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How to represent a data list by arrows?

Mathematica Asked by SAC on May 23, 2021

I have a code that builds a plot with 7 functions and mark 4 points. Each level of list data describes a function (see below).
The curves are created from the "data" input from ListLinePlot. The points e0, e1, e2, and e3 are created from Graphics.

e0={0,0};
e1={0.230769, 0};
e2={0, 0.230769};
e3={0.104895, 0.104895};
data= {{{0.1, 0.1}, {0.1014, 0.1014}, {0.102414, 0.102414}, {0.10314, 
   0.10314}, {0.103658, 0.103658}, {0.104025, 0.104025}, {0.104284, 
   0.104284}, {0.104466, 0.104466}, {0.104594, 0.104594}, {0.104684, 
   0.104684}, {0.104747, 0.104747}, {0.104792, 0.104792}, {0.104823, 
   0.104823}, {0.104844, 0.104844}, {0.10486, 0.10486}, {0.10487, 
   0.10487}, {0.104878, 0.104878}, {0.104883, 0.104883}, {0.104887, 
   0.104887}, {0.104889, 0.104889}, {0.104891, 0.104891}, {0.104892, 
   0.104892}, {0.104893, 0.104893}, {0.104894, 0.104894}, {0.104894, 
   0.104894}, {0.104894, 0.104894}, {0.104895, 0.104895}, {0.104895, 
   0.104895}, {0.104895, 0.104895}, {0.104895, 0.104895}, {0.104895, 
   0.104895}, {0.104895, 0.104895}, {0.104895, 0.104895}, {0.104895, 
   0.104895}, {0.104895, 0.104895}, {0.104895, 0.104895}, {0.104895, 
   0.104895}, {0.104895, 0.104895}, {0.104895, 0.104895}, {0.104895, 
   0.104895}, {0.104895, 0.104895}, {0.104895, 0.104895}, {0.104895, 
   0.104895}, {0.104895, 0.104895}, {0.104895, 0.104895}, {0.104895, 
   0.104895}, {0.104895, 0.104895}, {0.104895, 0.104895}, {0.104895, 
   0.104895}, {0.104895, 0.104895}, {0.104895, 0.104895}, {0.104895, 
   0.104895}, {0.104895, 0.104895}, {0.104895, 0.104895}, {0.104895, 
   0.104895}, {0.104895, 0.104895}, {0.104895, 0.104895}, {0.104895, 
   0.104895}, {0.104895, 0.104895}, {0.104895, 0.104895}, {0.104895, 
   0.104895}, {0.104895, 0.104895}, {0.104895, 0.104895}, {0.104895, 
   0.104895}, {0.104895, 0.104895}, {0.104895, 0.104895}, {0.104895, 
   0.104895}, {0.104895, 0.104895}, {0.104895, 0.104895}, {0.104895, 
   0.104895}, {0.104895, 0.104895}, {0.104895, 0.104895}, {0.104895, 
   0.104895}, {0.104895, 0.104895}, {0.104895, 0.104895}, {0.104895, 
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   0.104895}, {0.104895, 0.104895}, {0.104895, 0.104895}, {0.104895, 
   0.104895}, {0.104895, 0.104895}}, {{0.1, 0.2}, {0.0858, 
   0.1768}, {0.0783055, 0.16554}, {0.0736041, 0.159356}, {0.0703449, 
   0.155852}, {0.0679125, 0.153928}, {0.0659829, 
   0.152997}, {0.0643694, 0.152717}, {0.0629585, 
   0.152878}, {0.0616782, 0.153343}, {0.0604819, 
   0.154023}, {0.0593386, 0.154858}, {0.0582279, 0.155805}, {0.057136,
    0.156836}, {0.0560538, 0.157931}, {0.0549752, 
   0.159075}, {0.0538963, 0.160259}, {0.0528147, 
   0.161474}, {0.0517288, 0.162717}, {0.0506381, 
   0.163981}, {0.0495423, 0.165265}, {0.0484415, 
   0.166566}, {0.0473363, 0.167881}, {0.0462272, 
   0.169209}, {0.0451149, 0.170548}, {0.0440004, 
   0.171897}, {0.0428845, 0.173254}, {0.0417685, 
   0.174617}, {0.0406532, 0.175986}, {0.0395398, 
   0.177359}, {0.0384295, 0.178733}, {0.0373234, 
   0.180109}, {0.0362227, 0.181484}, {0.0351286, 
   0.182857}, {0.0340423, 0.184225}, {0.032965, 0.185589}, {0.0318978,
    0.186945}, {0.0308419, 0.188293}, {0.0297985, 
   0.189631}, {0.0287686, 0.190957}, {0.0277532, 
   0.192271}, {0.0267535, 0.193569}, {0.0257704, 
   0.194851}, {0.0248048, 0.196116}, {0.0238576, 
   0.197362}, {0.0229295, 0.198588}, {0.0220214, 
   0.199793}, {0.0211338, 0.200975}, {0.0202674, 
   0.202133}, {0.0194228, 0.203267}, {0.0186003, 
   0.204375}, {0.0178004, 0.205458}, {0.0170233, 
   0.206513}, {0.0162693, 0.207541}, {0.0155386, 0.20854}, {0.0148313,
    0.209512}, {0.0141473, 0.210454}, {0.0134866, 
   0.211367}, {0.0128491, 0.212252}, {0.0122347, 
   0.213107}, {0.0116432, 0.213932}, {0.0110742, 
   0.214729}, {0.0105274, 0.215497}, {0.0100025, 
   0.216237}, {0.00949902, 0.216948}, {0.00901659, 
   0.217631}, {0.00855471, 0.218287}, {0.00811287, 
   0.218916}, {0.00769055, 0.219519}, {0.00728721, 
   0.220096}, {0.00690228, 0.220648}, {0.00653519, 
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   0.223866}, {0.00441613, 0.224243}, {0.00417077, 
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   0.225263}, {0.00350833, 0.225569}, {0.00331029, 
