A very welcome type-safe builders surprise

When Kotlin 1.0 came out, I tried type-safe builders a bit, with mixed feelings. They are a great way to create simple declarative DSLs for building hierarchies, but using them used to be quite a pain.

The main problem was that as the nesting got deeper, the DSL API would include methods from all the scopes. Only some of those methods were usable in the current scope. This was infuriating to use, since if you used a method in the wrong scope, it would often cause wrong behavior instead of an error. Here is an example using a simple XML DSL:

DSL gone bad example
A tag inside an attribute, WAT…

It makes no sense to have a tag inside an attribute, but this would not fail, but instead cause the below XML document to be created. It is valid XML, but probably not what was intended given the above nesting.

Resulting weird XML

Yesterday I needed to do create some XML, and I remembered type-safe builders to be great for this. I quickly whipped together the simple API above for that, but again was confronted with the scoping problem. Initially I figured out a very hacky way to provide nice errors at runtime, but then I thankfully read up on the Kotlin documentation, and in Kotlin 1.1, the @DslMarker annotation was added to ensure that only methods in the current builder scope is visible.

This moves type-safe builders from good to awesome in my book.

DSL now fails to compile
With @DslMarker annotation, the tag is not visible in the attribute scope, and this nonsense fails to compile.

I am late to the party, but this feels like a change that is easy to miss, and that does not get enough attention. Superb of the Kotlin team to address things like these!

♥ Princesses versus giraffes ♥

TLDR; I’m writing a coop multiplayer game with my daughter, this is the current result! Works in Firefox and Chrome. Use arrows to move and space to fire. Share a URL to play with a friend.

Some years ago, my daughter figured out I made some computer games, and she even played one of them quite a bit. After a while she wanted something new, and we figured we’ll make a game together. She would draw concepts and come up with ideas, and I would try to make them happen in game.

The initial concepts she drew were these:

We then together made them into vector with some modifications.

Princess and "giraffe"
A princess and a giraffe… I guess

Tips on kid friendly vector drawing programs would be very much appreciated, throw me an email or post a comment. We used Sketch, but Sketch is a bit overwhelming and distracting with all its features. I want a program which only have bezier patches and transformations on them, as well as fill, stroke and possibly opacity settings.

Going from concepts to a prototype

I had been wanting to try compile to JS with Kotlin for a while, so I started a project in IntelliJ and quickly threw something together using a plain HTLM5 Canvas.

We drew some more concepts, and after some evenings implementing we had an infinite randomly generated castle, an arrow firing princess, a hyperactive bow carrying giraffe, and a bunch of collision detection bugs (yay for rolling your own).

Wriggling out of hard requirements

After a lot of fun triggering bugs, my daughter came up with some new requirements.

I want to play with my friends, and we should all be princesses!

These are sort of hard to implement, disregarding networking, it would mean a total rewrite of how the world generation and camera worked. It would also need a solution for how to avoid someone getting stuck due to the camera movement of others and so on.

Those giraffes are in for a surprise.

After some bargaining we made some new concepts, and we agreed to add a player controlled cloud, and a bunch of new giraffes.

Adding networking

For me this meant that I would need to add some kind of networking to the game. For browser games, the choices are:

  1. Communicate with a server using WebSocket and have that relay state, or run the game on the server.
  2. Negotiate a WebRTC datachannel, and send communication directly between the browsers.
  3. Have players install a browser extension like netcode.io,and use it instead of WebSocket.

Since the game is cooperative, there is little reason to run the game on a server. Actually I really, really do not want to run the game on server, for a bunch of reasons, mostly for abuse and scaling troubles.

Using a server as a relay of state or input is also a bit funky, since it will introduce a lot of unnecessary latency. Since I am also willing to sacrifice some poor kids behind a symmetric NAT, I decided for option 2 and I have not regretted that.

I was cautious about doing this initially, since I had read this Gaffer on Games post which deemed WebRTC too complex, though that was in the context of server based architectures.

