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Normal with GeometricTransformation

  • To: mathgroup at
  • Subject: [mg110378] Normal with GeometricTransformation
  • From: "David Park" <djmpark at>
  • Date: Wed, 16 Jun 2010 05:36:56 -0400 (EDT)

The "More Information" for the GeometricTransformation function states: 


"Normal[expr] if possible replaces all GeometricTransformation[Subscript[g,
i],\[Ellipsis]] constructs by versions of the Subscript[g, i] in which the
coordinates have explicitly been transformed."


I just wonder if "if possible" means "never" because here is about as simple
a case as one can get.


gr = Line[{{0, 0}, {1, 0}, {1, 1}, {0, 1}, {0, 0}}]; 


Graphics[{gr, Red, 

  GeometricTransformation[gr, TranslationTransform[{.5, .5}]]}, 

 Frame -> True] 


Now try to make the translation explicit by using Normal.


GeometricTransformation[gr, TranslationTransform[{.5, .5}]] // Normal 


It does nothing. There are cases where it would be useful to have the actual
transformed points. Any ideas on how to make this work?



David Park

djmpark at


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