7
$\begingroup$

Is there a way to include specific points in a plot?

The Exclusions option of Plot (and related plotting functions) allows us to tell Plot to avoid specific points, (e.g. because we know the plotted function is singular at that point). I want to do the opposite, tell Plot to include specific points in the initial points in the plot (before any recursion), because we know the plotted function will have a particularly sharp feature at that point, that might otherwise be missed.

As MWE consider the following:

f[x_?NumericQ] := Exp[-10^4 (x - \[Pi])^2]
Plot[f[x], {x, 5/2, 4}, PlotRange -> 1, PlotPoints -> 5]

With these settings Plot misses the Gaussian peak at x=Pi. Is there a way to tell Plot to specifically include x=Pi in the plotted points. (Of course, we can just krank up the PlotPoints to make sure we hit the feature, but this is not viable in the real world application I am dealing with.)

Improve this question
$\endgroup$
2
  • $\begingroup$ PlotPoints -> 5 is too low. Increase PlotPoints and use MaxRecursion, e.g., PlotPoints -> 6, MaxRecursion -> 10 $\endgroup$
    – Bob Hanlon
    Commented Sep 26 at 16:22
  • $\begingroup$ Use Show and Graphics along with PlotRange to get Show[Plot[f[x],{x,5/2,4},PlotRange->{{5/2,4},{0,1}}, PlotPoints->5],Graphics[Point[{Pi,Exp[0]}]]] to include a specific point with a plot. Then you can deal with pushing the plot resolution to be what you want. $\endgroup$
    – Bill
    Commented Sep 26 at 16:45

1 Answer 1

Reset to default
10
$\begingroup$

I can't find the appropriate question right now, but the syntax is:

  • PlotPoints -> {None, pts} (initial sampling only at points pts) or
  • PlotPoints -> {Automatic, pts} (initial sampling at points pts and at equidistant points)
f[x_?NumericQ] := Exp[-10^4 (x - π)^2]
Plot[f[x], {x, 5/2, 4}, PlotRange -> 1, PlotPoints -> {Automatic, {Pi}}]

enter image description here

Improve this answer
$\endgroup$
3
  • 3
    $\begingroup$ One ref for functions of two variables: mathematica.stackexchange.com/questions/19121/… $\endgroup$
    – Michael E2
    Commented Sep 26 at 18:54
  • $\begingroup$ @MichaelE2 Thanks! That was almost exactly what I needed. I actually need the syntax for ParametricPlot3D , which does not seem to follow the same syntax as Plot3D (surprisingly). Do you happen to know if anyone looked into the ParametricPlot3D case? $\endgroup$
    – TimRias
    Commented Sep 27 at 7:24
  • $\begingroup$ @TimRias I know I looked into it and failed to discover a way. I decided it probably isn't implemented in all *Plot*[] functions. But I don't know for sure. $\endgroup$
    – Michael E2
    Commented Sep 27 at 14:06

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.