Christoph Peters

One of my favorite modern dithering methods is blue-noise dithering (see Figure 3b): https://developer.nvidia.com/blog/rendering-in-real-time-with-spatiote… The only catch is that generating blue noise is a roughly O(n^2) algorithm. Its not feasible to be generated on the fly, so in practice you just pregenerate a bunch of blue-noise textures and tile them. If you google 'pregenerated blue noise' you find plenty of them: https://momentsingraphics.de/BlueNoise.html

Agreed - blue noise dithering is very commonly used in computer graphics because it’s cheap and great, but it might be worth mentioning that it’s a kind of ordered dithering, which is mentioned in the article. Christoph Peters’s free blue noise textures are the most commonly used, for people who can’t be bothered running void and cluster themselves: https://momentsingraphics.de/BlueNoise.html

The library only solves up to cubic equations, and the comments have a link to the following page: https://momentsingraphics.de/CubicRoots.html For general polynomials, it matters a great deal in what basis it is represented. The typical monomial basis is usually not the best from a numerical standpoint. I am aware of some modern methods such as this: https://arxiv.org/pdf/1611.02435 For polynomials expressed in e.g. a Bernstein basis, there are often much faster and stable tailored methods working solving for the eigenvalues of a companion matrix of a different form.

It's an array of pre-calculated values that I extracted from an image donated to the Public Domain by Christoph Peters (the link is an interesting read about bluenoise - recommend!) - http://momentsingraphics.de/BlueNoise.html No textures or masks, just brute computing on the CPU.

I quite like Moments in graphics by Christoph Peters - http://momentsingraphics.de/

The major dithering algorithm that's missing from this list is blue-noise dithering. This is very similar to "ordered dithering"; you can think of ordered dithering as either thresholding the pixel values with a different threshold value on each pixel, following a regular pattern, or as adding a different offset value to each pixel, following a regular pattern, and thresholding the result with a constant threshold. Blue-noise dithering replaces the regular pattern with a random pattern that's been high-pass filtered. This has all the advantages of ordered dithering, in particular avoiding "crawling" patterns during animation, but avoids the repetitive patterns and line artifacts it introduces. https://nelari.us/post/quick_and_dirty_dithering/ is the best quick introduction to the technique that I've seen. There's a more comprehensive introduction at https://momentsingraphics.de/BlueNoise.html. https://bartwronski.com/2016/10/30/dithering-part-three-real-world-2d-… also demonstrates it, comparing it to other dithering algorithms. Ulichney introduced blue noise to dithering in 01988 as a refinement of "white-noise dithering", also known as "random dithering", where you just add white noise before thresholding: https://cv.ulichney.com/papers/1988-blue-noise.pdf. Ulichney's paper is also a pretty comprehensive overview of dithering algorithms at the time, and he also makes some interesting observations about high-pass prefiltering ("sharpening", for…

Blue noise dithering also gives some pretty nice results: https://momentsingraphics.de/BlueNoise.html

This is interesting if you are after retro effects. State of the art dithering however works with blue noise threshold textures[1] because we have plenty of memory available these days. Here is a nice comparison of all kinds of dithering algorithms that also shows the clear superiority of blue noise dithering: [2]. 1.: http://momentsingraphics.de/BlueNoise.html 2.: https://surma.dev/things/ditherpunk/

You are doing the polynomial evaluation wrong for Taylor Series. First of all you should be using Horner's Method to reduce the number of multiplications needed and then you should be using FMA to increase precision of the solution. https://momentsingraphics.de/FMA.html