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ReflectionMatrix

ReflectionMatrix[v]
gives the matrix that represents reflection of points in a mirror normal to the vector v.
  • The reflection is in a mirror that goes through the origin.
  • ReflectionMatrix works in any number of dimensions. In 2D it reflects in a line; in 3D it reflects in a plane.
Reflect along the axis, or equivalently reflect in the axis:
Reflect along the vector or equivalently in the plane given by :
Reflect along the axis, or equivalently reflect in the axis:
In[1]:=
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Out[1]//MatrixForm=
In[2]:=
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Out[2]=
 
Reflect along the vector or equivalently in the plane given by :
In[1]:=
Click for copyable input
Out[1]//MatrixForm=
Reflect along the vector or equivalently in the plane given by :
Points in the reflection plane remain fixed:
Points outside the reflection plane get reflected in the plane:
Reflection matrix for symbolic unit vector :
Vectors normal to remain unchanged:
Transformation applied to a 2D shape:
Transformation applied to a 3D shape:
Flipping a surface:
The determinant of a reflection matrix is :
The inverse of a reflection matrix is the matrix itself:
Reflection can be thought of as a special case of scaling:
Reflection changes the orientation of polygons:
Reflections of a cuboid in vertical planes:
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