Having some more experience with WebRTC now, I agree a bit about the complexity, though I think it has gotten way better, especially with a more stable standard and more complete alternative implementations like rawrtc. I also ♥ how WebRTC abstracts away most of the P2P complications behind a very nice API.

Autorative peer or GGPO?

To share state in the game, I needed to come up with an architecture for networking. Initially I evaluated using something like GGPO, but in the end I chose to go with using the princess peer as an autorative peer, and sync the state to the cloud playing peer continuously, while the cloud peer only sends input. I chose this mostly for simplicity and time constraints. Since the game is cooperative, a lack of fairness is also not really a problem.

For the amount of work i put in, I am very pleased with how the networking worked out. Right now it is not tuned at all, just JSON over the datachannel, but even without tuning and no extra speculative integration, it has worked fairly well.

Where to go from here.

While the game is in a state of continuous updates, I think it is mostly just going to be small changes from now on. Maybe some sound effects and new graphics when we feel like it.

Rendering is currently also quite slow, and takes a lot of the frame budget. I would like to migrate to a framework with a WebGL based renderer. But sadly that seems like quite a bit of work, mostly due to using SVGs for graphics.

For future projects game projects, I will for sure start with a WebGL based framework, or possibly Unity tiny, and raster based images.

That is all for now, go and see how far you can get in our game!

Attempting to solve Get 1000

For quite some time I have been trying to completely solve the Get 1000 game. More specifically I am trying to find the strategy in a 1 on 1 game of Get 1000 that maximises the chance to win.

Analysis of a game with one choice left. If I analyse this sub-game using expected value, I return the average of the distances to 1000. In this case 184 for strategy 1 (S1) and 107 for strategy 2 (S2). This is the wrong metric though, a better metric (if the goal is to win in a 1 on 1 game) is to count wins for each strategy. In this case 1 draw, 1 win for strategy 1 and 4 wins for strategy 2.

Solving for expected value rather then winning

My initial attempt at solving the game failed spectacularity, since I attempted to solve the game by minimising the average distance of the expected value to a 1000. This is an easy to compute strategy (using a sort of bottom up dynamic programming, where I start with the easy sub-games above, and calculate backwards to the top), but it is the wrong goal. This leads to a strategy minimising the distance to 1000 on average. This interestingly enough differs quite a lot from the goal I wanted to solve, which was to maximise the chance to win any 1 on 1 game.

The strategy that bases itself of minimising the distance to 1000 curiously has a big lump of results around a distance of 50, while the win based strategy has more games at distance of 0 and 100, as well as more games with very heavy over or undershoot.

Since Get 1000 is quite small I can calculate how much the two strategies differ by running all possible games. Above is the result of such a calculation. The two strategies draw 41.2% of the time, while the win based wins 30.8% and the distance based wins 28% of the time.

Trouble with situations where choices are equally good

After figuring out I had the wrong goal, I found a way to create a strategy based on wins rather than expected value (this is much harder to compute, even using the same bottom up approach, since it is not possible to collapse results to an average, and ever growing lists of results must be compared). These strategies I suspect are very close to optimal, but there was something funky going on.

There are situations in my calculations where two placement choices have equal amounts of winning sub-games. Initially I thought I could just set an order of preference of my choice for these, but the resulting strategies beat each other when applied to all possible games. If the order of preference did not matter this should not happen.

For the longest time I could not figure out why this happened. I started questioning whether the markov property held in the game (I am still not 100% sure it does).

Enlightenment

At this point I took a few steps back and looked at what would be the correct framework to model this game in. Turns out it can be modelled as a Markov Decision Process. That in itself was not very helpful, but it eventually got me reading about the expectiminimax algorithm. Expectiminimax is a version of minimax for games with chance involved. While I had to modify it a bit for a simultaneous turn game, I implemented it for some subproblems of get 1000, which I could calculate to the bottom.

