Tag Archives: fonts

Raspbian update: supporting different screen sizes

Post Syndicated from Simon Long original https://www.raspberrypi.org/blog/raspbian-update-screen-sizes/

You may have noticed that we released a updated Raspbian software image yesterday. While the main reason for the new image was to provide support for the new Raspberry Pi 3 Model B+, the image also includes, alongside the usual set of bug fixes and minor tweaks, one significant chunk of new functionality that is worth pointing out.

Updating Raspbian on your Raspberry Pi

How to update to the latest version of Raspbian on your Raspberry Pi.

Compatibility

As a software developer, one of the most awkward things to deal with is what is known as platform fragmentation: having to write code that works on all the different devices and configurations people use. In my spare time, I write applications for iOS, and this has become increasingly painful over the last few years. When I wrote my first iPhone application, it only had to work on the original iPhone, but nowadays any iOS application has to work across several models of iPhone and iPad (which all have different processors and screens), and also across the various releases of iOS. And that’s before you start to consider making your code run on Android as well…

Screenshot of clean Raspbian desktop

The good thing about developing for Raspberry Pi is that there is only a relatively small number of different models of Pi hardware. We try our best to make sure that, wherever possible, the Raspberry Pi Desktop software works on every model of Pi ever sold, and we’ve managed to do this for most of the software in the image. The only exceptions are some of the more recent applications like Chromium, which won’t run on the older ARM6 processors in the Pi 1 and the Pi Zero, and some applications that run very slowly due to needing more memory than the older platforms have.

Raspbian with different screen resolutions

But there is one area where we have no control over the hardware, and that is screen resolution. The HDMI port on the Pi supports a wide range of resolutions, and when you include the composite port and display connector as well, people can be using the desktop  on a huge number of different screen sizes.

Supporting a range of screen sizes is harder than you might think. One problem is that the Linux desktop environment is made up of a large selection of bits of software from various different developers, and not all of these support resizing. And the bits of software that do support resizing don’t all do it in the same way, so making everything resize at once can be awkward.

This is why one of the first things I did when I first started working on the desktop was to create the Appearance Settings application in order to bring a lot of the settings for things like font and icon sizes into one place. This avoids users having to tweak several configuration files whenever they wanted to change something.

Screenshot of appearance settings application in Raspbian

The Appearance Settings application was a good place to start regarding support of different screen sizes. One of the features I originally included was a button to set everything to a default value. This was really a default setting for screens of an average size, and the resulting defaults would not have worked that well on much smaller or much larger screens. Now, there is no longer a single defaults button, but a new Defaults tab with multiple options:

Screenshot of appearance settings application in Raspbian

These three options adjust font size, icon size, and various other settings to values which ought to work well on screens with a high or low resolution. (The For medium screens option has the same effect as the previous defaults button.) The results will not be perfect in all circumstances and for all applications — as mentioned above, there are many different components used to create the desktop, and some of them don’t provide any way of resizing what they draw. But using these options should set the most important parts of the desktop and installed applications, such as icons, fonts, and toolbars, to a suitable size.

Pixel doubling

We’ve added one other option for supporting high resolution screens. At the bottom of the System tab in the Raspberry Pi Configuration application, there is now an option for pixel doubling:

Screenshot of configuration application in Raspbian

We included this option to facilitate the use of the x86 version of Raspbian with ultra-high-resolution screens that have very small pixels, such as Apple’s Retina displays. When running our desktop on one of these, the tininess of the pixels made everything too small for comfortable use.

Enabling pixel doubling simply draws every pixel in the desktop as a 2×2 block of pixels on the screen, making everything exactly twice the size and resulting in a usable desktop on, for example, a MacBook Pro’s Retina display. We’ve included the option on the version of the desktop for the Pi as well, because we know that some people use their Pi with large-screen HDMI TVs.

As pixel doubling magnifies everything on the screen by a factor of two, it’s also a useful option for people with visual impairments.

How to update

As mentioned above, neither of these new functionalities is a perfect solution to dealing with different screen sizes, but we hope they will make life slightly easier for you if you’re trying to run the desktop on a small or large screen. The features are included in the new image we have just released to support the Pi 3B+. If you want to add them to your existing image, the standard upgrade from apt will do so. As shown in the video above, you can just open a terminal window and enter the following to update Raspbian:

sudo apt-get update
sudo apt-get dist-upgrade

As always, your feedback, either in comments here or on the forums, is very welcome.

The post Raspbian update: supporting different screen sizes appeared first on Raspberry Pi.

Exploring free and open web fonts (opensource.com)

Post Syndicated from ris original https://lwn.net/Articles/748636/rss

Nathan Willis looks
beyond open web fonts
on opensource.com. “For starters, it’s critical to understand that Google Fonts and Open Font Library offer a specialized service—delivering fonts in web pages—and they don’t implement solutions for other use cases. That is not a shortcoming on the services’ side; it simply means that we have to develop other solutions.

There are a number of problems to solve. Probably the most obvious example is the awkwardness of installing fonts on a desktop Linux machine for use in other applications. You can download any of the web fonts offered by either service, but all you will get is a generic ZIP file with some TTF or OTF binaries inside and a plaintext license file. What happens next is up to you to guess.”

AWS Hot Startups for February 2018: Canva, Figma, InVision

Post Syndicated from Tina Barr original https://aws.amazon.com/blogs/aws/aws-hot-startups-for-february-2018-canva-figma-invision/

Note to readers! Starting next month, we will be publishing our monthly Hot Startups blog post on the AWS Startup Blog. Please come check us out.

As visual communication—whether through social media channels like Instagram or white space-heavy product pages—becomes a central part of everyone’s life, accessible design platforms and tools become more and more important in the world of tech. This trend is why we have chosen to spotlight three design-related startups—namely Canva, Figma, and InVision—as our hot startups for the month of February. Please read on to learn more about these design-savvy companies and be sure to check out our full post here.

Canva (Sydney, Australia)

For a long time, creating designs required expensive software, extensive studying, and time spent waiting for feedback from clients or colleagues. With Canva, a graphic design tool that makes creating designs much simpler and accessible, users have the opportunity to design anything and publish anywhere. The platform—which integrates professional design elements, including stock photography, graphic elements, and fonts for users to build designs either entirely from scratch or from thousands of free templates—is available on desktop, iOS, and Android, making it possible to spin up an invitation, poster, or graphic on a smartphone at any time.

To learn more about Canva, read our full interview with CEO Melanie Perkins here.

Figma (San Francisco, CA)

Figma is a cloud-based design platform that empowers designers to communicate and collaborate more effectively. Using recent advancements in WebGL, Figma offers a design tool that doesn’t require users to install any software or special operating systems. It also allows multiple people to work in a file at the same time—a crucial feature.

As the need for new design talent increases, the industry will need plenty of junior designers to keep up with the demand. Figma is prepared to help students by offering their platform for free. Through this, they “hope to give young designers the resources necessary to kick-start their education and eventually, their careers.”

For more about Figma, check out our full interview with CEO Dylan Field here.

InVision (New York, NY)

Founded in 2011 with the goal of helping improve every digital experience in the world, digital product design platform InVision helps users create a streamlined and scalable product design process, build and iterate on prototypes, and collaborate across organizations. The company, which raised a $100 million series E last November, bringing the company’s total funding to $235 million, currently powers the digital product design process at more than 80 percent of the Fortune 100 and brands like Airbnb, HBO, Netflix, and Uber.

Learn more about InVision here.

Be sure to check out our full post on the AWS Startups blog!

-Tina

SUPER game night 3: GAMES MADE QUICK??? 2.0

Post Syndicated from Eevee original https://eev.ee/blog/2018/01/23/super-game-night-3-games-made-quick-2-0/

Game night continues with a smorgasbord of games from my recent game jam, GAMES MADE QUICK??? 2.0!

The idea was to make a game in only a week while watching AGDQ, as an alternative to doing absolutely nothing for a week while watching AGDQ. (I didn’t submit a game myself; I was chugging along on my Anise game, which isn’t finished yet.)

I can’t very well run a game jam and not play any of the games, so here’s some of them in no particular order! Enjoy!

These are impressions, not reviews. I try to avoid major/ending spoilers, but big plot points do tend to leave impressions.

Weather Quest, by timlmul

short · rpg · jan 2017 · (lin)/mac/win · free on itch · jam entry

Weather Quest is its author’s first shipped game, written completely from scratch (the only vendored code is a micro OO base). It’s very short, but as someone who has also written LÖVE games completely from scratch, I can attest that producing something this game-like in a week is a fucking miracle. Bravo!

For reference, a week into my first foray, I think I was probably still writing my own Tiled importer like an idiot.

Only Mac and Windows builds are on itch, but it’s a LÖVE game, so Linux folks can just grab a zip from GitHub and throw that at love.

FINAL SCORE: ⛅☔☀

Pancake Numbers Simulator, by AnorakThePrimordial

short · sim · jan 2017 · lin/mac/win · free on itch · jam entry

Given a stack of N pancakes (of all different sizes and in no particular order), the Nth pancake number is the most flips you could possibly need to sort the pancakes in order with the smallest on top. A “flip” is sticking a spatula under one of the pancakes and flipping the whole sub-stack over. There’s, ah, a video embedded on the game page with some visuals.

Anyway, this game lets you simulate sorting a stack via pancake flipping, which is surprisingly satisfying! I enjoy cleaning up little simulated messes, such as… incorrectly-sorted pancakes, I guess?

