How to transform a Graphics?

Questions
,
1

I have to transform (namely translate and rotate) any 2D Graphics. Of course, I know about TranslationTransform, RotationTransform, GeometricTransformation, and the like. But they all act on graphics primitives, not on a completed Graphics.

I’m afraid it’s a stupid question, but Is there some direct way to transform a Graphics? Something like:

g=Graphics[listOfPrimitives,options];
TranslationTransform[vShift]@*RotationTransform[theta, vOrigin] [g]

I could take the primitives and options of g by g[[1]] and Options[g] and write:

Graphics[GeometricTransformation[g[[1]], 
  TranslationTransform[vShift]@*RotationTransform[theta,vOrigin], 
 Options[g]]

but this looks pretty strange. And would it work with Images, Rasters within the primitives?

2

Hi Werner,

You can use Rotate to rotate.

g = Graphics[{Orange, RegularPolygon[3]}]
Rotate[g, Pi/2]

Edit
For translation use Translate

3

Operate over the complete Graphics command may produce undesired outputs, as the coordinates axes are not left fixed. One way is to use Rule transformations on the Graphics Primitives that you need as follows

Open in Wolfram Cloud ↗
4

That’s clear. But it transforms the primitives, just like GeometricTransformation, not the Graphics.
And it requires knowledge of all primitives within the Graphics.

5

I also don’t know but thank you to those who answer it. Now, I know.

6

Werner, maybe like this?

f[x_, theta_, vshift_] := Graphics[Translate[Rotate[First@x, theta, {0, 0}], vshift], Sequence @@ Rest@x]

g = Graphics[{EdgeForm[Black], Gray, Triangle[], Disk[{1, 1}, .25]}, 
  Axes -> True, AxesOrigin -> {0, 0}, PlotRange -> 2];

f[g, Pi/3, {0.6, 0.4}]

7858TransRotGraphics.png
7858TransRotGraphics.png365×368 2.51 KB

7

Another approach that might give you what you want is:

MapAt[Rotate[#, 30*Degree, {0, 0}] &, g, 1]

This gives:

5091Graphics1.png
5091Graphics1.png192×200 1.73 KB

Since the Head of the resulting expression is Graphics, the expression can be used in functions such as Show as in the following example:

Table[
  MapAt[Rotate[#, rot*Degree, {0, 0}] &, g, 1],
  {rot, 0, 360, 30}
  ] // Show

Which gives:

Graphics2.png
Graphics2.png192×200 4.45 KB

Hope this helps.

8

Isn’t that exactly what GeometricTransformation does?

9

Isn’t that exactly what GeometricTransformation does?

10

Yes, it basically works in a way similar to your GeometricTransformation example. Also similar to Ian’s MapAt. But what drawbacks do you see with these methods?