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)
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so the reflection of is given by
(2)
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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)
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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)
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This plane has normal vector
(5)
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and the signed point-plane distance is
(6)
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The position of the point reflected in the given plane is therefore given by
(7)
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(8)
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The reflection of a point with trilinear coordinates in a point is given by , where
(9)
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(10)
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(11)
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