This probably doesn’t work too well as a simulator for solving the general problem — you’d have to find an optimal solution for every permutation of N pancakes to be sure you were right. But it’s a nice interactive illustration of the problem, and if you know the pancake number for your stack size of choice (which I wish the game told you — for seven pancakes, it’s 8), then trying to restore a stack in that many moves makes for a nice quick puzzle.

FINAL SCORE: \(\frac{18}{11}\)

Framed Animals, by chridd

short · metroidvania · jan 2017 · web/win · free on itch · jam entry

The concept here was to kill the frames, save the animals, which is a delightfully literal riff on a long-running AGDQ/SGDQ donation incentive — people vote with their dollars to decide whether Super Metroid speedrunners go out of their way to free the critters who show you how to walljump and shinespark. Super Metroid didn’t have a showing at this year’s AGDQ, and so we have this game instead.

It’s rough, but clever, and I got really into it pretty quickly — each animal you save gives you a new ability (in true Metroid style), and you get to test that ability out by playing as the animal, with only that ability and no others, to get yourself back to the most recent save point.

I did, tragically, manage to get myself stuck near what I think was about to be the end of the game, so some of the animals will remain framed forever. What an unsatisfying conclusion.

Gravity feels a little high given the size of the screen, and like most tile-less platformers, there’s not really any way to gauge how high or long your jump is before you leap. But I’m only even nitpicking because I think this is a great idea and I hope the author really does keep working on it.

FINAL SCORE: $136,596.69

Battle 4 Glory, by Storyteller Games

short · fighter · jan 2017 · win · free on itch · jam entry

This is a Smash Bros-style brawler, complete with the four players, the 2D play area in a 3D world, and the random stage obstacles showing up. I do like the Smash style, despite not otherwise being a fan of fighting games, so it’s nice to see another game chase that aesthetic.

Alas, that’s about as far as it got — which is pretty far for a week of work! I don’t know what more to say, though. The environments are neat, but unless I’m missing something, the only actions at your disposal are jumping and very weak melee attacks. I did have a good few minutes of fun fruitlessly mashing myself against the bumbling bots, as you can see.

FINAL SCORE: 300%

Icnaluferu Guild, Year Sixteen, by CHz

short · adventure · jan 2017 · web · free on itch · jam entry

Here we have the first of several games made with bitsy, a micro game making tool that basically only supports walking around, talking to people, and picking up items.

I tell you this because I think half of my appreciation for this game is in the ways it wriggled against those limits to emulate a Zelda-like dungeon crawler. Everything in here is totally fake, and you can’t really understand just how fake unless you’ve tried to make something complicated with bitsy.

It’s pretty good. The dialogue is entertaining (the rest of your party develops distinct personalities solely through oneliners, somehow), the riffs on standard dungeon fare are charming, and the Link’s Awakening-esque perspective walls around the edges of each room are fucking glorious.

FINAL SCORE: 2 bits

The Lonely Tapes, by JTHomeslice

short · rpg · jan 2017 · web · free on itch · jam entry

Another bitsy entry, this one sees you play as a Wal— sorry, a JogDawg, which has lost its cassette tapes and needs to go recover them!

(A cassette tape is like a VHS, but for music.)

(A VHS is—)

I have the sneaking suspicion that I missed out on some musical in-jokes, due to being uncultured swine. I still enjoyed the game — it’s always clear when someone is passionate about the thing they’re writing about, and I could tell I was awash in that aura even if some of it went over my head. You know you’ve done good if someone from way outside your sphere shows up and still has a good time.

FINAL SCORE: Nine… Inch Nails? They’re a band, right? God I don’t know write your own damn joke

Pirate Kitty-Quest, by TheKoolestKid

short · adventure · jan 2017 · win · free on itch · jam entry

I completely forgot I’d even given “my birthday” and “my cat” as mostly-joking jam themes until I stumbled upon this incredible gem. I don’t think — let me just check here and — yeah no this person doesn’t even follow me on Twitter. I have no idea who they are?

BUT THEY MADE A GAME ABOUT ANISE AS A PIRATE, LOOKING FOR TREASURE

PIRATE. ANISE

PIRATE ANISE!!!

This game wins the jam, hands down. 🏆

FINAL SCORE: Yarr, eight pieces o’ eight

CHIPS Mario, by NovaSquirrel

short · platformer · jan 2017 · (lin/mac)/win · free on itch · jam entry

You see this? This is fucking witchcraft.

This game is made with MegaZeux. MegaZeux games look like THIS. Text-mode, bound to a grid, with two colors per cell. That’s all you get.

Until now, apparently?? The game is a tech demo of “unbound” sprites, which can be drawn on top of the character grid without being aligned to it. And apparently have looser color restrictions.

The collision is a little glitchy, which isn’t surprising for a MegaZeux platformer; I had some fun interactions with platforms a couple times. But hey, goddamn, it’s free-moving Mario, in MegaZeux, what the hell.

(I’m looking at the most recently added games on DigitalMZX now, and I notice that not only is this game in the first slot, but NovaSquirrel’s MegaZeux entry for Strawberry Jam last February is still in the seventh slot. RIP, MegaZeux. I’m surprised a major feature like this was even added if the community has largely evaporated?)

FINAL SCORE: n/a, disqualified for being probably summoned from the depths of Hell

d!¢< pic, by 573 Games

short · story · jan 2017 · web · free on itch · jam entry

This is a short story about not sending dick pics. It’s very short, so I can’t say much without spoiling it, but: you are generally prompted to either text something reasonable, or send a dick pic. You should not send a dick pic.

It’s a fascinating artifact, not because of the work itself, but because it’s so terse that I genuinely can’t tell what the author was even going for. And this is the kind of subject where the author was, surely, going for something. Right? But was it genuinely intended to be educational, or was it tongue-in-cheek about how some dudes still don’t get it? Or is it side-eying the player who clicks the obviously wrong option just for kicks, which is the same reason people do it for real? Or is it commentary on how “send a dick pic” is a literal option for every response in a real conversation, too, and it’s not that hard to just not do it — unless you are one of the kinds of people who just feels a compulsion to try everything, anything, just because you can? Or is it just a quick Twine and I am way too deep in this? God, just play the thing, it’s shorter than this paragraph.

I’m also left wondering when it is appropriate to send a dick pic. Presumably there is a correct time? Hopefully the author will enter Strawberry Jam 2 to expound upon this.

FINAL SCORE: 3½” 😉

Marble maze, by Shtille

short · arcade · jan 2017 · win · free on itch · jam entry

Ah, hm. So this is a maze navigated by rolling a marble around. You use WASD to move the marble, and you can also turn the camera with the arrow keys.

The trouble is… the marble’s movement is always relative to the world, not the camera. That means if you turn the camera 30° and then try to move the marble, it’ll move at a 30° angle from your point of view.

That makes navigating a maze, er, difficult.

Camera-relative movement is the kind of thing I take so much for granted that I wouldn’t even think to do otherwise, and I think it’s valuable to look at surprising choices that violate fundamental conventions, so I’m trying to take this as a nudge out of my comfort zone. What could you design in an interesting way that used world-relative movement? Probably not the player, but maybe something else in the world, as long as you had strong landmarks? Hmm.

FINAL SCORE: ᘔ

Refactor: flight, by fluffy

short · arcade · jan 2017 · lin/mac/win · free on itch · jam entry

Refactor is a game album, which is rather a lot what it sounds like, and Flight is one of the tracks. Which makes this a single, I suppose.

It’s one of those games where you move down an oddly-shaped tunnel trying not to hit the walls, but with some cute twists. Coins and gems hop up from the bottom of the screen in time with the music, and collecting them gives you points. Hitting a wall costs you some points and kills your momentum, but I don’t think outright losing is possible, which is great for me!

Also, the monk cycles through several animal faces. I don’t know why, and it’s very good. One of those odd but memorable details that sits squarely on the intersection of abstract, mysterious, and a bit weird, and refuses to budge from that spot.

The music is great too? Really chill all around.

FINAL SCORE: 🎵🎵🎵🎵

The Adventures of Klyde

short · adventure · jan 2017 · web · free on itch · jam entry

Another bitsy game, this one starring a pig (humorously symbolized by a giant pig nose with ears) who must collect fruit and solve some puzzles.

This is charmingly nostalgic for me — it reminds me of some standard fare in engines like MegaZeux, where the obvious things to do when presented with tiles and pickups were to make mazes. I don’t mean that in a bad way; the maze is the fundamental environmental obstacle.

A couple places in here felt like invisible teleport mazes I had to brute-force, but I might have been missing a hint somewhere. I did make it through with only a little trouble, but alas — I stepped in a bad warp somewhere and got sent to the upper left corner of the starting screen, which is surrounded by walls. So Klyde’s new life is being trapped eternally in a nowhere space.

FINAL SCORE: 19/20 apples

And more

That was only a third of the games, and I don’t think even half of the ones I’ve played. I’ll have to do a second post covering the rest of them? Maybe a third?

Or maybe this is a ludicrous format for commenting on several dozen games and I should try to narrow it down to the ones that resonated the most for Strawberry Jam 2? Maybe??

Backblaze B2 Supports CORS for Cross Origin Resource Sharing

Post Syndicated from Roderick Bauer original https://www.backblaze.com/blog/enable-cors-for-cross-origin-resource-sharing/

Host files between domains with B2 CORS Rules

Web pages do their magic by loading assets such as images, videos, fonts, text, and other resources from one or more servers on the internet. Most often, data for a website is stored on the same server where the webpages themselves are stored. Sometimes, though, websites will pull in data from servers located elsewhere on the internet.

