# Rotate polar region with occlusion [duplicate]

I am new to Mathematica, so partial answers and strategic advice are appreciated.

I have produced the following image:

Show[
Join[
Table[PolarPlot[{1}, {r, 0,2π}, Axes -> False], {ψ, 0, 1, 2.39996}],
Table[PolarPlot[{(θ- ψ)/π}, {θ, (0 + ψ), (π + ψ)}], {ψ, 0, 1, 2.39996}],
Table[PolarPlot[{(2 - θ/π)+(ψ/π)}, {θ, π + ψ, 2π + ψ}], {ψ, 0, 1, 2.39996}]
]
]


I want to fill the following region:

And do so in a way that is extensible to more iterations of my loop:

Show[
Join[
Table[PolarPlot[{1}, {r, 0,2π}, Axes -> False], {ψ, 0, 3, 2.39996}],
Table[PolarPlot[{(θ- ψ)/π}, {θ, (0 + ψ), (π + ψ)}], {ψ, 0, 3, 2.39996}],
Table[PolarPlot[{(2 - θ/π)+(ψ/π)}, {θ, π + ψ, 2π + ψ}], {ψ, 0, 3, 2.39996}]
]
]


My goal is to have these regions overlap with occlusion, with the edges, background, and fill to be three distinct colors.

• I'm not clear with how you want to shade the more complicated shape, but the simple one is not very hard: BoundaryDiscretizeRegion[RegionDifference[Disk[], First[Cases[PolarPlot[Abs[θ]/π, {θ, -π, π}], Line[l_] :> Polygon[l], ∞]]], MeshCellStyle -> {2 -> Black}] – J. M.'s technical difficulties Dec 22 '16 at 7:10
• I am voting to close this as "already has an answer here" (see link at the top of your post) -- if you find that the methods described are not applicable to the case at hand please edit your question to describe what you tried and reference the older question; this will automatically add your question to the Reopen Review Queue. – Mr.Wizard Dec 22 '16 at 17:30