Freya Holmér

I'm on my way to finally meet Siri today!! ❤️

she doesn't know it but she's responsible for my entire year of cat search/volunteering/cat photography, I'm excited!

In Defense Of Shoving All Your Toys Under The Couch

nah, polynomial splines are pretty much never arc length parameterized

wish I could remember the paper, they had useful names too! like, minimizing elastic energy vs minimizing bending energy vs whatever the third thing was

I saw a paper a while back that had a nice breakdown of three common energy minimization methods. iirc one approach was to minimize the integral of the square of curvature, although that gets kinda hairy to solve analytically. another one was to just use the square of the acceleration instead

it does! and I might just not know the right way to set up solvers in sympy to not take an hour

there's various definitions for energy minimization, but the one closest to fairness I think would be, iirc, minimizing the integral of the square of the curvature, since fairness usually is only about the shape, and less so about changing speed

a uniform quintic C2 continuous interpolating spline in matrix form

another issue with higher degrees is that they start to become unwieldy to solve by hand, which is why I've been looking into sympy/symbolic math library stuff!

a lot of these equations have like, factorial growth in size, so they're kinda nontrivial to compute

the uniform variant is clean tho!

"fairness" can be loosely thought of as looking smooth and effortless, or, minimizing energy

this is notably not the same thing as continuity! in fact, it's actually pretty easy to make a C-infinity spline, but its shape usually either explodes, or it's so stiff that it becomes nearly useless

I've been interested to experiment with this bc while cubic splines are super well explored, higher degree ones are a little less so!

now the issue with higher degrees is that it's hard to maintain "fairness"

an interpolating C² continuous quintic spline

good

not this one (there's multiple)

fuck it

matrix form

I just want my polynomial in ascending order and with the coefficient on the right but this is apparently a nightmare

and i can hear you all say "oh just use latex(expr, order='rev-lex')" but you see-

im losing my mind i stg it's impossible to format equations to look nice in sympy/ipynb

the REAL issue is that

a-b looks like subtraction but
a(-b) looks like a multiplication until I rename it
f(-b) where it now looks like a function call but
q*b is clearly not just q times b as q* is actually the quaternion conjugate because math notation

considering dying on the hill of "subtraction is evil and we should only ever add negative terms" but then I also want to die on the hill of "(-a+b) looks kinda dumb and I think we should always do (b-a) instead" so this might be a losing battle tbh

sympy formatting (-a/b)u^3 as u^3-a/b when I wanted to move u^3 to the left hand side using unevaluated expressions

asdadfsafg sympy pls i just wanted to move the u^3 to the left side this is an EVIL interpretation of unevaluated expressions 😭

closeup of some snow

i found some snow in case you need it

a real cool spline! hopefully

it's splines again for some reason

Salad flopped on the ground, flailing towards Gumpy, who is skipping about

OUH GUMPI VERY FASST !!!!!!

a 116,699 characters long math equation

I was wondering why python was taking an hour to process this equation but I suppose 116,699 characters is on the long end

a closeup of Salad's adorable little face

like the snake flag and all that :)

any second now :)

I've heard there's this amendment all about giving individuals and their state the freedom to bear arms in case there's a rogue federal government infringing on their rights. surely its supporters are now are up in arms and standing up for states rights in this moment, right?

checking in on US news - looks like today the masked government agents murdered another citizen, with the white house not only defending these actions, but using continued pressure as threat and leverage to get Minnesota to turn over voting records

am I getting this right?