Allowing websites to include data from other servers can pose possible security risks. To protect users, web browsers enforce security policies that allow scripts in one web page to access data in a second web page only if both web pages have the same origin (i.e. server). This prevents a malicious or faulty script on one page from obtaining access to data on another page that it shouldn’t.

There are many times, however, when one might want to load assets hosted on other servers across the internet. Resources such as fonts, videos, style sheets, images, and iframes are commonly loaded from other origins. It’s great to restrict access to content that might be unauthorized or dangerous, but the web developer needs to be able to specify when it’s okay to load a resource from a different origin.

That’s where CORS comes in.

What is CORS?

To enable web pages to load content that is stored in a different origin, W3C (World Wide Web Consortium), the international community that develops open standards to ensure the long-term growth of the Web, created the Cross-Origin Resource Sharing (CORS) mechanism that allows web pages to access data with a different origin.

The web page might be located on one origin, e.g.

http://origin-a.com

And some data the web page loads might be located on a different origin, e.g.

http://origin-b.com

CORS requires that the resource server explicitly declare that it’s OK to load the asset from a different origin. The browser accomplishes this by making a “preflight” request to ask the server whether it’s OK to make the cross-origin request. By default, servers will say “no” to preflight requests. Rules must be put into place to enable the server to reply to these preflight requests saying it’s OK to serve the asset to a different origin.

B2 Supports CORS for Cross Origin Resource Sharing

B2 is Backblaze’s general purpose cloud storage that can include any type of data that can be stored in the cloud. With pricing that’s ¼ of Amazon’s S3, web developers use B2 as an origin for web data, including text, numbers, scripts, fonts, images, stylesheets, iframes, and videos.

Backblaze supports the standard CORS mechanism that allows B2 customers to share the content of their buckets with web pages hosted in origins other than B2.

In keeping with CORS practices, B2 servers will say “no” to preflight requests to protect the unauthorized sharing of assets to other origins. Adding CORS rules to your bucket tells B2 which preflight requests to approve. CORS is a security feature that is in addition to normal B2 authorization mechanisms. Requests will still need to present normal B2 authorization tokens to download content from non-public buckets.

B2 Cloud Storage Buckets dialog

B2 Cloud Storage Buckets dialog

CORS Rules for BzFileShare

B2 CORS Rules settings dialog

Learn More about B2 and CORS

You can read all about B2’s support of CORS, and how to add rules to your B2 buckets to serve web assets cross-origin, on Backblaze’s website at CORS: Cross-Origin Resource Sharing.

The post Backblaze B2 Supports CORS for Cross Origin Resource Sharing appeared first on Backblaze Blog | Cloud Storage & Cloud Backup.

Physics cheats

Post Syndicated from Eevee original https://eev.ee/blog/2018/01/06/physics-cheats/

Anonymous asks:

something about how we tweak physics to “work” better in games?

Ho ho! Work. Get it? Like in physics…?

Hitboxes

Hitbox” is perhaps not the most accurate term, since the shape used for colliding with the environment and the shape used for detecting damage might be totally different. They’re usually the same in simple platformers, though, and that’s what most of my games have been.

The hitbox is the biggest physics fudge by far, and it exists because of a single massive approximation that (most) games make: you’re controlling a single entity in the abstract, not a physical body in great detail.

That is: when you walk with your real-world meat shell, you perform a complex dance of putting one foot in front of the other, a motion you spent years perfecting. When you walk in a video game, you press a single “walk” button. Your avatar may play an animation that moves its legs back and forth, but since you’re not actually controlling the legs independently (and since simulating them is way harder), the game just treats you like a simple shape. Fairly often, this is a box, or something very box-like.

An Eevee sprite standing on faux ground; the size of the underlying image and the hitbox are outlined

Since the player has no direct control over the exact placement of their limbs, it would be slightly frustrating to have them collide with the world. This is especially true in cases like the above, where the tail and left ear protrude significantly out from the main body. If that Eevee wanted to stand against a real-world wall, she would simply tilt her ear or tail out of the way, so there’s no reason for the ear to block her from standing against a game wall. To compensate for this, the ear and tail are left out of the collision box entirely and will simply jut into a wall if necessary — a goofy affordance that’s so common it doesn’t even register as unusual. As a bonus (assuming this same box is used for combat), she won’t take damage from projectiles that merely graze past an ear.

(One extra consideration for sprite games in particular: the hitbox ought to be horizontally symmetric around the sprite’s pivot — i.e. the point where the entity is truly considered to be standing — so that the hitbox doesn’t abruptly move when the entity turns around!)

Corners

Treating the player (and indeed most objects) as a box has one annoying side effect: boxes have corners. Corners can catch on other corners, even by a single pixel. Real-world bodies tend to be a bit rounder and squishier and this can tolerate grazing a corner; even real-world boxes will simply rotate a bit.

Ah, but in our faux physics world, we generally don’t want conscious actors (such as the player) to rotate, even with a realistic physics simulator! Real-world bodies are made of parts that will generally try to keep you upright, after all; you don’t tilt back and forth much.

One way to handle corners is to simply remove them from conscious actors. A hitbox doesn’t have to be a literal box, after all. A popular alternative — especially in Unity where it’s a standard asset — is the pill-shaped capsule, which has semicircles/hemispheres on the top and bottom and a cylindrical body in 3D. No corners, no problem.

Of course, that introduces a new problem: now the player can’t balance precariously on edges without their rounded bottom sliding them off. Alas.

If you’re stuck with corners, then, you may want to use a corner bump, a term I just made up. If the player would collide with a corner, but the collision is only by a few pixels, just nudge them to the side a bit and carry on.

An Eevee sprite trying to move sideways into a shallow ledge; the game bumps her upwards slightly, so she steps onto it instead

When the corner is horizontal, this creates stairs! This is, more or less kinda, how steps work in Doom: when the player tries to cross from one sector into another, if the height difference is 24 units or less, the game simply bumps them upwards to the height of the new floor and lets them continue on.

Implementing this in a game without Doom’s notion of sectors is a little trickier. In fact, I still haven’t done it. Collision detection based on rejection gets it for free, kinda, but it’s not very deterministic and it breaks other things. But that’s a whole other post.

Gravity

Gravity is pretty easy. Everything accelerates downwards all the time. What’s interesting are the exceptions.

Jumping

Jumping is a giant hack.

Think about how actual jumping works: you tense your legs, which generally involves bending your knees first, and then spring upwards. In a platformer, you can just leap whenever you feel like it, which is nonsense. Also you go like twenty feet into the air?

Worse, most platformers allow variable-height jumping, where your jump is lower if you let go of the jump button while you’re in the air. Normally, one would expect to have to decide how much force to put into the jump beforehand.

But of course this is about convenience of controls: when jumping is your primary action, you want to be able to do it immediately, without any windup for how high you want to jump.

(And then there’s double jumping? Come on.)

Air control is a similar phenomenon: usually you’d jump in a particular direction by controlling how you push off the ground with your feet, but in a video game, you don’t have feet! You only have the box. The compromise is to let you control your horizontal movement to a limit degree in midair, even though that doesn’t make any sense. (It’s way more fun, though, and overall gives you more movement options, which are good to have in an interactive medium.)

Air control also exposes an obvious place that game physics collide with the realistic model of serious physics engines. I’ve mentioned this before, but: if you use Real Physics™ and air control yourself into a wall, you might find that you’ll simply stick to the wall until you let go of the movement buttons. Why? Remember, player movement acts as though an external force were pushing you around (and from the perspective of a Real™ physics engine, this is exactly how you’d implement it) — so air-controlling into a wall is equivalent to pushing a book against a wall with your hand, and the friction with the wall holds you in place. Oops.

Ground sticking

Another place game physics conflict with physics engines is with running to the top of a slope. On a real hill, of course, you land on top of the slope and are probably glad of it; slopes are hard to climb!

An Eevee moves to the top of a slope, and rather than step onto the flat top, she goes flying off into the air

In a video game, you go flying. Because you’re a box. With momentum. So you hit the peak and keep going in the same direction. Which is diagonally upwards.

Projectiles

To make them more predictable, projectiles generally aren’t subject to gravity, at least as far as I’ve seen. The real world does not have such an exemption. The real world imposes gravity even on sniper rifles, which in a video game are often implemented as an instant trace unaffected by anything in the world because the bullet never actually exists in the world.

Resistance

Ah. Welcome to hell.

Water

Water is an interesting case, and offhand I don’t know the gritty details of how games implement it. In the real world, water applies a resistant drag force to movement — and that force is proportional to the square of velocity, which I’d completely forgotten until right now. I am almost positive that no game handles that correctly. But then, in real-world water, you can push against the water itself for movement, and games don’t simulate that either. What’s the rough equivalent?

The Sonic Physics Guide suggests that Sonic handles it by basically halving everything: acceleration, max speed, friction, etc. When Sonic enters water, his speed is cut; when Sonic exits water, his speed is increased.

That last bit feels validating — I could swear Metroid Prime did the same thing, and built my own solution around it, but couldn’t remember for sure. It makes no sense, of course, for a jump to become faster just because you happened to break the surface of the water, but it feels fantastic.

