Plotting jump function without vertical lines

Question

Consider this list plot:

ListPlot[{{0, 0}, {1, 2}, {3, 4}, {4, 2}, {6, 0}}]

I want to draw a jump function in this list plot such that for each point I get a line to the right until the next point occurs. I do not want to see the vertical lines (as is done automatically by ListLinePlot)! How can I achieve that?

Equivalently, how can I get rid of the vertical lines of a jump function in a ListLinePlot?

Answer 1

I believe this is what you want?

ListLinePlot[
  {{0, 0}, {1, 2}, {3, 4}, {4, 2}, {6, 0}},
  InterpolationOrder -> 0, 
  Frame -> True
] /. Line[x : {{_, _} ..}] :> (Line /@ Partition[x, 2])

Post-processing of the Graphics expression generated by ListLinePlot is used in the form of ReplaceAll. The Line is split into pairs of points using Partition, avoiding the drawing of vertical connecting segments.

---

Post-processing is a quick way to hack out a solution to a lot of plotting problems and it lets you work with the full range of e.g. ListLinePlot options. However it can also be slow and fragile. In the case above every Line expression is modified whether it originates from the plot itself or for example an Epilog option. I do in practice use post-processing and at times it can be the best solution. However often it is more robust and performs better to construct your own plotting function using Graphics directly. Here is a simple example:

myPlot[dat : {{_, _} ..}, opts : OptionsPattern[Graphics]] := 
  Module[{rhold},
    rhold[{{x_, y_}, {X_, Y_}}] := {{x, y}, {X, y}};
    Graphics[Line[ rhold /@ Partition[dat, 2, 1] ], opts]
  ]

And its use:

myPlot[{{0, 0}, {1, 2}, {3, 4}, {4, 2}, {6, 0}},
  BaseStyle -> {Red, AbsoluteThickness[2]},
  Frame -> True]

You can create custom Options for your plot function to further customize its syntax. See:

• Functions with Options

Answer 2

If you just wrap your data with TemporalData, you can Plot or DiscretePlot the "PathFunction". In either case, there is no need for additional post- or pre-processing of the data to deal with jumps.

data = {{0, .5}, {1, 2}, {3, 4}, {4, 2}, {6, 1}}; 
td = TemporalData[data];

Using Plot and the Exclusions option:

Plot[Quiet@td["PathFunction"][x], {x, 0, 7}, PlotRange -> {0, 5},
 Exclusions -> td["Times"][[1]], PlotStyle -> Directive[{Red, Thick}]]

Note: On v10.0.1 (Mac) you need to use td["Times"] instead of td["Times"][[1]] (Thanks: @BobHanlon)

Using DiscretePlot and the Extentsize option:

DiscretePlot[Quiet@td["PathFunction"][x], {x, 0, 7}, PlotRange -> {0, 5},
 ExtentSize -> Right, Filling -> None, PlotStyle -> Directive[{Red, Thick}]]

Update: In both cases, adding the option

Epilog -> {Blue, PointSize[.02], Point[td["Path"]]}

gives

Answer 3

As an alternative to post-processing the plot, you can pre-process the data.

data = {{0, 0}, {1, 2}, {3, 4}, {4, 2}, {6, 0}};

func[x_] = Total[Partition[data, 2, 1] /.
    {{x1_, y1_}, {x2_, y2_}} :>
     y1*(UnitStep[x - x1] - UnitStep[x - x2])] //
  Simplify

Piecewise[{{2, Inequality[1, LessEqual, x, Less, 3] || Inequality[4, LessEqual, x, Less, 6]}, {4, Inequality[3, LessEqual, x, Less, 4]}}, 0]

Plot[func[x],
 {x, Min[data[[All, 1]]], Max[data[[All, 1]]]},
 Epilog -> {Red, AbsolutePointSize[4], Point[data]},
 PlotRange -> All]