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   0.226395}, {0.00277742, 0.226643}, {0.00261862, 
   0.226876}, {0.00246849, 0.227098}, {0.0023266, 
   0.227307}, {0.00219253, 0.227505}, {0.0020659, 
   0.227692}, {0.00194631, 0.227869}, {0.00183341, 
   0.228037}, {0.00172685, 0.228194}, {0.0016263, 
   0.228344}, {0.00153144, 0.228484}, {0.00144196, 
   0.228617}, {0.00135758, 0.228742}, {0.00127803, 
   0.228861}, {0.00120303, 0.228972}}, {{0.1, 0.8}, {0, 0.0832}, {0, 
   0.100173}, {0, 0.118619}, {0, 0.137882}, {0, 0.157115}, {0, 
   0.175399}, {0, 0.191902}, {0, 0.20603}, {0, 0.217509}, {0, 
   0.226373}, {0, 0.232885}, {0, 0.23743}, {0, 0.240425}, {0, 
   0.242252}, {0, 0.243233}, {0, 0.243621}, {0, 0.243607}, {0, 
   0.243329}, {0, 0.242885}, {0, 0.242344}, {0, 0.241754}, {0, 
   0.241144}, {0, 0.240536}, {0, 0.239943}, {0, 0.239373}, {0, 
   0.23883}, {0, 0.238316}, {0, 0.237832}, {0, 0.237378}, {0, 
   0.236953}, {0, 0.236555}, {0, 0.236184}, {0, 0.235837}, {0, 
   0.235513}, {0, 0.235211}, {0, 0.234928}, {0, 0.234665}, {0, 
   0.234419}, {0, 0.234189}, {0, 0.233974}, {0, 0.233773}, {0, 
   0.233586}, {0, 0.23341}, {0, 0.233246}, {0, 0.233092}, {0, 
   0.232948}, {0, 0.232813}, {0, 0.232687}, {0, 0.232569}, {0, 
   0.232458}, {0, 0.232355}, {0, 0.232257}, {0, 0.232166}, {0, 
   0.232081}, {0, 0.232001}, {0, 0.231926}, {0, 0.231855}, {0, 
   0.231789}, {0, 0.231727}, {0, 0.231669}, {0, 0.231614}, {0, 
   0.231563}, {0, 0.231515}, {0, 0.231469}, {0, 0.231427}, {0, 
   0.231387}, {0, 0.23135}, {0, 0.231315}, {0, 0.231282}, {0, 
   0.231251}, {0, 0.231222}, {0, 0.231194}, {0, 0.231169}, {0, 
   0.231145}, {0, 0.231122}, {0, 0.231101}, {0, 0.231081}, {0, 
   0.231062}, {0, 0.231044}, {0, 0.231028}, {0, 0.231012}, {0, 
   0.230998}, {0, 0.230984}, {0, 0.230971}, {0, 0.230959}, {0, 
   0.230947}, {0, 0.230937}, {0, 0.230927}, {0, 0.230917}, {0, 
   0.230908}, {0, 0.2309}, {0, 0.230892}, {0, 0.230885}, {0, 
   0.230878}, {0, 0.230871}, {0, 0.230865}, {0, 0.230859}, {0, 
   0.230854}, {0, 0.230849}, {0, 0.230844}}, {{0.2, 0.1}, {0.1768, 
   0.0858}, {0.16554, 0.0783055}, {0.159356, 0.0736041}, {0.155852, 
   0.0703449}, {0.153928, 0.0679125}, {0.152997, 
   0.0659829}, {0.152717, 0.0643694}, {0.152878, 
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   0.0604819}, {0.154858, 0.0593386}, {0.155805, 
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    0.0549752}, {0.160259, 0.0538963}, {0.161474, 
   0.0528147}, {0.162717, 0.0517288}, {0.163981, 
   0.0506381}, {0.165265, 0.0495423}, {0.166566, 
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   0.0462272}, {0.170548, 0.0451149}, {0.171897, 
   0.0440004}, {0.173254, 0.0428845}, {0.174617, 
   0.0417685}, {0.175986, 0.0406532}, {0.177359, 
   0.0395398}, {0.178733, 0.0384295}, {0.180109, 
   0.0373234}, {0.181484, 0.0362227}, {0.182857, 
   0.0351286}, {0.184225, 0.0340423}, {0.185589, 0.032965}, {0.186945,
    0.0318978}, {0.188293, 0.0308419}, {0.189631, 
   0.0297985}, {0.190957, 0.0287686}, {0.192271, 
   0.0277532}, {0.193569, 0.0267535}, {0.194851, 
   0.0257704}, {0.196116, 0.0248048}, {0.197362, 
   0.0238576}, {0.198588, 0.0229295}, {0.199793, 
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   0.00144196}, {0.228742, 0.00135758}, {0.228861, 
   0.00127803}, {0.228972, 0.00120303}}, {{0.2, 1.}, {0, 0}, {0, 
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   0.104895}, {0.104895, 0.104895}, {0.104895, 0.104895}, {0.104895, 
   0.104895}, {0.104895, 0.104895}, {0.104895, 0.104895}, {0.104895, 
   0.104895}, {0.104895, 0.104895}, {0.104895, 0.104895}, {0.104895, 
   0.104895}, {0.104895, 0.104895}, {0.104895, 0.104895}, {0.104895, 
   0.104895}, {0.104895, 0.104895}, {0.104895, 0.104895}, {0.104895, 
   0.104895}, {0.104895, 0.104895}, {0.104895, 0.104895}, {0.104895, 
   0.104895}, {0.104895, 0.104895}, {0.104895, 0.104895}, {0.104895, 
   0.104895}, {0.104895, 0.104895}, {0.104895, 0.104895}, {0.104895, 
   0.104895}, {0.104895, 0.104895}, {0.104895, 0.104895}, {0.104895, 
   0.104895}, {0.104895, 0.104895}, {0.104895, 0.104895}, {0.104895, 
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   0.104895}, {0.104895, 0.104895}}}
set=ListLinePlot[data, PlotRange -> {{0, 0.5}, {0, 1}}, 
 Frame -> True]
Show[set, Graphics[{Black, PointSize[Large], Point[e0], Point[e1], 
   Point[e2], Point[e3]}]]