The thing I did was similar, except that I didn’t want to add a multiplier in a dozen places when you happen to be underwater (and remember which ones need it to be squared, etc.). So instead, I calculate everything completely as normal, so velocity is exactly the same as it would be on dry land — but the distance you would move gets halved. The effect seems to be pretty similar to most platformers with water, at least as far as I can tell. It hasn’t shown up in a published game and I only added this fairly recently, so I might be overlooking some reason this is a bad idea.

(One reason that comes to mind is that velocity is now a little white lie while underwater, so anything relying on velocity for interesting effects might be thrown off. Or maybe that’s correct, because velocity thresholds should be halved underwater too? Hm!)

Notably, air is also a fluid, so it should behave the same way (just with different constants). I definitely don’t think any games apply air drag that’s proportional to the square of velocity.

Friction

Friction is, in my experience, a little handwaved. Probably because real-world friction is so darn complicated.

Consider that in the real world, we want very high friction on the surfaces we walk on — shoes and tires are explicitly designed to increase it, even. We move by bracing a back foot against the ground and using that to push ourselves forward, so we want the ground to resist our push as much as possible.

In a game world, we are a box. We move by being pushed by some invisible outside force, so if the friction between ourselves and the ground is too high, we won’t be able to move at all! That’s complete nonsense physically, but it turns out to be handy in some cases — for example, highish friction can simulate walking through deep mud, which should be difficult due to fluid drag and low friction.

But the best-known example of the fakeness of game friction is video game ice. Walking on real-world ice is difficult because the low friction means low grip; your feet are likely to slip out from under you, and you’ll simply fall down and have trouble moving at all. In a video game, you can’t fall down, so you have the opposite experience: you spend most of your time sliding around uncontrollably. Yet ice is so common in video games (and perhaps so uncommon in places I’ve lived) that I, at least, had never really thought about this disparity until an hour or so ago.

Game friction vs real-world friction

Real-world friction is a force. It’s the normal force (which is the force exerted by the object on the surface) times some constant that depends on how the two materials interact.

Force is mass times acceleration, and platformers often ignore mass, so friction ought to be an acceleration — applied against the object’s movement, but never enough to push it backwards.

I haven’t made any games where variable friction plays a significant role, but my gut instinct is that low friction should mean the player accelerates more slowly but has a higher max speed, and high friction should mean the opposite. I see from my own source code that I didn’t even do what I just said, so let’s defer to some better-made and well-documented games: Sonic and Doom.

In Sonic, friction is a fixed value subtracted from the player’s velocity (regardless of direction) each tic. Sonic has a fixed framerate, so the units are really pixels per tic squared (i.e. acceleration), multiplied by an implicit 1 tic per tic. So far, so good.

But Sonic’s friction only applies if the player isn’t pressing or . Hang on, that isn’t friction at all; that’s just deceleration! That’s equivalent to jogging to a stop. If friction were lower, Sonic would take longer to stop, but otherwise this is only tangentially related to friction.

(In fairness, this approach would decently emulate friction for non-conscious sliding objects, which are never going to be pressing movement buttons. Also, we don’t have the Sonic source code, and the name “friction” is a fan invention; the Sonic Physics Guide already uses “deceleration” to describe the player’s acceleration when turning around.)

Okay, let’s try Doom. In Doom, the default friction is 90.625%.

Hang on, what?

Yes, in Doom, friction is a multiplier applied every tic. Doom runs at 35 tics per second, so this is a multiplier of 0.032 per second. Yikes!

This isn’t anything remotely like real friction, but it’s much easier to implement. With friction as acceleration, the game has to know both the direction of movement (so it can apply friction in the opposite direction) and the magnitude (so it doesn’t overshoot and launch the object in the other direction). That means taking a semi-costly square root and also writing extra code to cap the amount of friction. With a multiplier, neither is necessary; just multiply the whole velocity vector and you’re done.

There are some downsides. One is that objects will never actually stop, since multiplying by 3% repeatedly will never produce a result of zero — though eventually the speed will become small enough to either slip below a “minimum speed” threshold or simply no longer fit in a float representation. Another is that the units are fairly meaningless: with Doom’s default friction of 90.625%, about how long does it take for the player to stop? I have no idea, partly because “stop” is ambiguous here! If friction were an acceleration, I could divide it into the player’s max speed to get a time.

All that aside, what are the actual effects of changing Doom’s friction? What an excellent question that’s surprisingly tricky to answer. (Note that friction can’t be changed in original Doom, only in the Boom port and its derivatives.) Here’s what I’ve pieced together.

Doom’s “friction” is really two values. “Friction” itself is a multiplier applied to moving objects on every tic, but there’s also a move factor which defaults to \(\frac{1}{32} = 0.03125\) and is derived from friction for custom values.

Every tic, the player’s velocity is multiplied by friction, and then increased by their speed times the move factor.

$$
v(n) = v(n – 1) \times friction + speed \times move factor
$$

Eventually, the reduction from friction will balance out the speed boost. That happens when \(v(n) = v(n – 1)\), so we can rearrange it to find the player’s effective max speed:

$$
v = v \times friction + speed \times move factor \\
v – v \times friction = speed \times move factor \\
v = speed \times \frac{move factor}{1 – friction}
$$

For vanilla Doom’s move factor of 0.03125 and friction of 0.90625, that becomes:

$$
v = speed \times \frac{\frac{1}{32}}{1 – \frac{29}{32}} = speed \times \frac{\frac{1}{32}}{\frac{3}{32}} = \frac{1}{3} \times speed
$$

Curiously, “speed” is three times the maximum speed an actor can actually move. Doomguy’s run speed is 50, so in practice he moves a third of that, or 16⅔ units per tic. (Of course, this isn’t counting SR40, a bug that lets Doomguy run ~40% faster than intended diagonally.)

So now, what if you change friction? Even more curiously, the move factor is calculated completely differently depending on whether friction is higher or lower than the default Doom amount:

$$
move factor = \begin{cases}
\frac{133 – 128 \times friction}{544} &≈ 0.244 – 0.235 \times friction & \text{ if } friction \ge \frac{29}{32} \\
\frac{81920 \times friction – 70145}{1048576} &≈ 0.078 \times friction – 0.067 & \text{ otherwise }
\end{cases}
$$

That’s pretty weird? Complicating things further is that low friction (which means muddy terrain, remember) has an extra multiplier on its move factor, depending on how fast you’re already going — the idea is apparently that you have a hard time getting going, but it gets easier as you find your footing. The extra multiplier maxes out at 8, which makes the two halves of that function meet at the vanilla Doom value.

A graph of the relationship between friction and move factor

That very top point corresponds to the move factor from the original game. So no matter what you do to friction, the move factor becomes lower. At 0.85 and change, you can no longer move at all; below that, you move backwards.

From the formula above, it’s easy to see what changes to friction and move factor will do to Doomguy’s stable velocity. Move factor is in the numerator, so increasing it will increase stable velocity — but it can’t increase, so stable velocity can only ever decrease. Friction is in the denominator, but it’s subtracted from 1, so increasing friction will make the denominator a smaller value less than 1, i.e. increase stable velocity. Combined, we get this relationship between friction and stable velocity.

A graph showing stable velocity shooting up dramatically as friction increases

As friction approaches 1, stable velocity grows without bound. This makes sense, given the definition of \(v(n)\) — if friction is 1, the velocity from the previous tic isn’t reduced at all, so we just keep accelerating freely.

All of this is why I’m wary of using multipliers.

Anyway, this leaves me with one last question about the effects of Doom’s friction: how long does it take to reach stable velocity? Barring precision errors, we’ll never truly reach stable velocity, but let’s say within 5%. First we need a closed formula for the velocity after some number of tics. This is a simple recurrence relation, and you can write a few terms out yourself if you want to be sure this is right.

$$
v(n) = v_0 \times friction^n + speed \times move factor \times \frac{friction^n – 1}{friction – 1}
$$

Our initial velocity is zero, so the first term disappears. Set this equal to the stable formula and solve for n:

$$
speed \times move factor \times \frac{friction^n – 1}{friction – 1} = (1 – 5\%) \times speed \times \frac{move factor}{1 – friction} \\
friction^n – 1 = -(1 – 5\%) \\
n = \frac{\ln 5\%}{\ln friction}
$$

Speed” and move factor disappear entirely, which makes sense, and this is purely a function of friction (and how close we want to get). For vanilla Doom, that comes out to 30.4, which is a little less than a second. For other values of friction:

A graph of time to stability which leaps upwards dramatically towards the right

As friction increases (which in Doom terms means the surface is more slippery), it takes longer and longer to reach stable speed, which is in turn greater and greater. For lesser friction (i.e. mud), stable speed is lower, but reached fairly quickly. (Of course, the extra “getting going” multiplier while in mud adds some extra time here, but including that in the graph is a bit more complicated.)

I think this matches with my instincts above. How fascinating!

What’s that? This is way too much math and you hate it? Then don’t use multipliers in game physics.

Uh

That was a hell of a diversion!

I guess the goofiest stuff in basic game physics is really just about mapping player controls to in-game actions like jumping and deceleration; the rest consists of hacks to compensate for representing everything as a box.

Random with care

Post Syndicated from Eevee original https://eev.ee/blog/2018/01/02/random-with-care/

Hi! Here are a few loose thoughts about picking random numbers.

