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I have a question about comparing the points within two plots.

I would like to compare two plots and find the minimum distance among their points, in order to find the nearest/common points (i.e., those ones with minimum or zero-distance) and plot it (overlapping).

What I did was to extract the coordinates of the respectively points. But I do not know how to compare them and/or the two plots. I used the following line of code, but the result is completely different from what I am looking for.

Outer[EuclideanDistance, seq1, seq2, 1] // Flatten

seq1 = {{160.5, 262.5}, {105.5, 241.5}, {247.5, 241.5}, {333.5, 
  220.5}, {34.5, 199.5}, {239.5, 178.5}, {58.5, 136.5}, {159.5, 
  73.5}, {281.5, 178.5}, {124.5, 262.5}, {196.5, 152.5}, {92.5, 
  194.5}, {153.5, 239.5}, {120.5, 236.5}, {105.5, 173.5}, {88.5, 
  131.5}, {26.5, 110.5}, {96.5, 110.5}, {152, 89.5}, {2.5, 
  68.5}, {49.5, 47.5}, {281.5, 221.5}, {217.5, 200.5}, {172.5, 
  158.5}, {296.5, 179.5}, {51.5, 300.5}, {60.5, 279.5}, {171.5, 
  279.5}, {311, 216}, {350.5, 216.5}, {83.5, 153.5}, {239.5, 
  132.5}, {75.5, 111.5}, {79.5, 195.5}, {110.5, 195.5}, {126.5, 
  195.5}, {183.5, 153.5}, {49.5, 90.5}, {53.5, 158.5}, {111.5, 
  216.5}, {244.5, 258.5}, {110.5, 69.5}, {221.5, 237.5}, {276.5, 
  237.5}, {147.5, 299.5}, {165.5, 195.5}, {84.5, 299.5}, {92.5, 
  299.5}, {21.5, 257.5}, {29.5, 257.5}, {77.5, 89.5}, {60.5, 
  68.5}, {68.5, 47.5}, {76.5, 47.5}, {139.5, 257.5}, {36.5, 
  175.5}, {185.5, 175.5}, {99.5, 154.5}, {43.5, 133.5}, {43.5, 
  70.5}, {129.5, 70.5}, {4.5, 49.5}, {254.5, 195.5}, {264.5, 
  90.5}, {342.5, 90.5}, {175.5, 215.5}, {214.5, 215.5}, {307.5, 
  174.5}, {230.5, 258.5}, {144.5, 216.5}, {42.5, 153.5}, {190.5, 
  132.5}, {42.5, 111.5}, {66.5, 90.5}, {121.5, 90.5}, {96.5, 
  69.5}, {174.5, 48.5}, {228.5, 278.5}}

seq2 = {{160.5, 262.5}, {105.5, 241.5}, {247.5, 241.5}, {333.5, 
  220.5}, {34.5, 199.5}, {239.5, 178.5}, {58.5, 136}, {159.5, 
  73.5}, {281.5, 178.5}, {128, 262.5}, {196.5, 152.5}, {92, 
  194.5}, {153.5, 239.5}, {120.5, 236.5}, {105.5, 173.5}, {88.5, 
  131.5}, {26.5, 110.5}, {96.5, 110.5}, {152.5, 89.5}, {2.5, 
  68.5}, {49.5, 47.5}, {281.5, 221.5}, {217.5, 200.5}, {172.5, 
  158.5}, {296.5, 179.5}, {51.5, 300.5}, {60.5, 279.5}, {171.5, 
  279.5}, {311.5, 216.5}, {350.5, 216.5}, {83.5, 153.5}, {239.5, 
  132.5}, {75.5, 111.5}, {79.5, 195.5}, {110.5, 200.5}, {126.5, 
  195.5}, {183.5, 153.5}, {49.5, 90.5}, {53.5, 158.5}, {111.5, 
  216.5}, {244.5, 258.5}, {114.5, 69.5}, {221.5, 237.5}, {276.5, 
  237.5}, {147.5, 299.5}, {165.5, 195.5}, {84.5, 299.5}, {92.5, 
  299.5}, {22.5, 257.5}, {29.5, 257.5}, {77.5, 89.5}, {60.5, 
  68.5}, {68.5, 47.5}, {76.5, 47.5}, {139.5, 257.5}, {36.5, 
  175.5}, {185.5, 175.5}, {99.5, 154.5}, {43.5, 133.5}, {43.5, 
  70.5}, {129.5, 70.5}, {4.5, 49.5}, {254.5, 195.5}, {264.5, 
  90.5}, {342.5, 90.5}, {175.5, 215.5}, {214.5, 215.5}, {307.5, 
  174.5}, {230.5, 258.5}, {144.5, 216.5}, {42.5, 153.5}, {190.5, 
  132.5}, {42.5, 111.5}, {66.5, 90.5}, {121.5, 90.5}, {96.5, 
  69.5}, {174.5, 48.5}, {228.5, 278.5}}

