James Tauber

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Eldarion Launched

With my visa finally getting processed, me being able to be employed by the company I helped found and my return to the US, I am delighted to be able to announce that we've launched the Eldarion website and with it, the company.

http://eldarion.com/

Just a single page at the moment, but I think it's a good start. Thanks to Ryan Berg for turning my initial design into something good looking. And of course thanks to Greg Newman for the logo, which I've previously talked about.

by James Tauber : Created on June 29, 2009 : Last modified June 29, 2009 : Categories django announcements pinax : (permalink)

Affianced

Well, it's been a two-and-a-half month blog drought but it's worth breaking for this news.

Two weeks ago, the love of my life, Lisa, and I got engaged in Paris.

Of course if you follow me on Twitter or Facebook, you knew that at the time (or shortly thereafter) but it felt like it should be declared here too!

I first met (and fell for) Lisa in 1992 although didn't see her again until 1996. People often ask me what took me so long to ask. Truth is, I would have proposed in 1996 (okay, maybe 1997) if I thought she would have said yes. I guess entrepreneurs and lawyers have different risk profiles :-)

My time with her, especially the last four years, have been the best of my life.

I'd always imagined I'd marry my best friend. And now I will be.

by James Tauber : Created on June 25, 2009 : Last modified June 25, 2009 : Categories announcements personal : 6 comments (permalink)

Pinax Video and Move to GitHub

The audio isn't great (they didn't seem to be directly recording the mic I was holding) and it got cut short, but for what it's worth, here's the video of my talk on Pinax at PyCon 2009:

http://blip.tv/file/1952623

Following the conference proper, we had a great sprint that got us within a stone's throw of a 0.7 beta release. One of the first things we did was move from svn at Google Code Project Hosting to git at GitHub. The new home of the Pinax source code is now:

http://github.com/pinax/pinax/

We also moved our wiki and task tracking off Google Code Project Hosting to our own, Pinax-based system:

http://code.pinaxproject.com/

Enjoy!

by James Tauber : Created on April 7, 2009 : Last modified April 7, 2009 : Categories pycon pinax : 4 comments (permalink)

The Long Pay Off: Battlestar Galactica and Lost

NOTE: This may contain SPOILERS for Babylon 5, Battlestar Galactica and Lost.

I'm a big fan of episodic television with long arcs. I love pay-offs that are separated by months or even years from their initial set up, where you can go back and watch earlier episodes and see things you never noticed before.

Back when I was watching the X Files, it was always the so-called "myth arc" episodes I liked and never the "monster of the week". But it eventually became clear that even the myth arc episodes in the X Files were being made up as they went along. I felt duped.

So it was with great anticipation in 2000 that I started watching reruns of Babylon 5, a show famous for having been planned out in advance. Despite numerous flaws, this planning paid off multiple times. There were multiple OMFG moments where you realize how pieces of the puzzle from previous seasons fit perfectly together. In one classic multi-season arc there is a mysterious episode in season 1 involved time travel two years in the future. In season 3 you see the other half. Amazing stuff that would be very hard to pull off without the show being planned in advance.

Of course there are dangers with planning in advance. B5 suffered from story changes due to actors leaving.

This brings me to two of my favourite shows on TV at the moment: Battlestar Galactica and Lost.

Lost has supposedly been planned in advance and BSG largely made up as they went along.

If you'd asked me at the end of last year, I would have said the two shows were counter examples to the need for planning in advance. I didn't feel like Lost was giving me the payoffs and I felt like BSG was doing a great job without the long arcs. This year I've changed my mind. Lost is starting to get some pretty cool payoffs (although it could still screw things up) and BSG is breaking up under the stress of not being worked out in advance (although perhaps the finale will redeem it).

At least BSG had a definite end point planned for a while. There's nothing worse than a show that pretends to be teleological but is being written ad hoc with no real end in sight.

There are also opportunities available to the story teller when things aren't planned too much in advance. With BSG I didn't feel there were any truly amazing payoffs (again, the finale could prove me wrong) but there were certainly moments that were so out of left field and unpredictable it made for awesome story telling. It leads to a completely different kind of OMFG moment. Had BSG been planned in advance, those events might have been easier to see coming.

I guess that's the trade off. Plan in advance and you can get amazing payoffs but you run the risk of leaving too many clues so there are no real surprises. Write ad hoc and you can totally surprise the audience but also expose yourself to too many plot holes. BSG has one more shot to see if it can successfully close some of those holes.

Despite their flaws, I think Battlestar Galactica and Lost are both excellent examples of what works about each approach.