A word about crypto

DON’T ROLL YOUR OWN CRYPTO

This is all aimed at frivolous pursuits like video games. Hell, even video games where money is at stake should be deferring to someone who knows way more than I do. Otherwise you might find out that your deck shuffles in your poker game are woefully inadequate and some smartass is cheating you out of millions. (If your random number generator has fewer than 226 bits of state, it can’t even generate every possible shuffling of a deck of cards!)

Use the right distribution

Most languages have a random number primitive that spits out a number uniformly in the range [0, 1), and you can go pretty far with just that. But beware a few traps!

Random pitches

Say you want to pitch up a sound by a random amount, perhaps up to an octave. Your audio API probably has a way to do this that takes a pitch multiplier, where I say “probably” because that’s how the only audio API I’ve used works.

Easy peasy. If 1 is unchanged and 2 is pitched up by an octave, then all you need is rand() + 1. Right?

No! Pitch is exponential — within the same octave, the “gap” between C and C♯ is about half as big as the gap between B and the following C. If you pick a pitch multiplier uniformly, you’ll have a noticeable bias towards the higher pitches.

One octave corresponds to a doubling of pitch, so if you want to pick a random note, you want 2 ** rand().

Random directions

For two dimensions, you can just pick a random angle with rand() * TAU.

If you want a vector rather than an angle, or if you want a random direction in three dimensions, it’s a little trickier. You might be tempted to just pick a random point where each component is rand() * 2 - 1 (ranging from −1 to 1), but that’s not quite right. A direction is a point on the surface (or, equivalently, within the volume) of a sphere, and picking each component independently produces a point within the volume of a cube; the result will be a bias towards the corners of the cube, where there’s much more extra volume beyond the sphere.

No? Well, just trust me. I don’t know how to make a diagram for this.

Anyway, you could use the Pythagorean theorem a few times and make a huge mess of things, or it turns out there’s a really easy way that even works for two or four or any number of dimensions. You pick each coordinate from a Gaussian (normal) distribution, then normalize the resulting vector. In other words, using Python’s random module:

1
2
3
4
5
6
def random_direction():
    x = random.gauss(0, 1)
    y = random.gauss(0, 1)
    z = random.gauss(0, 1)
    r = math.sqrt(x*x + y*y + z*z)
    return x/r, y/r, z/r

Why does this work? I have no idea!

Note that it is possible to get zero (or close to it) for every component, in which case the result is nonsense. You can re-roll all the components if necessary; just check that the magnitude (or its square) is less than some epsilon, which is equivalent to throwing away a tiny sphere at the center and shouldn’t affect the distribution.

Beware Gauss

Since I brought it up: the Gaussian distribution is a pretty nice one for choosing things in some range, where the middle is the common case and should appear more frequently.

That said, I never use it, because it has one annoying drawback: the Gaussian distribution has no minimum or maximum value, so you can’t really scale it down to the range you want. In theory, you might get any value out of it, with no limit on scale.

In practice, it’s astronomically rare to actually get such a value out. I did a hundred million trials just to see what would happen, and the largest value produced was 5.8.

But, still, I’d rather not knowingly put extremely rare corner cases in my code if I can at all avoid it. I could clamp the ends, but that would cause unnatural bunching at the endpoints. I could reroll if I got a value outside some desired range, but I prefer to avoid rerolling when I can, too; after all, it’s still (astronomically) possible to have to reroll for an indefinite amount of time. (Okay, it’s really not, since you’ll eventually hit the period of your PRNG. Still, though.) I don’t bend over backwards here — I did just say to reroll when picking a random direction, after all — but when there’s a nicer alternative I’ll gladly use it.

And lo, there is a nicer alternative! Enter the beta distribution. It always spits out a number in [0, 1], so you can easily swap it in for the standard normal function, but it takes two “shape” parameters α and β that alter its behavior fairly dramatically.

With α = β = 1, the beta distribution is uniform, i.e. no different from rand(). As α increases, the distribution skews towards the right, and as β increases, the distribution skews towards the left. If α = β, the whole thing is symmetric with a hump in the middle. The higher either one gets, the more extreme the hump (meaning that value is far more common than any other). With a little fiddling, you can get a number of interesting curves.

Screenshots don’t really do it justice, so here’s a little Wolfram widget that lets you play with α and β live:

Note that if α = 1, then 1 is a possible value; if β = 1, then 0 is a possible value. You probably want them both greater than 1, which clamps the endpoints to zero.

Also, it’s possible to have either α or β or both be less than 1, but this creates very different behavior: the corresponding endpoints become poles.

Anyway, something like α = β = 3 is probably close enough to normal for most purposes but already clamped for you. And you could easily replicate something like, say, NetHack’s incredibly bizarre rnz function.

Random frequency

Say you want some event to have an 80% chance to happen every second. You (who am I kidding, I) might be tempted to do something like this:

1
2
if random() < 0.8 * dt:
    do_thing()

In an ideal world, dt is always the same and is equal to 1 / f, where f is the framerate. Replace that 80% with a variable, say P, and every tic you have a P / f chance to do the… whatever it is.

Each second, f tics pass, so you’ll make this check f times. The chance that any check succeeds is the inverse of the chance that every check fails, which is \(1 – \left(1 – \frac{P}{f}\right)^f\).

For P of 80% and a framerate of 60, that’s a total probability of 55.3%. Wait, what?

Consider what happens if the framerate is 2. On the first tic, you roll 0.4 twice — but probabilities are combined by multiplying, and splitting work up by dt only works for additive quantities. You lose some accuracy along the way. If you’re dealing with something that multiplies, you need an exponent somewhere.

But in this case, maybe you don’t want that at all. Each separate roll you make might independently succeed, so it’s possible (but very unlikely) that the event will happen 60 times within a single second! Or 200 times, if that’s someone’s framerate.

If you explicitly want something to have a chance to happen on a specific interval, you have to check on that interval. If you don’t have a gizmo handy to run code on an interval, it’s easy to do yourself with a time buffer:

1
2
3
4
5
6
timer += dt
# here, 1 is the "every 1 seconds"
while timer > 1:
    timer -= 1
    if random() < 0.8:
        do_thing()

Using while means rolls still happen even if you somehow skipped over an entire second.

(For the curious, and the nerds who already noticed: the expression \(1 – \left(1 – \frac{P}{f}\right)^f\) converges to a specific value! As the framerate increases, it becomes a better and better approximation for \(1 – e^{-P}\), which for the example above is 0.551. Hey, 60 fps is pretty accurate — it’s just accurately representing something nowhere near what I wanted. Er, you wanted.)

Rolling your own

Of course, you can fuss with the classic [0, 1] uniform value however you want. If I want a bias towards zero, I’ll often just square it, or multiply two of them together. If I want a bias towards one, I’ll take a square root. If I want something like a Gaussian/normal distribution, but with clearly-defined endpoints, I might add together n rolls and divide by n. (The normal distribution is just what you get if you roll infinite dice and divide by infinity!)

It’d be nice to be able to understand exactly what this will do to the distribution. Unfortunately, that requires some calculus, which this post is too small to contain, and which I didn’t even know much about myself until I went down a deep rabbit hole while writing, and which in many cases is straight up impossible to express directly.

Here’s the non-calculus bit. A source of randomness is often graphed as a PDF — a probability density function. You’ve almost certainly seen a bell curve graphed, and that’s a PDF. They’re pretty nice, since they do exactly what they look like: they show the relative chance that any given value will pop out. On a bog standard bell curve, there’s a peak at zero, and of course zero is the most common result from a normal distribution.

(Okay, actually, since the results are continuous, it’s vanishingly unlikely that you’ll get exactly zero — but you’re much more likely to get a value near zero than near any other number.)

For the uniform distribution, which is what a classic rand() gives you, the PDF is just a straight horizontal line — every result is equally likely.


If there were a calculus bit, it would go here! Instead, we can cheat. Sometimes. Mathematica knows how to work with probability distributions in the abstract, and there’s a free web version you can use. For the example of squaring a uniform variable, try this out:

1
PDF[TransformedDistribution[u^2, u \[Distributed] UniformDistribution[{0, 1}]], u]

(The \[Distributed] is a funny tilde that doesn’t exist in Unicode, but which Mathematica uses as a first-class operator. Also, press shiftEnter to evaluate the line.)

This will tell you that the distribution is… \(\frac{1}{2\sqrt{u}}\). Weird! You can plot it:

1
Plot[%, {u, 0, 1}]

(The % refers to the result of the last thing you did, so if you want to try several of these, you can just do Plot[PDF[…], u] directly.)

The resulting graph shows that numbers around zero are, in fact, vastly — infinitely — more likely than anything else.

What about multiplying two together? I can’t figure out how to get Mathematica to understand this, but a great amount of digging revealed that the answer is -ln x, and from there you can plot them both on Wolfram Alpha. They’re similar, though squaring has a much better chance of giving you high numbers than multiplying two separate rolls — which makes some sense, since if either of two rolls is a low number, the product will be even lower.

What if you know the graph you want, and you want to figure out how to play with a uniform roll to get it? Good news! That’s a whole thing called inverse transform sampling. All you have to do is take an integral. Good luck!


This is all extremely ridiculous. New tactic: Just Simulate The Damn Thing. You already have the code; run it a million times, make a histogram, and tada, there’s your PDF. That’s one of the great things about computers! Brute-force numerical answers are easy to come by, so there’s no excuse for producing something like rnz. (Though, be sure your histogram has sufficiently narrow buckets — I tried plotting one for rnz once and the weird stuff on the left side didn’t show up at all!)

