ReflectionMatrix

ReflectionMatrix[v]

gives the matrix that represents reflection of points in a mirror normal to the vector v.

Details

  • 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.

Examples

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Basic Examples  (2)

Reflect along the axis, or equivalently reflect in the axis:

Reflect along the vector or equivalently in the plane given by :

Scope  (4)

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 {u,v}:

Vectors normal to {u,v} remain unchanged:

Transformation applied to a 2D shape:

Transformation applied to a 3D shape:

Applications  (1)

Flipping a surface:

Properties & Relations  (3)

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:

Possible Issues  (1)

Reflection changes the orientation of polygons:

Neat Examples  (1)

Reflections of a cuboid in vertical planes:

Wolfram Research (2007), ReflectionMatrix, Wolfram Language function, https://reference.wolfram.com/language/ref/ReflectionMatrix.html.

Text

Wolfram Research (2007), ReflectionMatrix, Wolfram Language function, https://reference.wolfram.com/language/ref/ReflectionMatrix.html.

CMS

Wolfram Language. 2007. "ReflectionMatrix." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/ReflectionMatrix.html.

APA

Wolfram Language. (2007). ReflectionMatrix. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ReflectionMatrix.html

BibTeX

@misc{reference.wolfram_2023_reflectionmatrix, author="Wolfram Research", title="{ReflectionMatrix}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/ReflectionMatrix.html}", note=[Accessed: 22-September-2023 ]}

BibLaTeX

@online{reference.wolfram_2023_reflectionmatrix, organization={Wolfram Research}, title={ReflectionMatrix}, year={2007}, url={https://reference.wolfram.com/language/ref/ReflectionMatrix.html}, note=[Accessed: 22-September-2023 ]}