Superposition de calques monochromes d'opacités variables
This work addresses a theoretical problem in image processing or graphics, likely incremental as it builds on existing superposition principles.
The paper tackles the problem of mathematically modeling the superposition of monochrome layers with variable opacities, deriving a standard formula and validating it through generalization and comparison with alternative formulas.
For a monochrome layer $x$ of opacity $0\le o_x\le1 $ placed on another monochrome layer of opacity 1, the result given by the standard formula is $$\smallΠ\left({\bf C}_\varphi\right)=1+\sum_{n=1}^2\left(2-n-(-1)^no_{χ(\varphi+1)}\right)\left(χ(n+\varphi-1)-o_{χ(n+\varphi-1)}\right),$$ 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.