Creating new graphics primitive (EdgeForm, FaceForm)

Question

My question is strongly related to this question, nevertheless I would like to bring it to everyone's attention. Let's say I want to create a new graphics primitive Boing which should look like this

Boing[] := 
 Polygon[Join[#1, Reverse[#2]] & @@@ 
   Partition[
    Table[{2 x/Pi, y/2*Cos[x]}, {x, -Pi/2, Pi/2, 
      Pi/10}, {y, {-1, 1}}], 2, 1]]

Graphics[{Opacity[0.3, Blue], Boing[]}, 
 AspectRatio -> Automatic]

As a new primitive, it should clearly work like other primitives like Disk, Rectangle, etc. When I define a FaceForm and EdgeForm one sees that this does not work because the settings are applied to the underlying Polygons

Graphics[{EdgeForm[Black], FaceForm[Opacity[0.3, Blue]], 
  Boing[]}, AspectRatio -> Automatic]

In this case one could slightly re-arrange the points and create one overall polygon to circumvent the issue

Boing[] := 
 Polygon[Join[#1, Reverse[#2]] & @@ 
   Transpose[
    Table[{2 x/Pi, y/2*Cos[x]}, {x, -Pi/2, Pi/2, 
      Pi/10}, {y, {-1, 1}}]]]
Graphics[{EdgeForm[Black], FaceForm[Opacity[0.3, Blue]], Boing[]}, 
 AspectRatio -> Automatic]

Unless I am mistaken, this is in general not possible without having access to the current values of FaceForm and EdgeForm. Consider the following example where I don't see a direct way

Question:

What is the simplest solution to create a new graphics primitive which works like e.g. a polygon? To clarify: I want to be able to manually construct a new primitive and define how the settings of the current graphics state like FaceForm or EdgeForm (Texture, Specularity or Lighting are further examples which change the state of the graphics engine) are handled.

Update:

The answer of rm-rf was promising but unfortunately, Graphics`Mesh`PolygonCombine seems to have the same issues as I encountered above. This means, that for my target application it will not work. Consider the following example

points[r1_, r2_, n_] :=
  With[{dphi = 2.0 Pi/(n - 1)},
   Table[r {Cos[phi], Sin[phi]}, {phi, 0, 2 Pi, dphi}, {r, {r1, r2}}]
   ];

Graphics@{EdgeForm[{Black, Thick}], FaceForm[Opacity[0.3, Red]],
  Polygon[
   Function[{p1, p2}, Join[p1, Reverse[p2]]] @@@ 
    Partition[points[0.3, 0.7, 30], 2, 1]]}

And with Graphics`Mesh`PolygonCombine we get

Answer 1

I think you will need to use FilledCurve to create objects with holes in.

For example:

points[r1_, r2_, n_] := With[{dphi = 2.0 Pi/(n - 1)}, 
   Table[r {Cos[phi], Sin[phi]}, {phi, 0, 2 Pi, dphi}, {r, {r1, r2}}]];

poly = Polygon[Function[{p1, p2}, Join[p1, Reverse[p2]]] @@@ 
    Partition[points[0.3, 0.7, 30], 2, 1]];

prim = FilledCurve[Thread[Graphics`Mesh`PolygonCombine @ poly] /. 
    Polygon[data_] :> {Line[data]}];

To make something that behaves more like a graphics primitive I will use my answer from here

SetAttributes[createPrimitive, HoldAll];
createPrimitive[patt_, expr_] := 
 Typeset`MakeBoxes[p : patt, fmt_, Graphics] := 
  Typeset`MakeBoxes[Interpretation[expr, p], fmt, Graphics]

createPrimitive[donut, Evaluate@prim]

Now you can use donut in Graphics:

Graphics@{EdgeForm[{Black, Thick}], FaceForm[Opacity[0.3, Red]], donut}

Because donut has no downvalues, it remains unevaluated in the graphics expression:

InputForm[%]
(* Graphics[{EdgeForm[{GrayLevel[0], Thickness[Large]}], 
    FaceForm[Opacity[0.3, RGBColor[1, 0, 0]]], donut}] *)

Answer 2

You can use the undocumented PolygonCombine to create a single polygon which behaves well with EdgeForm and FaceForm:

Boing2[] := Graphics`Mesh`PolygonCombine@Boing[]
Graphics[{EdgeForm[Black], FaceForm[Opacity[0.3, Blue]], Boing2[]}, AspectRatio -> Automatic]

In Mathematica 10/Wolfram Language/Mathematica-RPi, the function can be found under Graphics`PolygonUtils`. There might be some issues with self-intersecting polygons (I haven't looked into it), but this is a good start.

Answer 3

In Mathematica 12 BoundaryMeshRegion objects can be used as a Graphics primitive. So, another idea is to use a BoundaryMeshRegion as your primitive. For example:

Typeset`MakeBoxes[
    CutoutEllipse[center_, out_, in_],
    form_,
    Graphics
] := With[
    {
    new = Replace[
        RegionDifference[Disk[center, out], Disk[center, in]],
        b_BooleanRegion :> BoundaryDiscretizeRegion[b]
    ]
    },
    Typeset`MakeBoxes[new, form, Graphics]
]

Examples:

Graphics[{Pink, EdgeForm[Blue], CutoutEllipse[{0,0}, {4,2}, .9 {1,2}]}]

Graphics[{Pink, EdgeForm[Blue], CutoutEllipse[{0,0}, {4,2}, 1.1 {1,2}]}]

You can use this answer to get the above approach to work in earlier versions of Mathematica.

Answer 4

FilledCurve seems to do exactly what you want

Answer 5

Posting a separate answer, as this is really a completely different approach. While it seems impossible to access the current setting for FaceForm and EdgeForm in between the drawing steps, it is possible to temporarily change them for a particular primitive with Style.

So you can show the original polygon with no edges, and the combined polygon with no faces:

points[r1_, r2_, n_] := With[{dphi = 2.0 Pi/(n - 1)}, 
   Table[r {Cos[phi], Sin[phi]}, {phi, 0, 2 Pi, dphi}, {r, {r1, r2}}]];

poly = Polygon[Function[{p1, p2}, Join[p1, Reverse[p2]]] @@@ 
    Partition[points[0.3, 0.7, 30], 2, 1]];

Graphics[{EdgeForm[{Black, Thick}], FaceForm[Opacity[0.3, Red]], 
  Style[poly, EdgeForm[]], 
  Style[Graphics`Mesh`PolygonCombine[poly], FaceForm[]]
  }]