Reflection

The operation of exchanging all points of a mathematical object with their mirror images (i.e., reflections in a mirror). Objects that do not change handedness under reflection are said to be amphichiral; those that do are said to be chiral.

Consider the geometry of the left figure in which a point is reflected in a mirror (blue line). Then

(1)

so the reflection of is given by

(2)

The term reflection can also refer to the reflection of a ball, ray of light, etc. off a flat surface. As shown in the right diagram above, the reflection of a points off a wall with normal vector satisfies

(3)

If the plane of reflection is taken as the -plane, the reflection in two- or three-dimensional space consists of making the transformation for each point. Consider an arbitrary point and a plane specified by the equation

(4)

This plane has normal vector

(5)

and the signed point-plane distance is

(6)

The position of the point reflected in the given plane is therefore given by

			(7)
			(8)

The reflection of a point with trilinear coordinates in a point is given by , where

			(9)
			(10)
			(11)

Wolfram Web Resources