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Currently Playing: Smooth-Maximum, the most useful function

The smooth-maximum function is one of the most useful tools that you should definitely have in your mathematical toolbox. It can help you repair other functions and control artistically the look of shapes, among other things. Support this channel: https://www.patreon.com/inigoquilez Subscribe: https://www.youtube.com/c/inigoquilez X: https://x.com/iquilezles Bsky: https://bsky.app/profile/iquilezles.bsky.social Tiktok: https://www.tiktok.com/@inigoquilez 0:00 - Introduction 0:51 - Rewriting the maximum as a middlepoint plus a distance 2:41 - Deriving the Smooth-Maximum formula 4:50 - Using it to patch other functions 6:01 - A zoo of Smooth-Maximum functions 7:36 - Softening other branchy functions 8:25 - Using it in an artwork