117 lines
No EOL
4.1 KiB
Markdown
117 lines
No EOL
4.1 KiB
Markdown
## stuff i've plotted in desmos
|
|
|
|
in some order idk
|
|
|
|
### [circumcircle](https://www.desmos.com/calculator/zaf29i2xrk)
|
|
|
|
drag around the three points to see how their circumcircle is affected.
|
|
sorry, i never finished simplifying the math here.
|
|
|
|
### [parabola arc length](https://www.desmos.com/calculator/hrokhmphrf)
|
|
|
|
not closed form, sorry. drag the points around like it's a jumprope.
|
|
|
|
### ["diode"](https://www.desmos.com/calculator/vappug98ky)
|
|
|
|
i didn't name this function; i have no idea if or how it relates to a diode.
|
|
the red line (the line of interest) is actually just the 12th order smoothstep.
|
|
|
|
btw, you can find smoothstep coefficients for any order
|
|
by the triangular table of this integer sequence:
|
|
[OEIS A091811](http://oeis.org/A091811)
|
|
|
|
[punching it into wolfram][smoothie] (try changing n)
|
|
|
|
[smoothie]: https://www.wolframalpha.com/input/?i=ReplaceAll%5BBinomial%5Bn+%2B+k+-+2,+k+-+1%5D+Binomial%5B2+n+-+1,+n+-+k%5D,+%7Bk+-%3E+Range%5B1,n%5D%7D%5D+where+n+%3D+12
|
|
|
|
### [smoothstep alternatives](https://www.desmos.com/calculator/ibigyiumzb)
|
|
|
|
refer to shadertoy:
|
|
|
|
* [Inverse Smoothstep](https://www.shadertoy.com/view/MsSBRh)
|
|
* [gain()](https://www.shadertoy.com/view/ldBfR1)
|
|
* [Alt smoothstep](https://www.shadertoy.com/view/lsBfz1)
|
|
|
|
### [tanh approximation](https://www.desmos.com/calculator/k3jzkhmoid)
|
|
|
|
approximating tanh by taking its continued fraction form and (externally) optimizing the constants.
|
|
probably not useful.
|
|
|
|
### [TanhTest lolremez approx](https://www.desmos.com/calculator/carcltkgem)
|
|
|
|
a polynomial approximation of a scaled tanh function
|
|
made with [the excellent lolremez](https://github.com/samhocevar/lolremez).
|
|
|
|
### [e^(-2/x) approximations](https://www.desmos.com/calculator/q8jtxgnmlh)
|
|
|
|
i forget where i read about this but basically you can
|
|
approximate `e^(-2/x)` by `(x-1)/(x+1)` when x is large.
|
|
|
|
the black line shows the absolute error.
|
|
|
|
### [compressor gain](https://www.desmos.com/calculator/rizrdxsrbg)
|
|
|
|
trying to design a cheap-to-compute gain curve for a dynamic range compressor.
|
|
this thing uses just one division.
|
|
iirc it didn't wind up being all that useful.
|
|
|
|
both axes are in power decibels. note that it acts as a gate under -70 dB.
|
|
|
|
### [compressor approx stuff](https://www.desmos.com/calculator/5wbup88lev)
|
|
|
|
trying to compute abs(x) by polynomials, or something. weird stuff.
|
|
|
|
### [doom turnspeeds](https://www.desmos.com/calculator/zfscpmsdbk)
|
|
|
|
i used this to help design turnspeed smoothing in [my zdoom patch.](https://eaguru.guru/t/zdoom_smoothstep.diff)
|
|
|
|
*note to self: i think i have a more recent version of that patch lying around somewhere.*
|
|
|
|
### [Biweight Funtimes](https://www.desmos.com/calculator/mlnqmf6ogp)
|
|
|
|
messing around with a variations of Tukey's Biweight?
|
|
i think the only reason i kept this around was 'cause it's fun to watch animated.
|
|
|
|
### [sincmod](https://www.desmos.com/calculator/lqgl4o0naz)
|
|
|
|
something something windowing functions i dunno.
|
|
|
|
### [SGDR](https://www.desmos.com/calculator/hlgqmyswy2)
|
|
|
|
simple case of a [SGDR](https://arxiv.org/abs/1608.03983) curve.
|
|
i just kept this around 'cause the logarithmic plot complements
|
|
the linear plot in a kinda cool way.
|
|
|
|
### [sqr/abs generalization](https://www.desmos.com/calculator/fagjg9vuz7)
|
|
|
|
self-explanitory.
|
|
|
|
### [SELU](https://www.desmos.com/calculator/bqu264oprw)
|
|
|
|
[it's SELU!](https://arxiv.org/abs/1706.02515)
|
|
|
|
### [GELU](https://www.desmos.com/calculator/ydzgtccsld)
|
|
|
|
[GELU activation](https://arxiv.org/abs/1606.08415)
|
|
alongside an approximation i lifted off reddit or someplace.
|
|
|
|
### [erf cdf approximations](https://www.desmos.com/calculator/22r29cude2)
|
|
|
|
approximate gaussian stuff, with inversions and integrals.
|
|
|
|
### [squish](https://www.desmos.com/calculator/1qdx4ovpb6)
|
|
|
|
possibly useful functions for squishing values.
|
|
mostly based on sigmoidal functions.
|
|
|
|
### [sin LUT approx 2](https://www.desmos.com/calculator/zdbgkxadns)
|
|
|
|
approximating a quadrant of sin(x) with a polynomial and a LUT.
|
|
|
|
### [circle calculus](https://www.desmos.com/calculator/yd5hyagaoj)
|
|
|
|
some fun curves relating to unit circles.
|
|
|
|
### [archimedes spiral](https://www.desmos.com/calculator/63vi3wnqug)
|
|
|
|
it's just Archimedes' Spiral, plus some related functions. |