While implementing it I realised that I again would have to code resolution for when two choices are equally good. While googling a bit about that, I randomly read about Nash Equilibrium, and mixed strategies. I was already aware of most of this, but it suddenly it dawned on me that my game might contain mixed strategies which could effect the outcome my expectiminimax calculation, and which I needed to take into account.

Wrong payoffs propagated in expectiminimax

Indeed, after searching for a bit, I found several cases where a mixed strategy is needed. The example below shows a expectiminimax situation where a mixed strategy is needed to get the best outcome.

A Get 1000 situation as solved by expectiminimax. The two games on top are the current situation for two players. To make a decision in expectiminimax we must then compute the payoff matrix by recursively analysing all possible sub-games until the end (returning expected payoffs), and then solve the payoff matrix. Using the solver here, this particular sub-game has the payoff of -98/39 (- means in favour of player 2). In this situation: Player 1 should play ones at ratio of 23/39 and hundreds 16/39, and player 2 should play tens at a ratio of 11/39 and hundreds 28/39.

While this exact situation will probably not arise assuming perfect play, the result still might matter since expectiminimax depends on all subgames propagating correct payoffs.

The road ahead

I need to include the support enumeration or theLemke-Howson algorithm for finding nash equlibrium in the placement situations that require it, and then I need to somehow make expectiminimax run for the full game. Currently I can only run expectiminimax (without Lemke-Howson) in reasonable time, for a game which has 6 placements left.

From AI: A modern approach, it seems A/B pruning can be used, but it seems to be less effective on games with chance. I guess it is worth a shot.

Gl hf to me…

Scary pitfalls when using Spring annotation based transactions

transactions and exceptions

Spring annotation based declarative transactions uses AOP to very easily add transactions around methods. Using it looks like this.

@Transactional
public Stuff createStuff(Input input) {
       Stuff stuff = new Stuff(input);
       dao.storeStuff(stuff);
       dao2.registerStuff(stuff2);
       return stuff;
}

Explained very quickly: If the method returns successfully then it commits, if a runtime exception passes the proxy boundary around the method, or if the transaction is marked rollback-only, then the transaction manager will do a rollback of the transaction.

It is incredibly easy to use, and it saves a lot of boilerplate compared to a more procedural approach where commit and rollback calls are specified explicitly. While useful, it comes with the cost of being tied to the scope of the annotated method, along with several other more hidden risks and costs.

Below are several examples of problematic code I have seen caused by annotation based transactions. Similar code examples and tests can be found in this repo on Github.

Catching exceptions in a transaction annotated method

In the method below, it is very easy to think that all errors are handled, and that this method will never throw, but if the transaction is marked as rollback only, this method will throw outside the try catch block. Breaking expectations and causing unexpected errors.

@Transactional
public Stuff createStuff(Input input) {
       Stuff stuff = null;
       try {
           stuff = new Stuff(input);
           dao.storeStuff(stuff);
           dao2.registerStuff(stuff2);
       }
       catch(RuntimeException e) {
           logger.info("No problem…");
           //Do more stuff
       }
       return stuff;
}

This is much more visible with a explicit transaction scope. I have seen this several times, even by experienced developers. These errors are hard to test for, and when they happen lead to very weird behaviour, since the exception is absolutely not expected where it suddenly occurs.

Order of proxies can change outcome of transaction

It is critical that AOP interceptors are stacked in a sensible order. We usually do not want to commit a transaction, and then get a timeout error from Hystrix. Or have the transaction commit, and then have validation constraints on the Stuff instance fail. Ask yourself. Do you know in which order each annotation will be applied here? Does everyone on your team know?

@Transactional
@HystrixCommand("abc")
@Valid
@OtherAOPstuff
@EvenMoreAOPStuff
public Stuff createStuff(Input input) {
       Stuff stuff = new Stuff(input);
       dao.storeStuff(stuff);
       dao2.registerStuff(stuff2);
       return stuff;
}

The order by default is (though due to this Hystrix bug/feature validation will never be applied O_o) :

  • Transaction start
  • Hystrix
  • Validation
  • Validation
  • Hystrix
  • Transaction commit/rollback

It would be nice to have Hystrix outside the Transaction, since that avoids the transaction boundary when the short-circuit is open. This is possible with ordering the AOP interceptors,at the same time, it is important to avoid Validation happening outside the Transaction, since then we might commit and then throw an exception (typically a rollback is wanted if data is invalid).

