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• Mathematics

Homography

A homography is a transformation of the complex plane which associates its image to a complex number z

$z^'=\frac{az+b}{cz+d}$

providing the four numbers a, b, c, d are such that $ad-bc\neq 0$.

The formula is only valid if z is different from -d/c (in which case the denominator cancels). This pitfall disappears, however, in projective geometry where homographies appear spontaneously as bijections.

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