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ReflectionTransform[v]

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.

Details
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Examples  
Basic Examples  
Scope  
Applications  
Properties & Relations  
Possible Issues  
Neat Examples  
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ReflectionTransform

ReflectionTransform[v]

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.

Details

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_2025_reflectiontransform, author="Wolfram Research", title="{ReflectionTransform}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/ReflectionTransform.html}", note=[Accessed: 15-August-2025]}

BibLaTeX

@online{reference.wolfram_2025_reflectiontransform, organization={Wolfram Research}, title={ReflectionTransform}, year={2007}, url={https://reference.wolfram.com/language/ref/ReflectionTransform.html}, note=[Accessed: 15-August-2025]}