Nested transactions joins existing transaction by default

This is very nefarious, and I have no idea why nesting transactions does not cause an exception by default.

The example that I think best shows this problem, is when you reuse a method in a service class which uses a transaction further down the call chain. That method uses a transaction to ensure it is rolled back if it throws an exception, but the calling method catches that exception and does some business decision based on the exception.

Now along comes an unsuspecting victim who has a transactional method that wants to use this method for some business purpose.

What happens now, is that the second transaction joins the first. Then an exception is thrown by one of the database queries in moveStuffInDB. That exception passes the first transaction boundary marking the transaction rollback only but is then caught. Processing continues, and then the exception reappears at the last boundary on commit. This means that the semantics of reusedMethod might have been changed a lot, and there is no way createStuff can see from the outside that this will happen.

@Transactional
public Stuff createStuff(Input input) {
       Stuff stuff = new Stuff(input);
       dao.storeStuff(stuff);
       reused.reusedMethod(stuff.getInfo());
       return stuff;
}

//A method in another class calling another transactional method.
public void reusedMethod(String input) {
     try {
         deepClass.moveStuffInDB(input);
     }
     catch(RuntimeException e) {
         //Swallow exception and do some action
     }
}

//Tx method with several db update calls
@Transactional
public void moveStuffInDB(String input) {
      dao.moveStuff(input);
      dao2.moveStuff(input);
}

To add to the confusion, use checked exceptions

When a checked exception passes the boundary of an @Transactional annotated method, it does not cause rollback by default (it can be changed in the annotation though). Add Spring Batch, which will also start transactions that a nested transactions will happily join, and transaction outcomes become even more foggy and hard to reason about.

I think using nested transactions usually is a bad idea, and it should be an opt in feature. In the normal case throwing an exception if a transaction within a transaction is encountered seems sensible to me.

Lambdas provide a much better API for transactions

In any language with good support for lambdas, I think it is very natural to do declarative transaction management using them. Spring sort of supports this, but you need to depend on a platformTransactionManager and a TransactionTemplate. This seems weird to me, given that the annotation based transactions does not make you depend on these.

With lambdas, transactions can be done like below (example is using Kotlin). This is declarative, while providing explicit transaction boundaries. It is therefore very easy to catch around the transaction, and the transaction does not have an unclear order when combined with other annotations.


fun createStuff(stuff : Input ) : Stuff {
       return doInTransaction { //Explicit tx scope
           val stuff = new Stuff(input);
           dao.storeStuff(stuff);
           dao2.registerStuff(stuff2);
           stuff 
       }
}

fun multipleTransactionsInMethod(stuff : Input ) : Stuff {
       val res = doInTransaction {
           val stuff = dao.storeStuff(stuff);
           stuff;
       }

       val res2 = doInTransaction {
           val stuff = dao2.storeStuff(stuff);
           stuff;
       }

       try {
           doInTransaction {
              dao.storeStuff(stuff);
            }
       } catch(e : RuntimeException) {
           //Handle stuff
       }
} 


Along with the previously mentioned advantages, this also makes transactions much more visible, and allows easy inspection of the transaction code by developers.

To be honest I am a bit uncertain how good it is to rely on exceptions passing boundaries to do rollback in the first place, but if that is the chosen way, I think the above approach is much better then annotation based transactions. I am really looking forward to try Exposed, which is an ORM tool from JetBrains that seems to go in this direction.

Draft Engine

Start a draft

For a while I have been working on a generic draft engine for card games. In trading card games (TCGs), drafting is a way to distribute cards in a semi random way, where players interact with how cards are distributed. In the TCG world this is distinct from sealed deck (semi randomly distributed cards, but no player interaction during dustribution) and constructed (you design your deck before playing from a set of allowed cards).

