I hope someone can assist me as I am pretty new to Mathematica and understanding the language is a bit of a hurdle.

I am trying to rotate a plot of interlaced circles by some angle without rotating the axis and this is the method that somewhat worked the best.

    Normal[someplot] /. prim : _Line | _Point | _Polygon :> 
           GeometricTransformation[prim, RotationTransform[Pi/20]], PlotRange -> All, AspectRatio -> Automatic

From the highest rated answer in the link below:

How to rotate the curve but not the axes?

I would please like to know what the code below is doing. Particularly the "/. prim : _Line | _Point | _Polygon :>" part.

Thank you dearly.

  • 1
    $\begingroup$ In Mathematica, highlight any unknown symbol and press F1 for help. /. links to ReplaceAll, : links to Pattern, _ links to Blank, and :> links to RuleDelayed. Mathematica provides easy access to docs. $\endgroup$
    – Bob Hanlon
    Nov 11, 2021 at 16:25

1 Answer 1


Normal[p] is needed to replace GraphicsComplex by a full form with all coodinates.

prim : _Line | _Point | _Polygon is a pattern that matches a line, point or polygon.

:> GeometricTransform[prim,..] replaces the matched line, point or polygon by a rotated version of it.

Here is a small example:

p= Graphics[{Line[{{0, 0}, {1, 1}}], Point[{1, 0.5}]}, Axes -> True]

p /. prim : _Line | _Point | _Polygon :> 
  GeometricTransformation[prim, RotationTransform[Pi/2]] 

enter image description here

  • $\begingroup$ Thank you very much. This was of much help! $\endgroup$
    – Jetty
    Nov 21, 2021 at 19:52

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