Thread by @FreyaHolmer

my favorite way to see if a point is inside or outside a path, is using its winding number🍥

traverse the path from the perspective of a point and add up the amount of turning along the way

if it made a full turn, it's inside
if it wound back to 0, it's outside

it's so neat~💖

this is one of my favorite techniques, because it works not only for convex paths, but for concave ones too, which, is kinda rare and beautiful

plus it's real fast if you measure quadrant traversal rather than real angles~

more info here geomalgorithms.com/a03-_inclusion…

if you want more math and game dev shenanigans, do consider supporting me on patreon, if you are able to and want to 💖
patreon.com/acegikmo

many of you have been asking what happens if you're on the path rather than inside or outside

in this case it's kinda like asking if you should turn left or right to face something directly behind you!

there's no right answer, and it's entirely implementation-dependent

many of you have also asked-

what if a point is outside the path yet completely surrounded by it?

even in this case, the algorithm still works~