enter image description here

enter image description here

The result should show the points on the plot equal (almost in common) between the two plots.

Could you please help me?

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  • 1
    $\begingroup$ Some working code to reproduce the problem would make it more likely that someone would help. $\endgroup$
    – Michael E2
    Sep 23, 2019 at 23:13
  • $\begingroup$ I added the sequences that I am considering. Thanks Michael E2. $\endgroup$
    – Val
    Sep 23, 2019 at 23:27

2 Answers 2

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Since most of the points in your two data sets coincide and none of them has a nearest neighbor that is very far away when the total scale of the two plots is taken into consideration, I recommend visualizing the spacial relation between the points by plotting the points of one dataset and showing the offset of the nearest point in the other by color. Like so:

Data

seq1 = 
  {{160.5, 262.5}, {105.5, 241.5}, {247.5, 241.5}, {333.5, 220.5}, 
   {34.5, 199.5}, {239.5, 178.5}, {58.5, 136.5}, {159.5, 73.5}, 
   {281.5, 178.5}, {124.5, 262.5}, {196.5, 152.5}, {92.5, 194.5}, 
   {153.5, 239.5}, {120.5, 236.5}, {105.5, 173.5}, {88.5, 131.5}, 
   {26.5, 110.5}, {96.5, 110.5}, {152, 89.5}, {2.5, 68.5}, 
   {49.5, 47.5}, {281.5, 221.5}, {217.5, 200.5}, {172.5, 158.5}, 
   {296.5, 179.5}, {51.5, 300.5}, {60.5, 279.5}, {171.5, 279.5}, 
   {311, 216}, {350.5, 216.5}, {83.5, 153.5}, {239.5, 132.5}, 
   {75.5, 111.5}, {79.5, 195.5}, {110.5, 195.5}, {126.5, 195.5}, 
   {183.5, 153.5}, {49.5, 90.5}, {53.5, 158.5}, {111.5, 216.5}, 
   {244.5, 258.5}, {110.5, 69.5}, {221.5, 237.5}, {276.5, 237.5}, 
   {147.5, 299.5}, {165.5, 195.5}, {84.5, 299.5}, {92.5, 299.5}, 
   {21.5, 257.5}, {29.5, 257.5}, {77.5, 89.5}, {60.5, 68.5}, 
   {68.5, 47.5}, {76.5, 47.5}, {139.5, 257.5}, {36.5, 175.5}, 
   {185.5, 175.5}, {99.5, 154.5}, {43.5, 133.5}, {43.5, 70.5}, 
   {129.5, 70.5}, {4.5, 49.5}, {254.5, 195.5}, {264.5, 90.5}, 
   {342.5, 90.5}, {175.5, 215.5}, {214.5, 215.5}, {307.5, 174.5}, 
   {230.5, 258.5}, {144.5, 216.5}, {42.5, 153.5}, {190.5, 132.5}, 
   {42.5, 111.5}, {66.5, 90.5}, {121.5, 90.5}, {96.5, 69.5}, 
   {174.5, 48.5}, {228.5, 278.5}};
seq2 = 
  {{160.5, 262.5}, {105.5, 241.5}, {247.5, 241.5}, {333.5, 220.5}, 
   {34.5, 199.5}, {239.5, 178.5}, {58.5, 136}, {159.5, 73.5}, 
