Intuitively, it’s not too difficult to understand why this is the case. Remember that error-diffusion works in response to the relationship between the input value and the quantised value. In other words, the colour palette is already factored in during the dithering process. On the other hand, ordered dithering is completely agnostic to the colour palette being used. Images are perturbed the same way every time, regardless of the given palette.
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Knowing this, we can modify the N-Convex algorithm covered earlier such that the candidate weights are given by the barycentric coordinates of the input pixel after being projected onto a triangle whose vertices are given by three surrounding colours, abandoning the IDW method altogether1. This results in a fast and exact minimisation of , with the final dither being closer in quality to that of Knoll’s Algorithm.