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An inversion is a chromosome rearrangement in which a segment of a chromosome becomes inverted within its original position. An inversion occurs when a chromosome undergoes a two breaks within the chromosomal arm, and the segment between the two breaks inserts itself in the opposite direction in the same chromosome arm.
This is called circle inversion or plane inversion. The inversion taking any point P (other than O ) to its image P ' also takes P ' back to P , so the result of applying the same inversion twice is the identity transformation which makes it a self-inversion (i.e. an involution).
A hypercentric or pericentric lens is a lens system where the entrance pupil is located in front of the lens, in the space where an object could be located. In a certain region, objects that are further away from the lens produce larger images than objects that are closer to the lens.
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As noted above, the inverse with respect to a circle of a curve of degree n has degree at most 2n.The degree is exactly 2n unless the original curve passes through the point of inversion or it is circular, meaning that it contains the circular points, (1, ±i, 0), when considered as a curve in the complex projective plane.
Inversion was first noted in 1822 by the French zoologist Étienne Geoffroy Saint-Hilaire, when he dissected a crayfish (an arthropod) and compared it with the vertebrate body plan. The idea was heavily criticised, but periodically resurfaced, and is now supported by some molecular embryologists.
Inversion in a point, or point reflection, a kind of isometric (distance-preserving) transformation in a Euclidean space; Inversion transformation, a conformal transformation (one which preserves angles of intersection) Method of inversion, the image of a harmonic function in a sphere (or plane); see Method of image charges
The same techniques are equally applicable to video. While an image can be transformed in various ways, pure warping means that points are mapped to points without changing the colors. This can be based mathematically on any function from (part of) the plane to the plane. If the function is injective the original can be reconstructed.