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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

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

MORE INFORMATION

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.

The point p can lie anywhere in the mirror.

EXAMPLES

CLOSE ALL

Basic Examples (2)

Reflection in the

line:

Reflection in the

plane:

Reflection in the

line:

In[1]:=

Out[1]=

In[2]:=

Out[2]=

Reflection in the

plane:

In[1]:=

Out[1]=

In[2]:=

Out[2]=

Scope (3)

Reflection transform for symbolic unit vector

Vectors normal to

remain unchanged:

Transformation applied to a 2D shape:

Transformation applied to a 3D shape:

Applications (2)

Reflecting a graphic:

Reflections of a sine wave:

Properties & Relations (3)

The reflection transformation is its own inverse:

The determinant of the transformation matrix is

ReflectionTransform can be represented as a scaling transform:

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: