René's URL Explorer Experiment

{"@context":"https://schema.org","@type":"DiscussionForumPosting","headline":"Interesting research into your \"disparity circle\" formula along with a new, smoother one","articleBody":"I was chatting in my Discord with Aphitorite on GitHub, and they actually dug into your \"disparity curve\" formula a bit. Some interesting stuff was discovered, and we wanted to share it with you!\n\nSo first of all, we _were_ talking about my modified version of your formula from my fork that's able to handle arbitrary array lengths, which is the following:\n```\ndouble len = ((ArrayVisualizer.getCurrentLength() / 2d) - Math.min(Math.min(Math.abs(i - array[i]), Math.abs(i - array[i] + ArrayVisualizer.getCurrentLength())), Math.abs(i - array[i] - ArrayVisualizer.getCurrentLength()))) / (ArrayVisualizer.getCurrentLength() / 2d);\n```\n\nYeah, I know... I didn't refactor it after changing it around, and the line of code it takes up is an absolute mess. _But_ it turns out that you had written up a partial triangle wave function (without using trig functions)!\n\nhttps://cdn.discordapp.com/attachments/592103638034415647/733325936417570926/SharedScreenshot.jpg\n\n_That's_ why the peaks of the disparity circle visual are always jagged! You can especially see that here:\n\nYour original formula:\nhttps://cdn.discordapp.com/attachments/592103638034415647/733197874434932807/Screenshot_516.png\n\nversus Aphitorite's new cosine wave formula:\nhttps://cdn.discordapp.com/attachments/592103638034415647/733197892264656946/Screenshot_515.png\n\nTheir new cosine wave formula is as follows:\n```\ndouble len = (1 + Math.cos((Math.PI * (array[i] - i)) / (ArrayVisualizer.getCurrentLength() * 0.5))) * 0.5;\n```\n\nI personally found this super fascinating; hope this was interesting for you too!   ","author":{"url":"https://github.com/MusicTheorist","@type":"Person","name":"MusicTheorist"},"datePublished":"2020-07-16T16:15:29.000Z","interactionStatistic":{"@type":"InteractionCounter","interactionType":"https://schema.org/CommentAction","userInteractionCount":1},"url":"https://github.com/22/ArrayVisualizer/issues/22"}