By the way, I learned something from futzing with Mathematica here! Taking the square root (to bias towards 1) gives a PDF that’s a straight diagonal line, nothing like the hyperbola you get from squaring (to bias towards 0). How do you get a straight line the other way? Surprise: \(1 – \sqrt{1 – u}\).

Okay, okay, here’s the actual math

I don’t claim to have a very firm grasp on this, but I had a hell of a time finding it written out clearly, so I might as well write it down as best I can. This was a great excuse to finally set up MathJax, too.

Say \(u(x)\) is the PDF of the original distribution and \(u\) is a representative number you plucked from that distribution. For the uniform distribution, \(u(x) = 1\). Or, more accurately,

$$
u(x) = \begin{cases}
1 & \text{ if } 0 \le x \lt 1 \\
0 & \text{ otherwise }
\end{cases}
$$

Remember that \(x\) here is a possible outcome you want to know about, and the PDF tells you the relative probability that a roll will be near it. This PDF spits out 1 for every \(x\), meaning every number between 0 and 1 is equally likely to appear.

We want to do something to that PDF, which creates a new distribution, whose PDF we want to know. I’ll use my original example of \(f(u) = u^2\), which creates a new PDF \(v(x)\).

The trick is that we need to work in terms of the cumulative distribution function for \(u\). Where the PDF gives the relative chance that a roll will be (“near”) a specific value, the CDF gives the relative chance that a roll will be less than a specific value.

The conventions for this seem to be a bit fuzzy, and nobody bothers to explain which ones they’re using, which makes this all the more confusing to read about… but let’s write the CDF with a capital letter, so we have \(U(x)\). In this case, \(U(x) = x\), a straight 45° line (at least between 0 and 1). With the definition I gave, this should make sense. At some arbitrary point like 0.4, the value of the PDF is 1 (0.4 is just as likely as anything else), and the value of the CDF is 0.4 (you have a 40% chance of getting a number from 0 to 0.4).

Calculus ahoy: the PDF is the derivative of the CDF, which means it measures the slope of the CDF at any point. For \(U(x) = x\), the slope is always 1, and indeed \(u(x) = 1\). See, calculus is easy.

Okay, so, now we’re getting somewhere. What we want is the CDF of our new distribution, \(V(x)\). The CDF is defined as the probability that a roll \(v\) will be less than \(x\), so we can literally write:

$$V(x) = P(v \le x)$$

(This is why we have to work with CDFs, rather than PDFs — a PDF gives the chance that a roll will be “nearby,” whatever that means. A CDF is much more concrete.)

What is \(v\), exactly? We defined it ourselves; it’s the do something applied to a roll from the original distribution, or \(f(u)\).

$$V(x) = P\!\left(f(u) \le x\right)$$

Now the first tricky part: we have to solve that inequality for \(u\), which means we have to do something, backwards to \(x\).

$$V(x) = P\!\left(u \le f^{-1}(x)\right)$$

Almost there! We now have a probability that \(u\) is less than some value, and that’s the definition of a CDF!

$$V(x) = U\!\left(f^{-1}(x)\right)$$

Hooray! Now to turn these CDFs back into PDFs, all we need to do is differentiate both sides and use the chain rule. If you never took calculus, don’t worry too much about what that means!

$$v(x) = u\!\left(f^{-1}(x)\right)\left|\frac{d}{dx}f^{-1}(x)\right|$$

Wait! Where did that absolute value come from? It takes care of whether \(f(x)\) increases or decreases. It’s the least interesting part here by far, so, whatever.

There’s one more magical part here when using the uniform distribution — \(u(\dots)\) is always equal to 1, so that entire term disappears! (Note that this only works for a uniform distribution with a width of 1; PDFs are scaled so the entire area under them sums to 1, so if you had a rand() that could spit out a number between 0 and 2, the PDF would be \(u(x) = \frac{1}{2}\).)

$$v(x) = \left|\frac{d}{dx}f^{-1}(x)\right|$$

So for the specific case of modifying the output of rand(), all we have to do is invert, then differentiate. The inverse of \(f(u) = u^2\) is \(f^{-1}(x) = \sqrt{x}\) (no need for a ± since we’re only dealing with positive numbers), and differentiating that gives \(v(x) = \frac{1}{2\sqrt{x}}\). Done! This is also why square root comes out nicer; inverting it gives \(x^2\), and differentiating that gives \(2x\), a straight line.

Incidentally, that method for turning a uniform distribution into any distribution — inverse transform sampling — is pretty much the same thing in reverse: integrate, then invert. For example, when I saw that taking the square root gave \(v(x) = 2x\), I naturally wondered how to get a straight line going the other way, \(v(x) = 2 – 2x\). Integrating that gives \(2x – x^2\), and then you can use the quadratic formula (or just ask Wolfram Alpha) to solve \(2x – x^2 = u\) for \(x\) and get \(f(u) = 1 – \sqrt{1 – u}\).

Multiply two rolls is a bit more complicated; you have to write out the CDF as an integral and you end up doing a double integral and wow it’s a mess. The only thing I’ve retained is that you do a division somewhere, which then gets integrated, and that’s why it ends up as \(-\ln x\).

And that’s quite enough of that! (Okay but having math in my blog is pretty cool and I will definitely be doing more of this, sorry, not sorry.)

Random vs varied

Sometimes, random isn’t actually what you want. We tend to use the word “random” casually to mean something more like chaotic, i.e., with no discernible pattern. But that’s not really random. In fact, given how good humans can be at finding incidental patterns, they aren’t all that unlikely! Consider that when you roll two dice, they’ll come up either the same or only one apart almost half the time. Coincidence? Well, yes.

If you ask for randomness, you’re saying that any outcome — or series of outcomes — is acceptable, including five heads in a row or five tails in a row. Most of the time, that’s fine. Some of the time, it’s less fine, and what you really want is variety. Here are a couple examples and some fairly easy workarounds.

NPC quips

The nature of games is such that NPCs will eventually run out of things to say, at which point further conversation will give the player a short brush-off quip — a slight nod from the designer to the player that, hey, you hit the end of the script.

Some NPCs have multiple possible quips and will give one at random. The trouble with this is that it’s very possible for an NPC to repeat the same quip several times in a row before abruptly switching to another one. With only a few options to choose from, getting the same option twice or thrice (especially across an entire game, which may have numerous NPCs) isn’t all that unlikely. The notion of an NPC quip isn’t very realistic to start with, but having someone repeat themselves and then abruptly switch to something else is especially jarring.

The easy fix is to show the quips in order! Paradoxically, this is more consistently varied than choosing at random — the original “order” is likely to be meaningless anyway, and it already has the property that the same quip can never appear twice in a row.

If you like, you can shuffle the list of quips every time you reach the end, but take care here — it’s possible that the last quip in the old order will be the same as the first quip in the new order, so you may still get a repeat. (Of course, you can just check for this case and swap the first quip somewhere else if it bothers you.)

That last behavior is, in fact, the canonical way that Tetris chooses pieces — the game simply shuffles a list of all 7 pieces, gives those to you in shuffled order, then shuffles them again to make a new list once it’s exhausted. There’s no avoidance of duplicates, though, so you can still get two S blocks in a row, or even two S and two Z all clumped together, but no more than that. Some Tetris variants take other approaches, such as actively avoiding repeats even several pieces apart or deliberately giving you the worst piece possible.

Random drops

Random drops are often implemented as a flat chance each time. Maybe enemies have a 5% chance to drop health when they die. Legally speaking, over the long term, a player will see health drops for about 5% of enemy kills.

Over the short term, they may be desperate for health and not survive to see the long term. So you may want to put a thumb on the scale sometimes. Games in the Metroid series, for example, have a somewhat infamous bias towards whatever kind of drop they think you need — health if your health is low, missiles if your missiles are low.

I can’t give you an exact approach to use, since it depends on the game and the feeling you’re going for and the variables at your disposal. In extreme cases, you might want to guarantee a health drop from a tough enemy when the player is critically low on health. (Or if you’re feeling particularly evil, you could go the other way and deny the player health when they most need it…)

The problem becomes a little different, and worse, when the event that triggers the drop is relatively rare. The pathological case here would be something like a raid boss in World of Warcraft, which requires hours of effort from a coordinated group of people to defeat, and which has some tiny chance of dropping a good item that will go to only one of those people. This is why I stopped playing World of Warcraft at 60.

Dialing it back a little bit gives us Enter the Gungeon, a roguelike where each room is a set of encounters and each floor only has a dozen or so rooms. Initially, you have a 1% chance of getting a reward after completing a room — but every time you complete a room and don’t get a reward, the chance increases by 9%, up to a cap of 80%. Once you get a reward, the chance resets to 1%.

The natural question is: how frequently, exactly, can a player expect to get a reward? We could do math, or we could Just Simulate The Damn Thing.

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
from collections import Counter
import random

histogram = Counter()

TRIALS = 1000000
chance = 1
rooms_cleared = 0
rewards_found = 0
while rewards_found < TRIALS:
    rooms_cleared += 1
    if random.random() * 100 < chance:
        # Reward!
        rewards_found += 1
        histogram[rooms_cleared] += 1
        rooms_cleared = 0
        chance = 1
    else:
        chance = min(80, chance + 9)

for gaps, count in sorted(histogram.items()):
    print(f"{gaps:3d} | {count / TRIALS * 100:6.2f}%", '#' * (count // (TRIALS // 100)))
 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
  1 |   0.98%
  2 |   9.91% #########
  3 |  17.00% ################
  4 |  20.23% ####################
  5 |  19.21% ###################
  6 |  15.05% ###############
  7 |   9.69% #########
  8 |   5.07% #####
  9 |   2.09% ##
 10 |   0.63%
 11 |   0.12%
 12 |   0.03%
 13 |   0.00%
 14 |   0.00%
 15 |   0.00%

We’ve got kind of a hilly distribution, skewed to the left, which is up in this histogram. Most of the time, a player should see a reward every three to six rooms, which is maybe twice per floor. It’s vanishingly unlikely to go through a dozen rooms without ever seeing a reward, so a player should see at least one per floor.