Supported draft styles

My draft engine supports two styles of draft:

  • Grid draft: A draft style for two people where you select rows or columns of cards from 9 face up cards.
  • Regular draft: In this draft style you pick a card from a pack and pass the pack to the next player. It works with 2-8 players, but 6-8 is recommended.

grid draft
The draft engine in action. This example is an Magic the Gathering grid draft.

These forms of draft can be used for most kinds of TCGs. Since the engine is not tied to any specific kind of game, you can draft anything you can give a name and an image. You can draft your family photos if you want to.

Drafts with custom content

The engine works by using a very simple JSON structure to supply card names and card images, it looks like this:

[
  [
    {
      "name": "CardOnePackOne",
      "url": "http://crazymedia.com/cardonepackone.png",
      "id": 0
    },
    {
      "name": "CardTwoPackOne",
      "url": "http://crazymedia.com/cardtwopackone.png",
      "id": 0
    }
  ],
  [
    {
      "name": "CardOnePackTwo",
      "url": "http://crazymedia.com/cardonepacktwo.png",
      "id": 0
    },
    {
      "name": "CardTwoPackTwo",
      "url": "http://crazymedia.com/cardtwopacktwo.png",
      "id": 0
    }
  ]
]

The values are pretty self explanatory, but for clarity:

  • “name” – The name of the card, which you can export when finished drafting.
  • “url” – An URL pointing to an image of the card.
  • “id” – Not in use, so 0 is a fine value.

The engine comes with several predefined card list. Packs will then be drawn from those lists, but if you want to supply your own set (for example a cube or your own game) it is possible to start a draft where you send in any number of packs of cards using the JSON format shown above.

Have fun drafting.

Writing a WebRTC data channel implementation

After looking at webtorrent a while ago I really wanted to dig deep down into WebRTC to see how it actually worked. WebRTC is a web standard that allows two browsers to set up a peer to peer connection (usually browsers only talk through intermediary servers). It also brings unreliable and unordered networking to the browser, which is great for some kinds of applications.

WebRTC

Searching for WebRTC and Java on Github mostly gave me some very simple applications that use a Java server to set up a peer to peer application between two browsers. There also seemed to be some unmaintained JNI wrappers for the WebRTC libs. What I wanted was a pure Java WebRTC implementation so that I could talk directly to the browser more on my terms.

Since this was lacking I decided to try to write my own Java WebRTC implementation. To limit the scope, I decided that I would only try to talk to Firefox, and only support an unordered unreliable DataChannel. Which is WebRTC’s greatest selling point for me. What I ended up with can be found on my profile on GitHub. It is not pretty or solid, but it sort of works.

Protocols

WebRTC is made up of bunch of protocols: ICE (to establish communication), STUN (binding and NAT traversal), DTLS (encryption), SCPT (over UDP) (message flow control), TURN (fallback for difficult network situations, which I have chosen to ignore).

The initial part of starting a WebRTC connection uses the ICE protocol, the ICE protocol is typically carried out over an encrypted WebSocket connection, though you can use encrypted pigeons if you like.

To be honest I have not looked a lot at ICE, but the parts most relevant for WebRTC works a bit like this:

  • A goes: This is my password and certificate signature, this is referred to as an offer.
  • B goes: This is my password and certificate signature, this is referred to as an answer.
  • Then A and B send each other different options of connectivity as candidates. I am currently blissfully ignorant of how this is supposed to work, in my current implementation I just send the first candidate from the browser and replace IP, port and auth data in the response.

The message format used in the browsers WebRTC implementation for offers and answers is JSON containing an SDP. The SDP contains tons of information that is not used (afaik). The values I have touched are marked in green below, for more information about the fields, this is a great overview.

The green highlights the important parts of the offer and candidate
The important parts of the offer and candidates, this is SDPARTA!

