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.)
PlotPoints -> 5is too low. IncreasePlotPointsand useMaxRecursion, e.g.,PlotPoints -> 6, MaxRecursion -> 10$\endgroup$ShowandGraphicsalong withPlotRangeto getShow[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. $\endgroup$