Perfect Jumps in SM64 - Arctan Straining Explained

A deep dive into Arctan Straining in Super Mario 64, a method for performing perfect jumps from A to B in the shortest possible time allowed by the game's code. Discovered by the Tool Assisted Speedrun and A Button Challenge community a few years ago, it allows one to construct *The Iwerlipse*, the complete set of positions Mario can occupy while moving in the air. This is the first video to explain it in detail - we look at the proof, visualize it with animations, go through practical examples, and along the way, look at the history behind the discoveries. ------ Please donate for more videos and a personal shout-out in my next video: ------ https://buymeacoffee.com/omedas ------ Timestamps: ------ 00:00 Part 0: Introduction 04:05 Part 1: Basic Mechanism 07:35 Part 2: The Question 10:43 Part 3: update_air_without_turn 15:43 Part 4: Single Frame Proof 19:38 Part 5: General Proof 26:13 Part 6: The Iwerlipse 32:43 Part 7: Calculus of Variations 34:04 Part 8: Quartersteps 35:52 Part 9: Practical Demo 40:25 Part 10: XX.99 Trick 43:23 Part 11: Conclusion ------ Additional Notes: ------ Showing Iwer's proof and deriving the Iwerlipse equations (including superellipse exponent lookup table) https://drive.google.com/file/d/1xDmg... Showing Silverstrawb's proof https://drive.google.com/file/d/1df97... ------ Bibliography (in order of appearance): ------ [TAS] N64 Super Mario 64 "1 Key"    • [TAS] N64 Super Mario 64 "1 Key" in 04:18....   Super Mario 64 Decomp https://github.com/n64decomp/sm64 SuperMario64 Technical Runtime Observer and Object Processor (STROOP) https://github.com/SM64-TAS-ABC/STROOP https://github.com/FramePerfection/ST... UncommentatedPannen - HMC Watch for Rolling Rocks 0xA    • HMC Watch for Rolling Rocks 0xA   UncommentatedPannen - LLL Elevator Tour in the Volcano 0xA    • LLL Elevator Tour in the Volcano 0xA   Pannenkoek2012 - Every Goomba Glitch in Super Mario 64    • Every Goomba Glitch in Super Mario 64   Ukikipedia https://ukikipedia.net/wiki/Iwerlipse Crackhex - Arctan straining tutorial for TASers   / 2463407535   GRsmash - Saltiest Controller Spikes in Super Smash Bros    • Saltiest Controller Spikes in Super Smash ...   Pannenkoek2012 - Watch for Rolling Rocks - 0.5x A Presses [OUTDATED]    • SM64 - Watch for Rolling Rocks - 0.5x A Pr...   Tyler Kehne - JRB Blast to the Stone Pillar 0xA (Confirmed)    • JRB Blast to the Stone Pillar 0xA (Confirmed)   UncommentatedPannen - JRB Speed Conservation to Chest Star    • JRB Speed Conservation to Chest Star   UncommentatedPannen - TTC Pedro Spot on Pendulum Box    • TTC Pedro Spot on Pendulum Box   [TAS] N64 Super Mario 64 "all 120 stars"    • [TAS] [Obsoleted] N64 Super Mario 64 "all ...   UncommentatedPannen - TTM DR into Scale the Mountain Star Idea    • TTM DR into Scale the Mountain Star Idea   Tyler Kehne - 0xA Scale the Mountain DR Strat (New Fastest Strat)    • 0xA Scale the Mountain DR Strat (New Faste...   Krithalith - Carpetless Setup [SM64]    • Carpetless Setup [SM64]   SM64 Input Direction Lua https://github.com/mupen64/SM64LuaRedux Omedas - Solving BLJs in Super Mario 64    • Solving BLJs in Super Mario 64   ------ People: ------ Iwer Sonsch    / @iwersonsch5131   bad_boot    / @bad_boot   Crackhex    / @crackhex   Krithalith    / @krithalith   Pannenkoek2012    / @pannenkoek2012      / @uncommentatedpannen   Tyler Kehne    / @tylerkehne