in my opinion, advent of code is definitely the most exciting part of december (i’d rather not think about what that says about me). every year i pick a theme to complete the puzzles (previous years have included uiua, k, polyglot, etc.) and last year’s theme was concise python. sounds pretty boring, i know, but i did learn some neat tricks along the way. i used to dread the “annoying grid days”, of which my main complaints were:

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i’m sure many of you are familiar with the famous donut.c, but for those of you who aren’t, i highly recommend checking it out. following andy’s writeup, i wrote my own implementation in c a few years back. my implementation spanned ~70 lines of code—i think we can do better this time around.

torus math

a torus is defined by its major ($R$) and minor ($r$) radii. $R$ is the distance between the center of the torus and the center of the tube, and $r$ is the radius of the tube. while donut.c iterates in $\theta$ and $\phi$ steps to plot points lying on the surface of the torus, i’m going to leverage uiua’s voxels renderer by going in the opposite direction. for a given voxel in a 3d linspace, we can decide whether or not that voxel should be rendered by determining if its coordinates lie inside of the torus. to do this, we check if the point is within $r$ of the nearest point along the circle defined by $R$ (shown in black above).

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