Скачать или смотреть Super Mario 64's Drag Problem is Finally Solved

In my previous video "Perfect Jumps in Super Mario 64" (   • Perfect Jumps in SM64  - Arctan Straining ...  ) we saw how the game's Tool Assisted Speedrun and A Button Challenge Community used the game's source code to figure out the mathematically optimal way of moving Mario in the air. But this was only perfect when we ignore the "drag thresholds" that slow Mario down when his velocity becomes too large. In this video, I solve this problem for the first time, and we can now work out the optimal controller inputs to gain the most distance in the shortest amount of time, with no restrictions on the velocity or drag. This work is possible thanks to some initial work done by Xander (   / @epicrandomgamingchannel  ) and Cryolite, in producing a Mixed Integer Non-Linear Programming model for TAS Optimization - which is a powerful result in its own right.

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Please donate to support future work and be thanked in my next video
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https://buymeacoffee.com/omedas

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Timestamps:
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00:00 Part 0: Introduction
01:47 Part 1: Arctan Straining Recap
03:10 Part 2: The XX.99 Trick
06:24 Part 3: Modifying The Arctan Formula
09:32 Part 4: The Drag Problem
11:44 Part 5: The MINLP
15:05 Part 6: The Lagrangian
18:40 Part 7: KKT Conditions
23:27 Part 8: Puzzle Pieces
27:08 Part 9: Solution Types
32:25 Part 10: Choosing A Solution
35:36 Part 11: The Iwerlipse
41:37 Part 12: Zero Snapping

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Bibliography:
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Perfect Jumps in SM64 - Arctan Straining Explained
   • Perfect Jumps in SM64  - Arctan Straining ...  

Epic Random Gaming Channel (ERGC) Xander
   / @epicrandomgamingchannel  

Xander’s MINLP Notes
https://github.com/MikeXander/SM64Scr...

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...

Ukikipedia
https://ukikipedia.net/wiki/Straining
https://ukikipedia.net/wiki/Iwerlipse

SM64 Input Direction Lua
https://github.com/mupen64/SM64LuaRedux

Render96 HD Texture Pack
https://github.com/pokeheadroom/RENDE...