Superposition de calques monochromes d'opacités variables

Abstract

For a monochrome layer $x$ of opacity $0\le o_x\le 1$ placed on another monochrome layer of opacity 1, the result given by the standard formula is $$\Pi \left({\mathbf{C}}_{\phi }\right)=1+\sum _{n=1}^2\left(2-n-(-1{)}^n{o}_{\chi (\phi +1)}\right)\left(\chi (n+\phi -1)-o_{\chi (n+\phi -1)}\right),$$ the formula being of course explained in detail in this paper. We will eventually deduce a very simple theorem, generalize it and then see its validity with alternative formulas to this standard containing the same main properties here exposed.

poor research and unrigorous