Important SDP values:

  • fingerprint:sha-256 – DTLS certificate sha-256 fingerprint.
  • ice-pwd – Your chosen password for STUN.
  • ice-ufrag – Your chosen user for STUN.
  • 192.168.1.100 58713 – Your offered address and port.

STUN

Once candidates have been exchanged, a STUN binding request is sent to establish connectivity, this request must be responded to with a binding response with a xor mapped address. The received message integrity hash is a HMAC-SHA1 which can be checked against the message hashed with the ice-pwd as key.

DTLS

After the STUN the next step is a DTLS handshake. Thank you Legion of the Bouncy Castle, without you I would have given up here.

Over the same UDP socket where DTLS is running, STUN must be multiplexed. STUN is here used to send “consent” requests every X seconds. If you do not respond to the STUN the browser reports ICE error and shuts down the connection. Bouncy Castle DTLS will silently drop these STUN “consent” packets, so this was a pain to figure out and debug.

SCTP

Once the DTLS is set up an SCTP connection is initiated. SCTP can be configured to work in all constellations of ordered/unordered and reliable/unreliable.

SCTP over UDP challenges

With SCTP over UDP several issues crop up. My main languages are all JVM based (Kotlin, Java). There is no SCTP implementation in Java, but there is an API for the systems SCTP. The API is very hard to integrate with an UDP socket though (I tried a bit, but it seemed very hard), so the simpler solution is probably to use a userland C lib like the one used by libjitsi.

Sadly i did not know libjitsi existed so I started hacking my own SCTP implementation in Java land. Way more fun…

Writing my own SCTP implementation

The SCTP spec is mostly ok, if a bit unclear in some parts. Once I found the SCTP parameter list it got better. It should also be mentioned that SCTP uses a CRC32C for checksums, this differs from the one used by STUN. This took me quite a while to figure out.

I currently have a very minimal “working” SCTP implementation. Meaning that it can talk to a browser, but does not shut down nicely, and does not do congestion control, and does not handle resends properly. These are very tricky areas to do well, and I have no clue, so I will probably change to use the lib used by libjitsi.

Getting the all important firefox logs

To not go in blind when debugging, logging from the connected browser is invaluable. This is my script to run firefox with WebRTC logging. The different modules can be turned on and off by not including them in the NSPR_LOG_MODULES. It took me a while to figure out the correct modules, so hopefully this helps someone else.

#!/bin/bash
dat=`echo ~`
path="$dat/webrtc_firefox.log"
export NSPR_LOG_FILE=$path
export NSPR_LOG_MODULES='signaling:5,mtransport:5,SCTP:5'
export R_LOG_LEVEL=9
export R_LOG_DESTINATION=stderr
open /Applications/Firefox.app/

Where is the code?

If this was interesting and you want to take a look at the source code. It is available on my GitHub profile.

Webtorrent; we get signal.

Lately I have been looking into WebRTC which is an open standard for real time communication between browsers. It allows communication styles in the browser which previously were not possible.

WebTorrent uses WebRTC for a protocol similar to bittorrent. Instead of having to download a program or install a browser plugin, you can download a webtorrent (which currently must be seeded as a webtorrent, by forexample instant.io) directly in the browser.

To test Webtorrent, I made a small javascript project. WT-widgets, is a collection of graphics for starting webtorrent downloads and showing download progress. Below is an example where you can download Artifact for Mac OS X using webtorrent.

No seeds

If there are no seeds, you can seed the file yourself by visiting the differently styled button below. This button uses a feature of WT-widgets that does a fallback to XMLHttpRequest after 5 seconds. When it is finished downloading the file, it will start seeding. Then the first button should work, since there is a seed.


The file will be downloaded in your browser, and you can then copy it to your filesystem by clicking the link that appears when the file finished downloading. This does not follow the usual download flow, so one of the aims of WT-widgets is to ensure that it clear to the user that a download is happening. I am not sure how well my widgets succeed in that regard, as my current widgets might not be the best at communicating that there is a download happening.

