Joystick Angles
Glitchy Wall Kicks [failure to analyze]
There are 2 types of GWKs, quarter frame GWKs and bonk GWKs. We didn't know this at first. Bonk GWKs are more complicated. The GWK I studied happened to be a bonk GWK. Shenanigans ensued, followed by more confusion. Progress stalled until SM64 Decomp was worked on.
my first 4koma. (Studying angle changes of a bonk GWK every quarter of a frame, along with SilentSlayer. These angle changes reflect off of 1 or both of the 2 walls.)
https://cdn.discordapp.com/attachments/267091914027696129/379482773507014656/unknown.png
Walking
SM64 1 Key study after-the-fact
2336 ( 3,-3) +3,-3
2337 (14,-1) +11,+2
2354 ( 6, 3) -8,+4
2354 A (kill speed)
2356 A (kill speed)
2365 ( 0, 0) -6,-3
this is an OJ. no other explanation needed.
https://cdn.discordapp.com/attachments/309838966125756416/372970560696614916/unknown.png
Bismuth made an excellent commentated video explaining the entire 1 Key TAS.
TTC Pendulum
The Pendulum Ladder Map chains all possible amplitudes a random-setting pendulum can swing at, which forms rails, branches, and indices within the branches for each swing. I made an unscripted commentated video about it, which leads into discussing Pell Equations and Brahmagupta's identity.
https://cdn.discordapp.com/attachments/309838966125756416/349389479967981579/unknown.png
https://cdn.discordapp.com/attachments/309838966125756416/349389742409908225/unknown.png
Cog Misa
It's just a desmos graph. A specific of cog rotation and 4 frames of air straining form the least wall obstructions that allow Mario to reach a previously impossible goal. My one A press save. Still proud of it.
TTM DR (Tall Tall Mountain Dive Recover)
Proved TTM is impossible without a breakthrough. Tyler Kehne then finds breakthrough.
Bowser in the Fire Sea 0x (Wii VC)
The oscillating platform converges and reaches 0 after 2-3 months. Must find bad_boot's graph again to confirm.
The platform rises at a constant rate per oscillation cycle, except when it reaches a y=2^n boundary, when its vertical velocity changes based on the arcsin function.
Jolly Roger Bay's Hyperspeed Punch
Approximated the speed cap to be 160. If mario can keep punching on the pillar for an extended 1 more frame, spd can reach 170 or more. i forgot my approximated 2nd value.
Crouch Sliding:
(1) the 10k glitch step
The fwd component of your joystick tilt is multiplied by (speed+100)/200. (It's intended that the result is your fwd component is halved or stays the same cuz your max slide speed should be 100 unit/f. But ofc, you hyperspeed, and you can do the 10k glitch.) We'll name this the "modified fwd".
(2) turn mario
based on the sideward component of stick tilt (which i define as "side"), rotate mario's velocity vector like this.
[ 1 0.05*side ] [velX]
[ -0.05*side 1 ] [velZ]
And then you do v\*oldSpd/newSpd for both x and z component, cuz the game wants to not change your speed. You can think about the implications of this yourself. (the max and min angle it can change depending on your speed, and other questions)
(3) update_sliding_angle
Your velocity vector is added by a vector of magnitude 7\*normal.H, pointing downhill.
Then the resulting vector is multiplied by the lossFactor, which is smth dumb defined by the slope type, and increases depending on the modified fwd. So this step does depend on your speed.
Finally, mario's facing angle changes by 2.8125 (360/128) degrees or less towards your velocity vector's angle.
C^ Sliding:
Speed - 4 + 1.7\*normal.H (range: -4 ≤ accel < -2.3)
HyperSpeed Punching:
Speed - 1 + 1.7\*normal.H (range: -1 ≤ accel < 0.7)
Effects Overlap for 1f between the C^ and the Punch:
Speed - 5 + 3.4\*normal.H (range: -5 ≤ accel < -1.6)
WF Tower platform rotation displacement
The tumbling bridge block rotates in a stupid way, but i managed to decompose its euler angle frequencies into parts. Turned out fucking useless cuz we could just fucking yeet ourselves onto the cannon with SDC, idk, ask iwer.
and i'll try to summarize my block of text here soon.
Arctan Strain
All but proven at every math-skill level. Implement in Mupen LUA by sm64Expert.
The Flight Equations
Update Pitch:
target = -stickY*v/5 (max=±12.8v)
pitchAccelTo0=64 pitchAccelTo∞=32
If crossed 0, cap |pitchVel1|<32 for 1f.
Update Yaw:
target = -stickX*v/4 (max=±32v)
If target<0< <yawVel , |yawAccel|=64 if <0<target<yawVel , |yawAccel|=32 If <0< <yawVel<target, |yawAccel|=16
If crossed 0, cap |yawVel|<16 for 1f.
a = -pitch/45° -.5[1-cos(yaw)] -1 cap v>=0
Update Flying:
if v>16, pitchVel2 = 6(v-32), Range: ( -96 ~ +∞ ] //positive if v>32 if 4<v≤16, pitchVel2 = 10(v-32), Range: (-280 ~ -160] if v≤ 4, pitchVel2 = -1024
cap |pitch|≤59.99634°
if nullWall collision, pitchVel3 = -512
La-Mulana Speedrun studies
https://clips.twitch.tv/FlirtyBrightKoalaVoteNay 1 pixel away from killing the boss in 1 cycle. I eventually solve this problem.
http://prntscr.com/edhko5 Boss battle analysis.
Misc.
Deep Underground [NSFW Memes (Bottom of the Iceburg)]
https://cdn.discordapp.com/attachments/270777797138579457/344927706208796674/20170417_233514.jpg
https://pbs.twimg.com/media/CmU8RS8VMAAcWpW.jpg:large
Me back when I was at a Halloween party. Despite everything, it went ok.