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.

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Timestamps:
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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

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Additional Notes:
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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...

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Bibliography (in order of appearance):
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[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Pannenkoek2012 - Watch for Rolling Rocks - 0.5x A Presses [OUTDATED]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] N64 Super Mario 64 "all 120 stars" i...  

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  

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People:
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Iwer Sonsch
   / @iwersonsch5131  

bad_boot
   / @bad_boot  

Crackhex
   / @crackhex  

Krithalith
   / @krithalith  

Pannenkoek2012
   / @pannenkoek2012  
   / @uncommentatedpannen  

Tyler Kehne
   / @tylerkehne