Suggestions or pull requests with fixes/additions are always welcome. I hope to expand WT-widgets with some widgets that show progress horizontally, as well as some widgets that more clearly show when it is in the different states of a download.

What Webtorrent sorely needs

While seeding in the browser works great, I do not want to have a browser fired up at all times to ensure there are seeds for my content. The best option I found for seeding webtorrents was webtorrent-hybrid, but when I tried it, I sadly could not get it to build.

Once Webtorrent has a solid solution for server side bootstrap seeding, I think it is will become a great alternative for distributing some kinds of content.

Take off every ‘ZIG’!!

Scape – a very ninja scripting language


I made a small scripting language that runs in the browser. It is very ninja. To see the ninja, first open Javascript console and write:

function recur() {recur()};recur();

Hopefully it blew the stack. Then type this into the Scape REPL:

def recur() recur(); recur();

When you are convinced it will infinitely loop without blowing the stack, hit ctrl-c to stop further processing.

Rincewinds rave, that is black magic! Also called tail call elimination. Scape code is not evaluated by snarfing functions from Javascript (JS functions do not have tail call elimination before ECMAScript 6), but instead is compiled to its own set of instructions, which are then run on a stack machine (running in the Javascript VM). During parsing Scape functions are checked for whether they can use tail call elimination. If they can, they get different instructions that reuse the existing stack frame.

More magic

Scape has forward mode automatic differentiation as a language feature. Automatic differentiation allows you to compute the derivative of a function, without having to define the derivative explicitly.

Without automatic differentiation, this would be the way to compute the partial derivative of the function f(x,y) =  x^{2}y^{2} for x and y:

def fun(x,y) * (* x x) (* y y);
def diff_fun(x,y) [* (* 2 x) (* y y),* (* 2 y) (* x x)];
diff_fun(4,5);
[200, 160]

With automatic differentiation in Scape, this is how it is done:

def fun(x,y) * (* x x) (* y y);
diff(fun(4,5));
[200, 160]

This is very useful for a number of numerical methods involving derivatives. The feature is currently experimental, it might interact with non-double types in funky ways.

Wai?

Mostly just for fun. I also started toying with the idea to make a safe scripting language for use in networked games. A language and runtime that would allow the player to define custom logic during gameplay without being able to ruin the experience for other players.

A dream would be a personalized Starcraft where it is you and your custom control scripts versus the other player and his scripts.

I hope to create a simple real time multiplayer game to show how I imagine it working. For now, playing with the Scape REPL is the only way to try the language.

Sayōnara

Prepare your Welding Blaster; play Artifact

I made a computer game together with Nils Eriksen Meling and Sven Meling; It is named Artifactgo try it! It plays similarly to Barrack, a favourite game from my youth. In addition to the action and strategy found in Barrack, Artifact also adds an aspect of resource management.

blaster
Prepare your Welding Blaster, the Artifact is a cruel mistress

In Artifact, each of 40 levels consists of a screen filled with a variety of different orbs. These orbs must be isolated by you. Once 75% of the playing field has been isolated, the level ends. You are rewarded for playing fast, and for ending the level with a high % of the screen isolated.

crystalsOn
Electricity is key

To accomplish your task you control a dual-direction Welding Blaster that can be transformed to fire vertically or horizontally. When fired, a welding beam will slowly traverse the screen in 2 directions. Once both ends reach a wall, the playing field will be cut, isolating balls on each side of the beam. However, care must be taken not to hit the orbs, as they will create a feedback surge, damaging the Welding Blaster.

future_whole
I hate orbs

Artifact is free and will stay so, but developing and maintaining it is not free. If you enjoy Artifact, I hope you will consider a donation. However, most of all, I hope you enjoy playing it.
If you have problems with installation on the supported platforms, please send a mail to: .