UPDATE: Here's a (spoiler filled) post on 12 Plotholes That Must Be Filled in the Battlestar Finale

by James Tauber : Created on March 20, 2009 : Last modified March 20, 2009 : 2 comments (permalink)

Eldarion Logo

For years, I've had "Eldarion" in the back of my mind as a name I'd like to use for some creative endeavour. It is a reference to Tolkien: Eldarion was the son of Aragorn and Arwen and the Second High King of the Reunited Kingdom.

Much to my surprise, the domain was available when I checked back in 2002, so I registered it immediately.

At first I thought I'd use the name for my film and music endeavours. When I attended SXSW Film and Music in 2005, I actually had business cards printed that said "Eldarion". They were black cards with white writing, a reference to the Gondorian flag.

I planned a logo that would feature the White Tree of Gondor and the seven stars of the House of Elendil but never had the skill to pull it off.

With a need for a logo coming up again recently, I approached my friend Greg Newman. My brief to him was pretty much as follows:

• use the text "eldarion" in Anivers (the font family I'd chosen a couple of months earlier)
• feature some reference to the White Tree and/or the Seven Stars
• make it silver on dark grey rather than white on black to give it more life

He blew me away with the result and the response has been phenomenal.

It may strike some as unusual to choose a fantasy reference for a high-tech startup. But I'm reminded of a wonderful scene in the British comedy Yes Prime Minister where the PM is advised that if his first television broadcast is to say nothing new and exciting then he should wear a modern suit, the background should feature abstract paintings and the opening music should be Stravinsky. On the other hand, if the broadcast is to contain radical new announcements, then he should wear a dark suit, the background should feature oak paneling, leather volumes and 18th century portraits and the opening music should be Bach.

The same idea applies, I think, to choosing ancient symbols from the legendarium of Tolkien for what is intended to be a very modern and forward thinking new company.

Stay tuned for lots more about Eldarion.

by James Tauber : Created on March 2, 2009 : Last modified March 2, 2009 : 6 comments (permalink)

Kindle 2: First Impressions

I was asleep when I heard a knock at the door. I knew it was UPS. I jumped up and threw some clothes on but by the time I got to the door, they had gone. I ran down the hall to the elevator. I had just missed them. Caught the next elevator and caught them in the lobby of my apartment building just as they were leaving. Phew! I had my Kindle 2.

I didn't have the original Kindle and I've never used any kind of electronic reader so this was a new experience for me. I love books and own A LOT of them. But spending time on three continents, at conferences and on airplanes means I'm looking forward to more books at my fingertips and avoiding the agony of "which 0.1% of my books can I take with me on this flight".

Here are my first impressions:

• they put thought into the unpackaging experience
• even though I've seen the photos, it still seemed smaller once I held it in my hand than I thought it would be
• the Amazon leather cover I bought adds a bit of weight and bulk to the device
• the fact the screen can show stuff while the device is turned off freaked me out at first
• the device is comfortable to hold and I imagine being able to read for long periods with this
• as an electronic-ink newbie, I was very impressed by the readability of the screen
• I didn't like the font when I first looked at it but once I started reading it didn't bother me
• it worked out of the box, was linked to my Amazon account and had a book I'd bought before the device arrived
• knowing how far I am through a book as a percentage is a little freaky at times
• it took me a little while to get the handle of the navigation (beyond basic turn pages, which is easy)
• text-to-speech is impressive but can't imagine using it
• I wish trying to go up from the first selection would wrap around to the bottom selection. It's too cumbersome to select a choice towards the end of the screen
• downloading books is FAST — couple of seconds for each of the two books I bought
• browsing web pages is like turning CSS off
• User Agent came through as "Mozilla/4.0 (compatible; Linux 2.6.10) NetFront/3.4 Kindle/1.0 (screen 600x800)"
• I'm already thinking about web applications for it (especially my graded reader ideas and flashcards)
• the immediacy and ease at which you can buy books could be dangerous :-)

I'm very happy so far and can imagine buying the majority of my books for the Kindle from now on. The real test will be whether I'll go back and re-buy any of my existing books (especially the ones back in storage in Australia)

UPDATE: just discovered the Web browser has an Advanced Mode that does CSS and Javascript. This site doesn't look too great with it, though :-)

by James Tauber : Created on Feb. 25, 2009 : Last modified Feb. 25, 2009 : Categories books kindle : 1 comment (permalink)

Leaving mValent

People who follow me on twitter or are friends on Facebook already know this, but last week I officially resigned from mValent.

