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Mathematica > Visualization and Graphics > Computational Geometry > Geometric Transforms >

Built-in Mathematica Symbol

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.

ReflectionTransform gives a TransformationFunction which can be applied to vectors.

ReflectionTransform works in any number of dimensions. In 2D it reflects in a line; in 3D it reflects in a plane.

Reflection in the

line:

Reflection in the

plane:

Reflection in the

line:

Reflection in the

plane:

Reflection transform for symbolic unit vector

Vectors normal to

remain unchanged:

Transformation applied to a 2D shape:

Transformation applied to a 3D shape:

Reflecting a graphic:

The reflection transformation is its own inverse:

The determinant of the transformation matrix is -1:

ReflectionTransform can be represented as a scaling transform:

Reflection changes the orientation of polygons:

Reflections of a sine wave: