Formula
Given a vector a in the Euclidean space Rn, the formula for the reflection of a across the point p is
In the case where p is the origin, point reflection is simply the negation of the vector a (see reflection through the origin).
In Euclidean geometry, the inversion of a point X in respect to a point P is a point X* such that P is the midpoint of the line segment with endpoints X and X*. In other words, the vector from X to P is the same as the vector from P to X*.
The formula for the inversion in P is
- x*=2a−x
where a, x and x* are the position vectors of P, X and X* respectively.
This mapping is an isometric involutive affine transformation which has exactly one fixed point, which is P.
Read more about this topic: Point Reflection
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—Aristotle (384–323 B.C.)
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