphics@g1, {0, 0}, Automatic, Scaled[.75]]. — kglr, Nov 16 '19 at 02:01
I've noticed something after coming back to this question. If you look at Update2 on the left, the plots seem to be flipped horizontally. The blue graph at the position 0 seems to be a mirror image of the original p[0] plot. I can't figure out why. — Rodrigo, May 20 '22 at 02:42
@Rodrigo, try replacing Subdivide[...] in cEF with Reverse @ Subdivide[...]? — kglr, May 20 '22 at 23:15

score 15 · Answer 2 · answered Nov 14 '19 at 20:02

Clear["Global`*"]

AllData = Import["https://pastebin.com/raw/DsVfiMZN", "Table"];
datai = Table[
   data[20*i] = AllData[[All, 2*i + 1 ;; 2*i + 2]], {i, 0, 17}];

ploti = Table[
   p[20*i] = ListLinePlot[data[20*i],
     PlotRange -> {{0.5, 7.5}, {0, 0.6}},
     Axes -> False,
     PlotStyle -> Black,
     ImageSize -> 36],
   {i, 0, 17}];

Graphics[{
  Circle[{0, 0}, 2],
  Line[{{0, 0.8}, {0, 1.2}}],
  Arrow[Reverse@Table[{Cos[t], Sin[t]},
     {t, -π, π/2, 0.1}]],
  Table[Line[{{2 Sin[θ], 2 Cos[θ]},
     {(2 - 0.2) Sin[θ], (2 - 0.2) Cos[θ]}}],
   {θ, 0, 2 π, π/9}],
  Text[Style[0, Large], {0, 0.6}],
  Inset[p[20*#], 2.35*
      {Sin[20*#*Degree], Cos[20*#*Degree]}] & /@ 
    Range[0, 17]}]

Insets around a clock

2 Answers2

Linked