Can someone please help me in breaking down what this code means?

Question

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.

Show[
    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.

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. — Bob Hanlon, Nov 11 '21 at 16:25

score 4 · Answer 1 · edited Nov 11 '21 at 19:12

4

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]]

edited Nov 11 '21 at 19:12

Jason B.

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answered Nov 11 '21 at 16:15

Daniel Huber

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Thank you very much. This was of much help! – Jetty Nov 21 '21 at 19:52

Can someone please help me in breaking down what this code means?

1 Answers1