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Mathematics Geometry Wolfram Language

Add a vector onto the specific column of TransformationFunction.

Hongyi Zhao

Posted 1 year ago

I've the following command: In[7]:= RotationTransform[Pi,{1,0,0},{x,1/2,1/4}] Out[7]= TransformationFunction[( \!\(\* TagBox[GridBox[{ {"1", "0", "0", "0"}, {"0", RowBox[{"-", "1"}], "0", "1"}, {"0", "0", RowBox[{"-", "1"}], FractionBox["1", "2"]}, {"0", "0", "0", "1"} }, AutoDelete->False, GridBoxDividers->{"Columns" -> {{False}}, "ColumnsIndexed" -> {-2 -> True}, "Rows" -> {{False}}, "RowsIndexed" -> {-2 -> True}}, GridBoxItemSize->{"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], #& ]\) )] And I want to add the vector {1/2,0,0} onto the first three rows of the last column, i.e., obtain the following form: TransformationFunction[( \!\(\* TagBox[GridBox[{ {"1", "0", "0", FractionBox["1", "2"]}, {"0", RowBox[{"-", "1"}], "0", "1"}, {"0", "0", RowBox[{"-", "1"}], FractionBox["1", "2"]}, {"0", "0", "0", "1"} }, AutoDelete->False, GridBoxDividers->{"Columns" -> {{False}}, "ColumnsIndexed" -> {-2 -> True}, "Rows" -> {{False}}, "RowsIndexed" -> {-2 -> True}}, GridBoxItemSize->{"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], #& ]\) )] How can I achieve this aim? Regards, Zhao

I've the following command:

In[7]:= RotationTransform[Pi,{1,0,0},{x,1/2,1/4}]

Out[7]= TransformationFunction[( \!\(\*
TagBox[GridBox[{
{"1", "0", "0", "0"},
{"0", 
RowBox[{"-", "1"}], "0", "1"},
{"0", "0", 
RowBox[{"-", "1"}], 
FractionBox["1", "2"]},
{"0", "0", "0", "1"}
},
AutoDelete->False,
GridBoxDividers->{"Columns" -> {{False}}, 
        "ColumnsIndexed" -> {-2 -> True}, "Rows" -> {{False}}, 
        "RowsIndexed" -> {-2 -> True}},
GridBoxItemSize->{"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}],
#& ]\) )]

And I want to add the vector {1/2,0,0} onto the first three rows of the last column, i.e., obtain the following form:

TransformationFunction[( \!\(\*
TagBox[GridBox[{
{"1", "0", "0", 
FractionBox["1", "2"]},
{"0", 
RowBox[{"-", "1"}], "0", "1"},
{"0", "0", 
RowBox[{"-", "1"}], 
FractionBox["1", "2"]},
{"0", "0", "0", "1"}
},
AutoDelete->False,
GridBoxDividers->{"Columns" -> {{False}}, 
        "ColumnsIndexed" -> {-2 -> True}, "Rows" -> {{False}}, 
        "RowsIndexed" -> {-2 -> True}},
GridBoxItemSize->{"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}],
#& ]\) )]

How can I achieve this aim?

Regards, Zhao

POSTED BY: Hongyi Zhao

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Hongyi Zhao

Posted 1 year ago

Hi Henrik Schachner, Thank you very much. It does the trick. N.B.: I noticed another wonderful example, helpful to understand the RotationTransform function in Mathematica Manipulate[ Module[{w={1,0,0},p={-2,2}}, Graphics3D[ { {Opacity->.4,GeometricTransformation[ {Cuboid[{0,0,0}]},RotationTransform[angle,w,{a,b,c}]] }, {Blue,PointSize[0.05],Point[{a,b,c}]}, {Red,Thick,Line[{{a,b,c},{a,b,c}+w}]} }, ImageSize->300, ImagePadding->2,AxesOrigin->{0,0,0}, ImageMargins->2,ViewAngle->All, Axes->True, Ticks->None, PlotRange->{p,p,p} ] ], {angle,0,2 \[Pi],ImageSize->Tiny}, {{a,0,"a"},0,1,.1,Appearance->"Labeled",ImageSize->Tiny}, {{b,0,"b"},0,1,.1,Appearance->"Labeled",ImageSize->Tiny}, {{c,0,"c"},0,1,.1,Appearance->"Labeled",ImageSize->Tiny}, ControlPlacement->Left ] Best, Zhao

Hi Henrik Schachner,

Thank you very much. It does the trick.

N.B.: I noticed another wonderful example, helpful to understand the RotationTransform function in Mathematica

Manipulate[
  Module[{w={1,0,0},p={-2,2}},
    Graphics3D[
    {
       {Opacity->.4,GeometricTransformation[
         {Cuboid[{0,0,0}]},RotationTransform[angle,w,{a,b,c}]]
        },

       {Blue,PointSize[0.05],Point[{a,b,c}]},
       {Red,Thick,Line[{{a,b,c},{a,b,c}+w}]}
    },

    ImageSize->300,
    ImagePadding->2,AxesOrigin->{0,0,0},
    ImageMargins->2,ViewAngle->All,
    Axes->True,
    Ticks->None,
    PlotRange->{p,p,p}
    ]
  ],

  {angle,0,2 \[Pi],ImageSize->Tiny},
  {{a,0,"a"},0,1,.1,Appearance->"Labeled",ImageSize->Tiny},
  {{b,0,"b"},0,1,.1,Appearance->"Labeled",ImageSize->Tiny},
  {{c,0,"c"},0,1,.1,Appearance->"Labeled",ImageSize->Tiny},

   ControlPlacement->Left
]

Best, Zhao

POSTED BY: Hongyi Zhao

Henrik Schachner

Henrik Schachner, Radiation Therapy Center, Weilheim, Germany

Posted 1 year ago

Zhao, here is one way: Let `g` be your original transformation function, g = RotationTransform[Pi, {1, 0, 0}, {x, 1/2, 1/4}] then what you need is an additional translation by `{1/2, 0, 0}`: TransformationFunction[TransformationMatrix[g].TransformationMatrix[TranslationTransform[{1/2, 0, 0}]]]

POSTED BY: Henrik Schachner

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