Of course, this simulated a single continuous playthrough; when starting the game from scratch, your chance at a reward always starts fresh at 1%, the worst it can be. If you want to know about how many rewards a player will get on the first floor, hey, Just Simulate The Damn Thing.

1
2
3
4
5
6
7
  0 |   0.01%
  1 |  13.01% #############
  2 |  56.28% ########################################################
  3 |  27.49% ###########################
  4 |   3.10% ###
  5 |   0.11%
  6 |   0.00%

Cool. Though, that’s assuming exactly 12 rooms; it might be worth changing that to pick at random in a way that matches the level generator.

(Enter the Gungeon does some other things to skew probability, which is very nice in a roguelike where blind luck can make or break you. For example, if you kill a boss without having gotten a new gun anywhere else on the floor, the boss is guaranteed to drop a gun.)

Critical hits

I suppose this is the same problem as random drops, but backwards.

Say you have a battle sim where every attack has a 6% chance to land a devastating critical hit. Presumably the same rules apply to both the player and the AI opponents.

Consider, then, that the AI opponents have exactly the same 6% chance to ruin the player’s day. Consider also that this gives them an 0.4% chance to critical hit twice in a row. 0.4% doesn’t sound like much, but across an entire playthrough, it’s not unlikely that a player might see it happen and find it incredibly annoying.

Perhaps it would be worthwhile to explicitly forbid AI opponents from getting consecutive critical hits.

In conclusion

An emerging theme here has been to Just Simulate The Damn Thing. So consider Just Simulating The Damn Thing. Even a simple change to a random value can do surprising things to the resulting distribution, so unless you feel like differentiating the inverse function of your code, maybe test out any non-trivial behavior and make sure it’s what you wanted. Probability is hard to reason about.

Instrumenting Web Apps Using AWS X-Ray

Post Syndicated from Bharath Kumar original https://aws.amazon.com/blogs/devops/instrumenting-web-apps-using-aws-x-ray/

This post was written by James Bowman, Software Development Engineer, AWS X-Ray

AWS X-Ray helps developers analyze and debug distributed applications and underlying services in production. You can identify and analyze root-causes of performance issues and errors, understand customer impact, and extract statistical aggregations (such as histograms) for optimization.

In this blog post, I will provide a step-by-step walkthrough for enabling X-Ray tracing in the Go programming language. You can use these steps to add X-Ray tracing to any distributed application.

Revel: A web framework for the Go language

This section will assist you with designing a guestbook application. Skip to “Instrumenting with AWS X-Ray” section below if you already have a Go language application.

Revel is a web framework for the Go language. It facilitates the rapid development of web applications by providing a predefined framework for controllers, views, routes, filters, and more.

To get started with Revel, run revel new github.com/jamesdbowman/guestbook. A project base is then copied to $GOPATH/src/github.com/jamesdbowman/guestbook.

$ tree -L 2
.
├── README.md
├── app
│ ├── controllers
│ ├── init.go
│ ├── routes
│ ├── tmp
│ └── views
├── conf
│ ├── app.conf
│ └── routes
├── messages
│ └── sample.en
├── public
│ ├── css
│ ├── fonts
│ ├── img
│ └── js
└── tests
└── apptest.go

Writing a guestbook application

A basic guestbook application can consist of just two routes: one to sign the guestbook and another to list all entries.
Let’s set up these routes by adding a Book controller, which can be routed to by modifying ./conf/routes.

./app/controllers/book.go:
package controllers

import (
    "math/rand"
    "time"

    "github.com/aws/aws-sdk-go/aws"
    "github.com/aws/aws-sdk-go/aws/endpoints"
    "github.com/aws/aws-sdk-go/aws/session"
    "github.com/aws/aws-sdk-go/service/dynamodb"
    "github.com/aws/aws-sdk-go/service/dynamodb/dynamodbattribute"
    "github.com/revel/revel"
)

const TABLE_NAME = "guestbook"
const SUCCESS = "Success.\n"
const DAY = 86400

var letters = []rune("ABCDEFGHIJKLMNOPQRSTUVWXYZ")

func init() {
    rand.Seed(time.Now().UnixNano())
}

// randString returns a random string of len n, used for DynamoDB Hash key.
func randString(n int) string {
    b := make([]rune, n)
    for i := range b {
        b[i] = letters[rand.Intn(len(letters))]
    }
    return string(b)
}

// Book controls interactions with the guestbook.
type Book struct {
    *revel.Controller
    ddbClient *dynamodb.DynamoDB
}

// Signature represents a user's signature.
type Signature struct {
    Message string
    Epoch   int64
    ID      string
}

// ddb returns the controller's DynamoDB client, instatiating a new client if necessary.
func (c Book) ddb() *dynamodb.DynamoDB {
    if c.ddbClient == nil {
        sess := session.Must(session.NewSession(&aws.Config{
            Region: aws.String(endpoints.UsWest2RegionID),
        }))
        c.ddbClient = dynamodb.New(sess)
    }
    return c.ddbClient
}

// Sign allows users to sign the book.
// The message is to be passed as application/json typed content, listed under the "message" top level key.
func (c Book) Sign() revel.Result {
    var s Signature

    err := c.Params.BindJSON(&s)
    if err != nil {
        return c.RenderError(err)
    }
    now := time.Now()
    s.Epoch = now.Unix()
    s.ID = randString(20)

    item, err := dynamodbattribute.MarshalMap(s)
    if err != nil {
        return c.RenderError(err)
    }

    putItemInput := &dynamodb.PutItemInput{
        TableName: aws.String(TABLE_NAME),
        Item:      item,
    }
    _, err = c.ddb().PutItem(putItemInput)
    if err != nil {
        return c.RenderError(err)
    }

    return c.RenderText(SUCCESS)
}

// List allows users to list all signatures in the book.
func (c Book) List() revel.Result {
    scanInput := &dynamodb.ScanInput{
        TableName: aws.String(TABLE_NAME),
        Limit:     aws.Int64(100),
    }
    res, err := c.ddb().Scan(scanInput)
    if err != nil {
        return c.RenderError(err)
    }

    messages := make([]string, 0)
    for _, v := range res.Items {
        messages = append(messages, *(v["Message"].S))
    }
    return c.RenderJSON(messages)
}

./conf/routes:
POST /sign Book.Sign
GET /list Book.List

Creating the resources and testing

For the purposes of this blog post, the application will be run and tested locally. We will store and retrieve messages from an Amazon DynamoDB table. Use the following AWS CLI command to create the guestbook table:

aws dynamodb create-table --region us-west-2 --table-name "guestbook" --attribute-definitions AttributeName=ID,AttributeType=S AttributeName=Epoch,AttributeType=N --key-schema AttributeName=ID,KeyType=HASH AttributeName=Epoch,KeyType=RANGE --provisioned-throughput ReadCapacityUnits=5,WriteCapacityUnits=5

Now, let’s test our sign and list routes. If everything is working correctly, the following result appears:

$ curl -d '{"message":"Hello from cURL!"}' -H "Content-Type: application/json" http://localhost:9000/book/sign
Success.
$ curl http://localhost:9000/book/list
[
  "Hello from cURL!"
]%

Integrating with AWS X-Ray

Download and run the AWS X-Ray daemon

The AWS SDKs emit trace segments over UDP on port 2000. (This port can be configured.) In order for the trace segments to make it to the X-Ray service, the daemon must listen on this port and batch the segments in calls to the PutTraceSegments API.
For information about downloading and running the X-Ray daemon, see the AWS X-Ray Developer Guide.

Installing the AWS X-Ray SDK for Go

To download the SDK from GitHub, run go get -u github.com/aws/aws-xray-sdk-go/... The SDK will appear in the $GOPATH.

Enabling the incoming request filter

The first step to instrumenting an application with AWS X-Ray is to enable the generation of trace segments on incoming requests. The SDK conveniently provides an implementation of http.Handler which does exactly that. To ensure incoming web requests travel through this handler, we can modify app/init.go, adding a custom function to be run on application start.

import (
    "github.com/aws/aws-xray-sdk-go/xray"
    "github.com/revel/revel"
)

...

func init() {
  ...
    revel.OnAppStart(installXRayHandler)
}

func installXRayHandler() {
    revel.Server.Handler = xray.Handler(xray.NewFixedSegmentNamer("GuestbookApp"), revel.Server.Handler)
}

The application will now emit a segment for each incoming web request. The service graph appears:

You can customize the name of the segment to make it more descriptive by providing an alternate implementation of SegmentNamer to xray.Handler. For example, you can use xray.NewDynamicSegmentNamer(fallback, pattern) in place of the fixed namer. This namer will use the host name from the incoming web request (if it matches pattern) as the segment name. This is often useful when you are trying to separate different instances of the same application.

