Parametric Region only showing half of region

I have defined the region as such:

Region[
ParametricRegion[
{r Cos[θ], r Sin[θ]},
{{θ, 0, 2π}, {r, 0, 2+Cos[θ]}}
], Axes -> True,
PlotRange -> All
]


However it only shows half of the limaçon:

Whereas the polar plot of the same function over the same interval [0,2π] represents the entire thing:

PolarPlot[2 + Cos[θ], {θ, 0, 2π}]


Now, I know I am using a workaround, by defining a polar plot with x and y, and this is likely the cause of the issue. So, how would I define the region that I want to, or any region really, using polar coordinates?

Note: Changing the interval to [-π,π] draws the full limaçon, but I would rather not have to play around with the interval every time I have a new function. I preferably want a solution that allows me to easily and correctly define a polar region.

• What is this Region function? It seems to be undefined in my version (v11.0)! Oct 21, 2017 at 21:24
• Are parametrized domains supported?
– Kuba
Oct 21, 2017 at 21:34
• No such problem with v12.2.0 on Win7-x64: Screenshot
– Syed
Sep 23, 2023 at 3:46

1 Answer

This works for me:

R = ImplicitRegion[(0 <= θ <= 2 π) && (0 <= r <= 2 + Cos[θ]), {r, θ}];
ParametricPlot[{r Cos[θ], r Sin[θ]}, {r, θ} ∈ R]