Given a color in CIE L*a*b* space, how does one change the saturation? This is what I know...
$$\mathrm{chroma} = \sqrt {(a^*)^2 + (b^*)^2}$$ $$\mathrm{hue} = \arctan \left( a^* \over b^* \right)$$ $$\mathrm{sat} = {\frac{\mathrm{chroma}}{\sqrt{(L^*)^2 + \mathrm{chroma}^2}}}$$
I want to add $\mathrm{satdiff}$ to $\mathrm{sat}$, keeping $\mathrm{hue}$ and $L^*$ constant. I need to determine how to recalculate $a^*$ and $b^*$.
Here is what I get: suppose your new total value of $sat$ is shown by $x$. Then you want to multiply the original $(a,b)$ by $t={{xL}\over{\sqrt{(a^2+b^2)(1-x^2)}}}$. I dropped all the stars!