In addition, HTTP-centric information such as method and URL is collected in the segment’s http subsection:

"http": {
    "request": {
        "url": "/book/list",
        "method": "GET",
        "user_agent": "curl/7.54.0",
        "client_ip": "::1"
    },
    "response": {
        "status": 200
    }
},

Instrumenting outbound calls

To provide detailed performance metrics for distributed applications, the AWS X-Ray SDK needs to measure the time it takes to make outbound requests. Trace context is passed to downstream services using the X-Amzn-Trace-Id header. To draw a detailed and accurate representation of a distributed application, outbound call instrumentation is required.

AWS SDK calls

The AWS X-Ray SDK for Go provides a one-line AWS client wrapper that enables the collection of detailed per-call metrics for any AWS client. We can modify the DynamoDB client instantiation to include this line:

// ddb returns the controller's DynamoDB client, instatiating a new client if necessary.
func (c Book) ddb() *dynamodb.DynamoDB {
    if c.ddbClient == nil {
        sess := session.Must(session.NewSession(&aws.Config{
            Region: aws.String(endpoints.UsWest2RegionID),
        }))
        c.ddbClient = dynamodb.New(sess)
        xray.AWS(c.ddbClient.Client) // add subsegment-generating X-Ray handlers to this client
    }
    return c.ddbClient
}

We also need to ensure that the segment generated by our xray.Handler is passed to these AWS calls so that the X-Ray SDK knows to which segment these generated subsegments belong. In Go, the context.Context object is passed throughout the call path to achieve this goal. (In most other languages, some variant of ThreadLocal is used.) AWS clients provide a *WithContext method variant for each AWS operation, which we need to switch to:

_, err = c.ddb().PutItemWithContext(c.Request.Context(), putItemInput)
    res, err := c.ddb().ScanWithContext(c.Request.Context(), scanInput)

We now see much more detail in the Timeline view of the trace for the sign and list operations:

We can use this detail to help diagnose throttling on our DynamoDB table. In the following screenshot, the purple in the DynamoDB service graph node indicates that our table is underprovisioned. The red in the GuestbookApp node indicates that the application is throwing faults due to this throttling.

HTTP calls

Although the guestbook application does not make any non-AWS outbound HTTP calls in its current state, there is a similar one-liner to wrap HTTP clients that make outbound requests. xray.Client(c *http.Client) wraps an existing http.Client (or nil if you want to use a default HTTP client). For example:

resp, err := ctxhttp.Get(ctx, xray.Client(nil), "https://aws.amazon.com/")

Instrumenting local operations

X-Ray can also assist in measuring the performance of local compute operations. To see this in action, let’s create a custom subsegment inside the randString method:


// randString returns a random string of len n, used for DynamoDB Hash key.
func randString(ctx context.Context, n int) string {
    xray.Capture(ctx, "randString", func(innerCtx context.Context) {
        b := make([]rune, n)
        for i := range b {
            b[i] = letters[rand.Intn(len(letters))]
        }
        s := string(b)
    })
    return s
}

// we'll also need to change the callsite

s.ID = randString(c.Request.Context(), 20)

Summary

By now, you are an expert on how to instrument X-Ray for your Go applications. Instrumenting X-Ray with your applications is an easy way to analyze and debug performance issues and understand customer impact. Please feel free to give any feedback or comments below.

For more information about advanced configuration of the AWS X-Ray SDK for Go, see the AWS X-Ray SDK for Go in the AWS X-Ray Developer Guide and the aws/aws-xray-sdk-go GitHub repository.

For more information about some of the advanced X-Ray features such as histograms, annotations, and filter expressions, see the Analyzing Performance for Amazon Rekognition Apps Written on AWS Lambda Using AWS X-Ray blog post.

E-Mail Tracking

Post Syndicated from Bruce Schneier original https://www.schneier.com/blog/archives/2017/12/e-mail_tracking_1.html

Good article on the history and practice of e-mail tracking:

The tech is pretty simple. Tracking clients embed a line of code in the body of an email­ — usually in a 1×1 pixel image, so tiny it’s invisible, but also in elements like hyperlinks and custom fonts. When a recipient opens the email, the tracking client recognizes that pixel has been downloaded, as well as where and on what device. Newsletter services, marketers, and advertisers have used the technique for years, to collect data about their open rates; major tech companies like Facebook and Twitter followed suit in their ongoing quest to profile and predict our behavior online.

But lately, a surprising­ — and growing­ — number of tracked emails are being sent not from corporations, but acquaintances. “We have been in touch with users that were tracked by their spouses, business partners, competitors,” says Florian Seroussi, the founder of OMC. “It’s the wild, wild west out there.”

According to OMC’s data, a full 19 percent of all “conversational” email is now tracked. That’s one in five of the emails you get from your friends. And you probably never noticed.

I admit it’s enticing. I would very much like the statistics that adding trackers to Crypto-Gram would give me. But I still don’t do it.

Weekly roundup: Apocalypse

Post Syndicated from Eevee original https://eev.ee/dev/2017/10/02/weekly-roundup-apocalypse/

Uh, hey. What’s up. Been a while. My computer died? Linux abruptly put the primary hard drive in read-only mode, which seemed Really Bad, but then it refused to boot up entirely. I suspect the motherboard was on its last legs (though the drive itself was getting pretty worn out too), so long story short, I lost a week to ordering/building an entirely new machine and rearranging/zeroing hard drives. The old one was six years old, so it was about time anyway.

I also had some… internet stuff… to deal with, so overall I’ve had a rollercoaster of a week. Oh, and now my keyboard is finally starting to break.

  • fox flux: I’m at the point where the protagonists are almost all done and I’ve started touching up particular poses (times ten). So that’s cool. If I hadn’t lost the last week I might’ve been done with it by now!

  • devops: Well, there was that whole computer thing. Also I suddenly have support for colored fonts (read: emoji) in all GTK apps (except Chromium), and that led me to spend at least half a day trying to find a way to get Twemoji into a font using Google’s font extensions. Alas, no dice, so I’m currently stuck with a fairly outdated copy of the Android emoji, which I don’t want to upgrade because Google makes them worse with every revision.

  • blog: I started on a post. I didn’t get very far. I still owe two for September. Oops.

  • book: Did some editing, worked on some illustrations. I figured out how to get math sections to (mostly) use the same font as body text, so inline math doesn’t look quite so comically out of place any more.

  • cc: Fixed some stuff I broke, as usual, and worked some more on a Unity GUI for defining and editing sprite animations.

I’m now way behind and have completely lost all my trains of thought, though I guess having my computer break is a pretty good excuse. Trying to get back up to speed as quickly as possible.

Oh, and happy October. 🎃

Say Hello to the New Atlassian

Post Syndicated from Chris De Santis original https://www.anchor.com.au/blog/2017/09/hello-new-atlassian/

Who is Atlassian?

Atlassian is an Australian IT company that develops enterprise software, with its best-known products being its issue-tracking app, Jira, and team collaboration and wiki product, Confluence.

In December 2015, Atlassian went public and made their initial public offering (IPO) under the symbol TEAM, valuing them at $4.37 billion. In summary, they big.

What happened?

A facelift

It’s a nice sunny day in Sydney in mid-September of 2017, and Atlassian, after 15 years of consistency, has rebranded, changing their look and feel for a brighter and funner one, compared to the dreary previous look.New Atlassian Branding VideoIt’s a hell of a lot simpler and, as they show in the above video, it’s going to be used with a lot more creativity and flair in mind—it’s flexible in a sense that they can use it in a lot more ways than before, with a lot more colours than before.

Atlassian Logo ComparisonThe blues they’re using now work super-well with the logos on a white background, whereas the white logos on their new champion, brand colour blue can go both ways: some can see it as a bold, daring step which is quite attractive, while others can see it as off-putting and not very user-friendly.

New Atlassian Logo Versions

What’s it all mean?

Symbolism

In his announcement blog, Atlassian Co-Founder & Co-CEO, Mike Cannon-Brookes, mentions that the branding change reflects their newly-shifted focus on the concept of teamwork. He continues to explain that their previous logo depicted the sky-holding Greek titan Atlas and symbolised legendary service and support. But, while it has become renown, they’re shifting their focus on the concept of teamwork—why focus on something you’ve already done right, right?

Atlassian Logo EvolutionThe new logo contains more symbolism than meets the eye, as can be interpreted as:

  • Two people high-fiving
  • A mountain to scale
  • The letter “A” (seen as two pillars reinforcing each other)
Product logos

Atlassian has created and acquired many products in their adventure so far, and they all seemed to have a similar art style, but something always felt off about their consistency. Well, needless to say, this was addressed with Atlassian’s very own “identity system”, which is a pretty cool term for a consistent logo-look for 14+ products, to fit them under one brand.

New Atlassian Product LogosThe result is a set of unique marks that “still feel very related to each other”. Whereas, I also see a new set of “unknown” Pokémon.

Typeface

New Atlassian TypefaceTo add a cherry on top, Atlassian will be using their own custom-made typeface called Charlie Sans, specifically designed to balance legibility with personality–that’s probably the best way to describe it. Otherwise, I’d say, out of purely-constructive criticism, that there isn’t much difference between itself and any of the other staple fonts; i.e. Arial, Verdana, etc. Then again, I’m not a professional designer.

It doesn’t look as distinct as their previous typeface, but, to be fair, it does look very slick next to the new product logos.

Well…

What do you think about it all?

 

Image credits: Atlassian

The post Say Hello to the New Atlassian appeared first on AWS Managed Services by Anchor.