Improve plotter output, introduce randomness

[stevenpetryk]

This improves the sample function central to Mafs' plotter.

Bug fix: duplicate points, incorrect subdivision

First, it corrects a bug that was causing duplicate points to be evaluated. For example, when sampling the domain [-16, 16] with sampling depth 4, these points were being generated:

[-16,-15,-13,-12,-12,-11,-9,-8,-8,-7,-5,-4,-4,-3,-1,0,0,1,3,4,4,5,7,8,8,9,11,12,12,13,15,16]

Of course, duplicates make no sense here, and we would actually expect a uniform distribution between -16 and 16. Also, we would expect depth 5 to produce 32 segments (33 points), not depth 4. So that was fixed by, thankfully, removing code.

Randomness

Additionally, for quite some time, I have been wanting to introduce some stable randomness to the sampling function, in a way that prevents the function from changing with every render. I finally decided to research that and introduce a pseudo-random hash function when evaluating the midpoint of the domain. This also required the midpoint function in sample to become a lerp, since we can no longer simply measure against the midpoint to compute errors.

[vercel]

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Name	Status	Preview	Comments	Updated (UTC)
mafs	✅ Ready (Inspect)	Visit Preview	💬 Add feedback	Jan 21, 2024 7:45pm