Does InterpolationOrder cause conflicts with PlotMarkers in ListPlot?

Question

Bug introduced in 7.0 or earlier and persisting through 13.2.0 or later

---

My code:

data = {MapIndexed[{First[#2], #1} &, 
    Accumulate[RandomInteger[{-1, 1}, {54}]]], 
   MapIndexed[{First[#2], #1} &, 
    Accumulate[RandomInteger[{-1, 1}, {34}]]]};

ListPlot[data,
 Axes -> False,
 AspectRatio -> 0.75,
 Frame -> True,
 InterpolationOrder -> {0, 0},
 ImageSize -> {400, 300},
 ImageMargins -> 0,
 Joined -> True,
 PlotMarkers -> {{"\[FilledCircle]", 11}, {"", 11}}
 ]

On OS X 10.6.8 V8.0.4 I get this output:

You will note that the filled circle plot markers have been "distributed" across both sets of data. However if I change the InterpolationOrder setting to say:

InterpolationOrder -> {0, None}

...then no markers appear for the second set of data (due to the markers being an empty string).

Could someone please advise me if the cause of this behaviour is due to me setting these options incorrectly? Any ideas?

Answer 1

According to the doc, the second result is correct, since $i$-th specification in PlotMakers should be used for $i$-th dataset. There seems to be a bug regarding how InterpolationOrder->0 is processing PlotMarkers.

When InterpolationOrder->0, it inserts PlotMarkers at the both end of each interval. Not so for all other cases (it inserts markers on the data point). While doing so, it seems that it always picks up the first plot marker for the end interval point, instead of the correct one (n-th plot maker for n-th data set).

It is easy to confirm. Define multi-data:

SeedRandom[2]; data = {MapIndexed[{First[#2], #1} &, 
   Accumulate[RandomInteger[{0, 1}, {10}]]], 
  MapIndexed[{First[#2], #1} &, 
   Accumulate[RandomInteger[{-1, 1}, {15}]]],
  MapIndexed[{First[#2], #1} &, 
   Accumulate[RandomInteger[{-1, 0}, {15}]]]};

Then run the plot with interpolation order 0:

ListPlot[data, Axes -> False, AspectRatio -> 0.75, Frame -> True, 
 InterpolationOrder -> {0, 0, 0}, ImageSize -> {400, 300}, 
 ImageMargins -> 0, Joined -> True, 
 PlotMarkers -> {{"\[FilledCircle]", 8}, {"\[FilledSquare]", 
    10}, {"\[FilledDiamond]", 10}}]

The result is:

When it should have looked like this:

(which is generated by:

Show[MapThread[
  ListPlot[#1, Axes -> False, AspectRatio -> 0.75, Frame -> True, 
    InterpolationOrder -> 0, ImageSize -> {400, 300}, 
    ImageMargins -> 0, Joined -> True, PlotMarkers -> #2, 
    PlotStyle -> #3] &, {data, {{"\[FilledCircle]", 
     8}, {"\[FilledSquare]", 10}, {"\[FilledDiamond]", 10}}, 
   ColorData[1, "ColorList"][[1 ;; 3]]}], PlotRange -> {{0, 15}, All}]

)