   {281.5, 178.5}, {128, 262.5}, {196.5, 152.5}, {92, 194.5}, 
   {153.5, 239.5}, {120.5, 236.5}, {105.5, 173.5}, {88.5, 131.5}, 
   {26.5, 110.5}, {96.5, 110.5}, {152.5, 89.5}, {2.5, 68.5}, 
   {49.5, 47.5}, {281.5, 221.5}, {217.5, 200.5}, {172.5, 158.5}, 
   {296.5, 179.5}, {51.5, 300.5}, {60.5, 279.5}, {171.5, 279.5}, 
   {311.5, 216.5}, {350.5, 216.5}, {83.5, 153.5}, {239.5, 132.5}, 
   {75.5, 111.5}, {79.5, 195.5}, {110.5, 200.5}, {126.5, 195.5}, 
   {183.5, 153.5}, {49.5, 90.5}, {53.5, 158.5}, {111.5, 216.5}, 
   {244.5, 258.5}, {114.5, 69.5}, {221.5, 237.5}, {276.5, 237.5}, 
   {147.5, 299.5}, {165.5, 195.5}, {84.5, 299.5}, {92.5, 299.5}, 
   {22.5, 257.5}, {29.5, 257.5}, {77.5, 89.5}, {60.5, 68.5}, 
   {68.5, 47.5}, {76.5, 47.5}, {139.5, 257.5}, {36.5, 175.5}, 
   {185.5, 175.5}, {99.5, 154.5}, {43.5, 133.5}, {43.5, 70.5}, 
   {129.5, 70.5}, {4.5, 49.5}, {254.5, 195.5}, {264.5, 90.5}, 
   {342.5, 90.5}, {175.5, 215.5}, {214.5, 215.5}, {307.5, 174.5}, 
   {230.5, 258.5}, {144.5, 216.5}, {42.5, 153.5}, {190.5, 132.5}, 
   {42.5, 111.5}, {66.5, 90.5}, {121.5, 90.5}, {96.5, 69.5}, 
   {174.5, 48.5}, {228.5, 278.5}};

Offset plot

nf = Nearest[seq1]
clusters = GroupBy[seq2, {# - nf[#][[1]]} &];
colors = ColorData[24] /@ Range @ Length @ clusters
Legended[
  Graphics[
    {AbsolutePointSize[10], MapThread[{#1, Point[#2]} &, {colors, Values @ clusters}]},
    Frame -> True,
    ImageSize -> Large],
  SwatchLegend[colors, Keys @ clusters, LegendLabel -> "Offset"]]

plot

Second thoughts

Perhaps using ListPlot with markers makes for a better visualization. 

nf = Nearest[seq1];
clusters = GroupBy[seq2, {# - nf[#][[1]]} &];
ListPlot[Values @ clusters,
  PlotMarkers -> {Automatic, 15},
  PlotLegends -> 
    PointLegend[HoldForm /@ (Keys @ clusters)[[All, 1]], LegendLabel -> "Offset"],
  Frame -> True,
  ImageSize -> Large]

plot

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  • $\begingroup$ Thank you so much, m_goldberg. I did not think to use different colours to represent the differences and their distance. The result is even better than what I expected $\endgroup$
    – Val
    Sep 24, 2019 at 18:07
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distance = DistanceMatrix[seq1, seq2]

points = Position[distance, x_ /; x < 0.1]

ListPlot[{seq1[[First /@ points]], seq2[[Last /@ points]]}]
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