It's time for another programming challenge!

Given a list of coordinate pairs on a 2D plane that describe the vertices of a polygon, determine whether the polygon is concave or convex.

Since a polygon could potentially be any shape if we don't specify which vertices connect to which, we'll assume that the coordinates are given in strict order such that adjacent coordinates in the list are connected. Specifically, if we call the list V[1, n] and say that V[i] <-> V[j] means "vertex i and vertex j are connected", then for each arbitrary V[i] we have V[i-1] <-> V[i] <-> V[i+1]. Moreover, since V[1] and V[n] are at the ends of the list, V[1] <-> V[n] holds (i.e. the list "wraps around").

Finally, for simplicity we can assume that all coordinates are unique, that all polygon descriptions generate valid polygons with 3 or more non-overlapping sides, and that, yes, we're working with coordinates that exist in the set of real numbers only. Don't over-complicate it :)

For those who want an even greater challenge, extend this out to work with 3D space!

I grew up playing DOOM, but if I were to boot up the original game I would find it frustrating to play by modern standards (e.g. mouse movement?!). Thankfully, there are a ton of source ports that modernize the engine and make the game more accessible to current gaming sensibilities (e.g. WASD-movement). They're basically community remasters of the game.

It got me wondering about what other games have strongly benefited from tools that exist outside of the game itself.

Examples of what I mean:

1. Source ports (e.g. DOOM)
2. Community bugfixes (e.g. Vampire: The Masquerade - Bloodlines)
3. Restored/extended content (e.g. Star Wars: Knights of the Old Republic II)
4. Significant mods (e.g. Frostfall for Skyrim)
5. Rulesets/challenges (e.g. Nuzlocke Challenge for Pokémon)
6. Anything else that doesn't fit the above categories

This can be anything, I'll accept "relaxing in front of the TV with a drink" as an answer.

Personally I've grown fond of Wednesdays, because that's when I sometimes get me a sandwich from my favorite place, and Sundays because that's when I often go to play board-games with some old friends.

Do you have something you look forward to in your week? Or maybe some advice for people who are looking for something to look forward to?

I have recently been getting into the Brave browser and they have a system called BAT. I'm still not totally clear on all the intricacies, but the basic idea is that they have a universal token that can be given to content creators, instead of using advertising. Here's a link because I probably messed up that description somehow. So what are your thoughts on it?

I was inspired to ask this because I see a lot of other groups like ~TV people have been doing periodic discussions, and I got to thinking it could work here too. Every now and then, we could hold a discussion on either a video game or board game, for example. If I were to start this up would anyone be interested?

Edit: Oh, and any suggestions for if I do start it up? What games I could start with etc?

New title to hopefully avoid people getting lost and posting the wrong media here, if you have a suggestion to make it less ugly then please say something.

Anyway, what have you been watching/reading this week?

Feel free to talk about something you saw that was cool, something that was bad, ask for recommendations, or anything else you can think of.

If you want to, feel free to find the thing you're talking about and link to its Anilist, MAL, or any other anime/manga database you use!

Today I stumbled upon a pdf of Peter Arnell's redesign of the Pepsi logo, touted by a person on twitter as "the height of human bullshit". And it reminded me of the time I worked at a small start-up company, where these kinds of overblown but substantially empty ideas were common currency.

So I'm wondering: do any of you have any funny or interesting stories of encounters with these kinds of things.

~news will be populated with mainly U.S news and also mainly U.S politics, ~worldnews could be a group for just world news and events.

also there is a sub r/globaltalk which is basically focused around soft-core news events from around the world. An example of this is this post: "Man tries to open plane’s door, thinks it’s way to the loo - Times of India." it is just like interesting news stories that aren't too serious from around the world. Not sure if that would fit here, just a sugesstion