\n

Fast iterative circles (and ellipses, and other figures).<\/h3>\n\n\n\n

Here’s the entire algorithm to compute points on an elliptical arc, very quickly:<\/p>\n\n\n\n

    while(true)\n    {\n        x += d * y;\n        y -= d * x;\n    }\n<\/pre>\n\n\n\n
Attributed to Marvin Minsky, 1972: HAKMEM, MIT AI Memo 239<\/a> (HTML version here<\/a>). Also on a PDP-1, David Mapes<\/a> talks about finding it independently. I’ve been using this to make circles since I found it by accident in the early 1980s (using a BBC Micro). Nowadays I’m using it to make music synthesizers (running on ARM Cortex M4).<\/p>\nSource: https:\/\/cabezal.com\/misc\/minsky-circles.html<\/a><\/cite><\/blockquote>\n","protected":false},"excerpt":{"rendered":"
Fast iterative circles (and ellipses, and other figures). Here’s the entire algorithm to compute points on an elliptical arc, very quickly: while(true) { x += d * y; y -= d * x; } Attributed to Marvin Minsky, 1972: HAKMEM, MIT AI Memo 239 (HTML version here). Also on a PDP-1, David Mapes talks about…<\/p>\n
Read more →<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false,"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"activitypub_content_warning":"","activitypub_content_visibility":"","activitypub_max_image_attachments":4,"activitypub_interaction_policy_quote":"anyone","activitypub_status":"federated","footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[1],"tags":[],"class_list":["post-13473","post","type-post","status-publish","format-standard","hentry","category-senza-categoria"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p6daft-3vj","jetpack-related-posts":[{"id":14169,"url":"https:\/\/monodes.com\/predaelli\/2025\/10\/24\/how-to-emulate-hand-drawn-shapes-algorithms-behind-roughjs-shihn-ca\/","url_meta":{"origin":13473,"position":0},"title":"How to emulate hand-drawn shapes \/ Algorithms behind RoughJS | shihn.ca","author":"Paolo Redaelli","date":"2025-10-24","format":false,"excerpt":"How to emulate hand-drawn shapes \/ Algorithms behind RoughJS | shihn.ca A dive into graphics algorithms used in RoughJS - A graphics library that lets you draw in a sketchy, hand-drawn-like, style. 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