Color wheel can be used to represent complex number (for example see the link: How do I draw a Circular Graph colored like this in Mathematica?)

Now I use the following code to draw my color scale (0~2Pi uses Hue color and the length strength uses transparency (100%: radial=0; 0%: radial=2)):

With[{pts = Append[#, First[#]] &@Table[{r {Cos[phi], Sin[phi]}, phi/(2 Pi)}, {phi, 0, 2 Pi, .1}, {r, 0, 2, .1}]}, Graphics[{Polygon[{{0, 0}, First[#1], First[#2]}, VertexColors -> (Hue /@ {{0, 0, 2}, Last[#1], Last[#2]})] & @@@Partition[pts[[All, -1, {1, 2}]], 2, 1]}]] 

The figure shows as the following (red is 0 or 2pi; green is pi/2):

Now I have two hypergraphs which shares one vertex (HypergraphPlot function from hypergraph plotting):

fig1 = HypergraphPlot[{{Subscript[d, 1], Subscript[d, 2]}, {Subscript[ d, 1], Subscript[d, 3]}}, "SubsetBoundaryStyle" -> (Directive[ EdgeForm[{Thickness[0.003], Black}], #] & /@ {Green, Red}), "SubsetBoundaryScale" -> {2, 2, 2, 2}, "SubsetEdge" -> False, PlotTheme -> "Classic"] 

So the fig1 is as:

I would like to know how to plot fig2 instead of fig1, merging the color into the shared region as the color wheel description?

Thank you very much in advance! If something is unclear, thank you for point out!