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1

I have a polygon on which I'm applying a GeometricTransform and I want to get the coordinates of the transformed polygon. Graphics[g] works and shows it nicely, but Normal@g doesn't seem to work. What am I doing wrong?

g = GeometricTransformation[
     Polygon[{
      {-0.36551249999999996`, -0.29021463333333336`}, 
      {-0.36509784999999995`, -0.2812481916666667`}, 
      {-0.3619309499999999`, -0.2645122083333334`}, 
      {-0.3592788999999999`, -0.25668636666666667`}, 
      {-0.3520880999999999`, -0.2419782333333334`}, 
      {-0.34271569999999996`, -0.22834049999999997`}, 
      {-0.3254433499999999`, -0.209398275`}, 
      {-0.3055169`, -0.19159769999999998`}, 
      {-0.26311249999999997`,-0.15638130000000006`}, 
      {-0.24333994999999997`, -0.13744537499999998`}, 
      {-0.22632409999999997`, -0.11661089999999996`}, 
      {-0.21717969999999998`, -0.10129116666666663`}, 
      {-0.21341764999999996`, -0.09311782500000006`}, 
      {-0.16110257499999997`, 0.0714712708333333`}, 
      {-0.1087875`, 0.23606036666666666`}, 
      {-0.3035939666666666`, -0.33778329166666676`}, 
      {-0.32013196666666666`, -0.3382103666666666`}, 
      {-0.33230609999999994`, -0.33689943333333333`}, 
      {-0.3425458333333333`, -0.3340813000000001`}, 
      {-0.3508735666666666`, -0.32955116666666673`}, 
      {-0.3558780916666666`, -0.3249068666666666`}, 
      {-0.36091372499999996`, -0.3168879333333333`}, 
      {-0.3634749`, -0.3093918333333333`}, 
      {-0.365004675`, -0.3005295333333334`}, 
      {-0.36551249999999996`, -0.29021463333333336`}}
     ], 
     {{-0.14929987960875826`, -1.065591641272026`}, 
      {1.0642599291951356`, -0.14911329363618442`}
     }
   ]
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I do not believe Normal will give you the coordinates, but Polygon[...][[1]] will. – rcollyer Oct 2 '12 at 18:41
@rcollyer he means the transformed coordinates. "When possible, Normal will perform the transformations explicitly:" – Mr.Wizard♦ Oct 2 '12 at 18:44
@Mr.Wizard ah, I see it now. And, I see his problem, too. – rcollyer Oct 2 '12 at 18:47
1  
@rcollyer Ohhh... you meant it looks bad in mma. Yes, that I agree with — I was bitching about it a lot in chat when I first got my laptop (which is the chat discussion I linked to). Hopefully v9 supports retina. But then, if you had it in mma, you would've seen that it had a second argument because the little red triangle didn't pop up :) – rm -rf♦ Oct 2 '12 at 19:42

1 Answer

up vote 1 down vote

I don't know why Normal does not work, but you can perform at least the transformation shown like this:

pts = {{-0.36551249999999996`, -0.29021463333333336`}, \
{-0.36509784999999995`, -0.2812481916666667`}, {-0.3619309499999999`, \
-0.2645122083333334`}, {-0.3592788999999999`, -0.25668636666666667`}, \
{-0.3520880999999999`, -0.2419782333333334`}, {-0.34271569999999996`, \
-0.22834049999999997`}, {-0.3254433499999999`, -0.209398275`}, \
{-0.3055169`, -0.19159769999999998`}, {-0.26311249999999997`, \
-0.15638130000000006`}, {-0.24333994999999997`, \
-0.13744537499999998`}, {-0.22632409999999997`, \
-0.11661089999999996`}, {-0.21717969999999998`, \
-0.10129116666666663`}, {-0.21341764999999996`, \
-0.09311782500000006`}, {-0.16110257499999997`, 
    0.0714712708333333`}, {-0.1087875`, 
    0.23606036666666666`}, {-0.3035939666666666`, \
-0.33778329166666676`}, {-0.32013196666666666`, \
-0.3382103666666666`}, {-0.33230609999999994`, \
-0.33689943333333333`}, {-0.3425458333333333`, -0.3340813000000001`}, \
{-0.3508735666666666`, -0.32955116666666673`}, {-0.3558780916666666`, \
-0.3249068666666666`}, {-0.36091372499999996`, -0.3168879333333333`}, \
{-0.3634749`, -0.3093918333333333`}, {-0.365004675`, \
-0.3005295333333334`}, {-0.36551249999999996`, -0.29021463333333336`}};

tf = AffineTransform[{{-0.14929987960875826`, -1.065591641272026`}, \
{1.0642599291951356`, -0.14911329363618442`}}];

Graphics@Polygon[tf /@ pts]

Mathematica graphics

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