The output of this code is the figure below.

enter image description here

Instead of using the continuous line to represent the function, I would like to use arrows, similar to the figure below.
In addition, I would like to bring the points forward so that they are not hidden.
The corresponding image of what I am looking for is similar to the following.
P.s. I tried using ListVectorPlot Plot and ListStreamPlot, but it didn’t work.
enter image description here

can anybody help me?

One Answer

Update 2: Show "only the arrows, without the filled line"

i. Use Dashing[{0, 1, 0}] to show only arrowheads:

llp /. Line -> Arrow /.  a_Arrow :> {Dashing[{0, 1, 0}], a}

enter image description here

ii. Use "→" as arrow head:

llp /. Line[x_] :> {LineColor -> White, 
   Arrowheads[{Automatic, #, Graphics[Text[Style["→", 14]]]} & /@ 
     Subdivide[If[ArcLength[Line[x]] < .5, 7, 15]]], Arrow[x]}

enter image description here

iii. Partition line coordinates and skip some portions:

Needs["GraphUtilities`"]

llp /. l : Line[x_] :> {Thin, Arrowheads[.015], 
   Arrow /@ 
     Partition[LineScaledCoordinate[x, #] & /@ N[Subdivide[100]],
          2, Round[Sqrt @ Length[x]]]}

enter image description here

Replace 2 with 5 in Partition[...] to get

enter image description here

Update 1: Using ParametricPlot + BSplineFunction

ParametricPlot[Evaluate[BSplineFunction[#][t] & /@ data], {t, 0, 1}, 
  AspectRatio -> 1/GoldenRatio, Frame -> True, 
  PlotRange -> All, ImageSize -> 500, 
  PlotRangePadding -> 0, PlotRangeClipping -> False, 
  Epilog -> {Black, PointSize[Large], Point[e0], Point[e1], Point[e2],
     Point[e3]}, 
  PlotStyle -> (Directive[Arrowheads[ConstantArray[.025, #]]] & /@ 
     Round[Sqrt @ Normalize[ArcLength /@ Line /@ data, Min]])] /. 
 Line -> Arrow

enter image description here

Original answer:

llp = ListLinePlot[data, PlotRange -> {{0, 0.5}, {0, 1}}, 
  PlotStyle -> Arrowheads[ConstantArray[.02, 10]], 
  Frame -> True, 
  ImageSize -> Large, 
  PlotRangeClipping -> False,
  Epilog -> {Black, PointSize[Large], Point[e0], Point[e1], Point[e2],
     Point[e3]}] ;

llp /. Line -> Arrow

enter image description here

Answered by kglr on May 23, 2021

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