Download Artifact

Useful if caught in overly simplistic space combat

One of my favorite games, and by far the one I used the most time creating content for during my youth is Escape Velocity Nova. The Escape Velocity series are 2D space RPGs, which means there is lots of 2D space combat. In these types of games you typically have three main types of weapons, non-turreted, turreted and homing. Non-turreted and homing weapons are not really that complicated. The non-turreted fire in one direction (typically forward), while the homing weapon typically turns as hard as it can towards the target at maximum speed. Turreted weapons were always a puzzle to me though, they somehow knew where you would be, and fired to intercept your ship. I always wondered how this was done.

Some years later during a visualization class (on how to find intersections between geometric primitives) I was wondering if I could use geometric equations to figure out where a spaceship needs to aim its torpedo, if it knows the position and velocity of the target. Below is the solution I came up with. It assumes constant speed for the target and the torpedo.

The positions of something moving at constant speed, can be described by this equation where t denotes time, \vec{v} the current velocity and \vec{p_o} is the starting position. This restricts the position of the target to a line, where the position on the line is determined by t.

(1)   \begin{equation*} \vec{p} = \vec{p_o} + \vec{v}t \end{equation*}

For 2 dimensions this is:

(2)   \begin{equation*} \begin{pmatrix}p_x\\p_y\end{pmatrix} = \begin{pmatrix}p_{xo}\\p_{yo}\end{pmatrix} + \begin{pmatrix}v_x\\v_y\end{pmatrix}t \end{equation*}

The possible locations p of a constant speed (s) bullet fired from point c in any direction, are given by this equation, where again time is denoted by t. This restrict the possible positions to a circle which expands with time.

(3)   \begin{equation*} (st)^{2} = (\vec{p} - \vec{c})^{2} \end{equation*}

For 2 dimensions this is:

(4)   \begin{equation*} (st)^2 = (p_{x} - c_x)^2 + (p_{y} - c_y)^2 \end{equation*}

Now inserting the restrictions on p_x and p_y from 2 into 4 gives a polynomial that only depends on t:

(5)   \begin{equation*} (st)^2 = ((p_{xo}+v_xt) - c_x)^2 + ((p_{yo}+v_yt) - c_y)^2 \end{equation*}

Rearranging gives:

(6)   \begin{equation*} s^2t^2 = (p_{xo}-c_x + v_xt)^2 + (p_{yo}-c_y + v_yt)^2 \end{equation*}

Simplifying by setting constants i = p_{xo}-c_x and j = p_{yo} - c_y and moving towards standard form:

(7)   \begin{equation*} s^2t^2 = (i)^2 + 2iv_xt + v_x^2t^2 + (j)^2 + 2jv_yt + v_y^2t^2 \end{equation*}

Rearranging to standard form:

(8)   \begin{equation*} 0 = (v_y^2 + v_x^2 - s^2)t^2 + 2(iv_x + jv_y)t + (i)^2 + (j)^2 \end{equation*}

This is a quadratic equation, with coefficients:

(9)   \begin{equation*} a = v_y^2 + v_x^2 - s^2 \end{equation*}

(10)   \begin{equation*} b=2(iv_x + jv_y) \end{equation*}

(11)   \begin{equation*} c=i^2 + j^2 \end{equation*}

Solving the quadratic equation gives two solution for t, if an answer is positive and has no imaginary part, there is a solution to the problem.

Inserting a solution for t in equation 1 gives the x,y coordinates where the torpedo should be aimed, and where it will hit the target.

Below is an implementation of this, where the constant speed of the torpedo can be set. If there are two solutions, the smallest t is chosen. If there is no solution (typically because the target it too fast for the torpedo to catch) the torpedo is never launched.

 

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As you can see in some cases, this does not take into account the size of the target, only the targets center. This can be remedied by using a representative selection of boundary points of the target instead, and firing if one of them would connect.

The solution does also not take into account how fast the target can change direction, or when the torpedo runs out of fuel. This can be handled by not firing if the time from the torpedo is fired to the impact is too long.

This method can also quite easily be expanded for an accelerating weapon or target. This will result in a higher degree polynomial though, which are mostly only possible to solve using numerical methods like Newtons’s method for example.