Reflection Across A Line in The Plane
Reflection across a line through the origin in two dimensions can be described by the following formula
Where v denotes the vector being reflected, l denotes any vector in the line being reflected in, and v·l denotes the dot product of v with l. Note the formula above can also be described as
Where the reflection of line l on a is equal to 2 times the projection of v on line l minus v. Reflections in a line have the eigenvalues of 1, and −1.
Read more about this topic: Reflection (mathematics)
Famous quotes containing the words reflection, line and/or plane:
“If the contemplation, even of inanimate beauty, is so delightful; if it ravishes the senses, even when the fair form is foreign to us: What must be the effects of moral beauty? And what influence must it have, when it embellishes our own mind, and is the result of our own reflection and industry?”
—David Hume (1711–1776)
“The line it is drawn
The curse it is cast
The slow one now
Will later be fast
As the present now
Will later be past
The order is
Rapidly fadin’.
And the first one now
Will later be last
For the times they are a-changin’.”
—Bob Dylan [Robert Allen Zimmerman] (b. 1941)
“In time the scouring of wind and rain will wear down the ranges and plane off the region until it has the drab monotony of the older deserts. In the meantime—a two-million-year meantime—travelers may enjoy the cruel beauties of a desert in its youth,....”
—For the State of California, U.S. public relief program (1935-1943)