# ReflectionTransform

gives a TransformationFunction that represents a reflection in a mirror through the origin, normal to the vector v.

ReflectionTransform[v,p]

gives a reflection in a mirror through the point p, normal to the vector v.

# Examples

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## Basic Examples(2)

Reflection in the line:

Reflection in the plane:

## Scope(3)

Reflection transform for symbolic unit vector {u, v, w}:

Vectors normal to {u, v, w} remain unchanged:

Transformation applied to a 2D shape:

Transformation applied to a 3D shape:

## Applications(4)

Reflecting a graphic:

Reflections of a sine wave:

Mirror an image:

Reflection transform of a 3D image with respect to the axis:

## Properties & Relations(5)

The reflection transformation is an isometric transform, i.e. preserves distances:

The reflection transformation is its own inverse:

The determinant of the transformation matrix is :

ReflectionTransform can be represented as a scaling transform:

Top-bottom image reflection using ImageTransformation:

Reflection across the main diagonal:

Reflection across the main antidiagonal:

## Possible Issues(1)

Reflection changes the orientation of polygons:

## Neat Examples(1)

Reflect a 3D object about a point p:

Along the axis, about the plane:

Along the axis, about the plane:

Along the axis, about the plane:

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

#### Text

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

#### CMS

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

#### APA

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

#### BibTeX

@misc{reference.wolfram_2024_reflectiontransform, author="Wolfram Research", title="{ReflectionTransform}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/ReflectionTransform.html}", note=[Accessed: 16-September-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_reflectiontransform, organization={Wolfram Research}, title={ReflectionTransform}, year={2007}, url={https://reference.wolfram.com/language/ref/ReflectionTransform.html}, note=[Accessed: 16-September-2024 ]}