Exclude one point from the RegionPlot

Question

I'd like to ask you about the way of excluding just one point from this example:

myArg[z_] := Mod[Arg@z, 2 Pi]
RegionPlot[y > x && myArg[x + I y] <= Pi, {x, -2, 2}, {y, -2, 2}]

I want to exclude the $z \neq i$ $\mapsto$ point $(0,1)$.

Something like this:

Excluding a point would look the same as not excluding it. Perhaps you want to exclude a small region around the point of interest? If so, would just placing a white Point be an acceptable solution to your needs? — rm -rf, Commented Oct 18, 2015 at 21:06
Hard to remove just one point, but here's a fake plot: RegionPlot[ y > x && myArg[x + I y] <= Pi && Abs[x + I y - I] > 0.05, {x, -2, 2}, {y, -2, 2}, PlotPoints -> 75] — J. M.'s missing motivation, Commented Oct 18, 2015 at 21:09
@R.M., I got your point. It's just for "educational usage" to show that $z \neq i$ is outside of the domain of a function. — Pawel Gumiela, Commented Oct 18, 2015 at 21:12
@J.M.isback., thank you so much. That's the most useful fake plot I've seen today ;). — Pawel Gumiela, Commented Oct 18, 2015 at 21:15

Community · Accepted Answer · 2017-04-13 12:55:53Z

8

Credits to J. M. and R. M.

J. M. suggested drawing a surface outside the circle:

Using the && operator he made the intersection of two sets:

RegionPlot[ y > x && myArg[x + I y] <= Pi 
&& Abs[x + I y - I] > 0.05, {x, -2, 2}, {y, -2, 2}, PlotPoints -> 75]

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answered Oct 18, 2015 at 21:35

Pawel Gumiela

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$\begingroup$ RegionPlot[y > x && myArg[x + I y] <= Pi, {x, -2, 2}, {y, -2, 2}, Epilog -> {White, AbsolutePointSize[6], Point[{0, 1}]}] $\endgroup$
– Bob Hanlon
Commented Oct 18, 2015 at 22:24
$\begingroup$ @BobHanlon, thank you. Another useful example. $\endgroup$
– Pawel Gumiela
Commented Oct 18, 2015 at 22:30

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