How to create custom Graphics primitive?

Question

How to create custom Graphics primitive?

It should have the following properties, resembling properties of built-in geometric figures, like Circle etc:

1. Has constant head, say RoundedRectangle. It should not evaluate to the list of lines, so as normal Rectangle.

2. Can serve as a subject for GeometricTransformation

Answer 1

Try this:

SetAttributes[createPrimitive, HoldAll]

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

Example:

createPrimitive[face[x_: 0.1],
 {Circle[{0, 0}, 1], Circle[{-0.3, 0.5}, x],
  Circle[{0.3, 0.5}, x], Line[{{-0.4, -0.2}, {0.4, -0.2}}]}]

It works as expected in Graphics:

g = Graphics[face[]]

face has no DownValues so it remains as face in InputForm:

InputForm[g]
(*  Graphics[face[]]  *)

(*  Graphics[face[], ImageSize -> {63., Automatic}]  *)

It works with GeometricTransformation:

Graphics[GeometricTransformation[face[0.2], ShearingTransform[Pi/4, {1, 0}, {0, 1}]]]

A note about colours

A commenter asked "How would you rewrite this function to color the different components differently?" The answer is that colours can be used in the definition of the custom primitive just as in any other graphics expression, but note that the expression that goes into Typeset`MakeBoxes must be something that the Front End understands, e.g. RGBColor[1,0,0] rather than Red. If you want to use named colours like Red you will need to let the kernel evaluate the expression to convert them to RGBColor directives.

So for example you could:

Manually specify the colours as RGBColor directives:

createPrimitive[myprim[x_], {RGBColor[1, 0, 0], Circle[{0, 0}, x]}]

Use named colours and override the hold attribute with Evaluate:

createPrimitive[myprim[x_], Evaluate @ {Red, Circle[{0, 0}, x]}]

Or just remove the hold attribute completely:

ClearAttributes[createPrimitive, HoldAll];
createPrimitive[myprim[x_], {Red, Circle[{0, 0}, x]}]

In the last two cases you should guard against x already having a value, e.g. with Block or by using \[FormalX] instead of x

Answer 2

I don't see how to do what you are asking for without modifying the built-in definition of Graphics, something I would be extremely reluctant to do. In my own work, the closest I have come to meeting your requirements is to define functions that define shapes by returning lists consisting of graphics directives and primitives. This has worked well enough to satisfy me so far.

Here is an example.

dashedPoly[pts : {{_, _} ..}, 
           fill : (_RGBColor | _GrayLevel | _Hue) : Transparent] :=
    {fill, EdgeForm[Dashing[Small]], Polygon[pts]}

And here are two examples of the function in use.

Module[{A, B, C},
  A = {0., 0.}; B = {0., 3.}; C = {4., 0.};
  Graphics[dashedPoly[{A, B, C}]]]

With[{blue = ColorData["HTML", "DeepSkyBlue"]}, 
  Module[{A, B, C},
    A = {0., 0.}; B = {0., 3.}; C = {4., 0.};
    Graphics[dashedPoly[{A, B, C}, blue]]]]