Suppose I have functions f[x] and g[x] which are defined in the region 0 ≤ x ≤ 1 and 2 ≤ x ≤ 3. If I want to plot either f or g separately, I can do the following:

Plot[f[x], {x, 0, 3}, RegionFunction -> (! 1 < # < 2 &)]

However, if I now wish to make a ParametricPlot of {f[x], g[x]} then the above RegionFunction no longer works. The reason being that the RegionFunction not operates on the (f,g)-plane, and not on the parameter x. Moreover, Exclusions also seems to only work on isolated values of x and not a range.

Is there a way to achieve this in a single call to ParametricPlot? (I could do one ParametricPlot per connected region in the parameter range, then combine the graphics, but this is a bit of a pain)


1 Answer 1


Use #3 instead of #. See the RegionFunction -> docs, "Details" section-

f[x_] := Sin@ x
g[x_] := x^2;
ParametricPlot[{g@x, f@x}, {x, 0, 3}, RegionFunction -> (! 1 < #3 < 2 &), AspectRatio -> 1]

Mathematica graphics

  • $\begingroup$ Perfect! Thanks and apologies for my oversight in looking through the docs. $\endgroup$ Nov 20, 2014 at 0:00

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