It was over seven years ago that Duane Tharp and Clyde Logue approached me about joining them in a new venture post-Bowstreet. I had already made the decision to move back to Australia from the US and they were still willing to hire me despite being remote. Within a year we were venture funded, had hired a CEO and VP Engineering (who became my boss) and were starting to build the team.

mValent went through distinct phases and so I don't necessarily feel like I've worked in the same place for seven years but rather three or four different companies. I don't think I ever really did the job I thought I would be doing, but I learnt a tremendous amount on the business side of things and made a number of really good friends.

But it's time for me to move on. The technology I helped create and the people I helped hire now have an excellent home at Oracle. I'm ready for something new.

As to what's that is: I hope to have more to say very soon...

by James Tauber : Created on Feb. 23, 2009 : Last modified Feb. 23, 2009 : Categories mvalent announcements personal entrepreneurship : 4 comments (permalink)

Reading Apple ][ DOS 3.3 Disk Images with Python

I was feeling nostalgic for the days of Apple ][ DOS 3.3 and started re-familiarizing myself with the disk layout (VTOC, catalog entries, track/sector lists, etc)

Of course, I couldn't help but then implement them in Python.

Here is a python module that reads Apple ][ DOS 3.3 disk images and can both list the disk catalog and also dump the contents of a file.

http://jtauber.com/2009/02/15/a2disk.py

Enjoy!

by James Tauber : Created on Feb. 15, 2009 : Last modified Feb. 15, 2009 : 3 comments (permalink)

Oracle to buy mValent

People who follow me on twitter already know this, but yesterday Oracle announced its intention to acquire mValent, the company I helped start in 2002. Congratulations to all involved! We built a great team, then a great product, then made our customers successful with that product. As with any startup, there was always a gap between what we wanted to do and what we could do given our resources. As part of Oracle, mValent is going to be able to close that gap in a huge way.

by James Tauber : Created on Feb. 5, 2009 : Last modified Feb. 5, 2009 : Categories mvalent : 7 comments (permalink)

Population Ratios of Top Three Urban Agglomerations

Some countries have a single large urban agglomeration that is much bigger than other urban areas in the country. Others have three or more major agglomerations that are pretty close in size.

For a while I've wanted to visualize different countries depending on whether they were more like the former or more like the latter.

So I took some data from http://www.citypopulation.de/ and used HTML Canvas to create a bubble plot of all countries with three or more agglomerations over one million people. I used the ratio of the population of the largest agglomeration and the second largest as the y coordinate and the ratio of the population of the second largest and the third largest as the x coordinate.

Here is the result:

Population Ratios of Top Three Urban Agglomerations

Besides this criterion, I can't immediately think of other similarities Argentina, the Philippines, France or South Korea have; or India, China, Italy and the Netherlands; or Russia and Bangladesh.

by James Tauber : Created on Feb. 2, 2009 : Last modified Feb. 2, 2009 : Categories human_development : 0 comments (permalink)

Moving to Distutils

reposted from http://code.google.com/p/django-hotclub/wiki/MovingToDistutils

the how and why of Pinax's move to distutils

Pinax is changing the way that external dependencies are brought in during development on trunk. Note that this document is only talking about changes in how things work and will work on trunk, NOT necessarily how they will work with a released version of Pinax.

Until recently, Pinax had two choices for a given external dependency:

• use svn:externals and point to the external dependency's svn repository
• include the external dependency code in the Pinax codebase

However, there are problems with this approach:

• it largely relies on external dependencies being in svn and this is increasingly not the case (although it was when Pinax started)
• it makes it difficult for Pinax itself to move away from svn
• there is no management of dependencies between external dependencies, nor between particular projects in Pinax and their individual dependencies

To solve these problems and more, Pinax is switching to a distutils-based approach. This means:

• externals dependencies are encouraged to be released as distutil-compliant packages with a valid setup.py and put on PyPI
• development versions of dependencies can be pulled in in a variety of different ways including from git, hg or bzr repositories

In order to develop from the Pinax trunk, you will need to use pip. Because some external dependencies are retrieved via git and bzr you will also need those if using Pinax trunk.

Although we will eventually have per-project requirements files, there are currently two requirements files that describe to pip what dependencies to bring in and how:

• pinax/requirements/libs.txt
• pinax/requirements/external_apps.txt

The former is actually a requirement of the latter so you can bring in all external dependencies with:

pip install -r pinax/requirements/external_apps.txt

We strongly recommend the use of virtualenv in conjunction with pip to allow isolated environments to be set up without Pinax having to hack PYTHONPATH.

by James Tauber : Created on Jan. 31, 2009 : Last modified Jan. 31, 2009 : Categories python django pinax : 2 comments (permalink)

Retweet

@gruber: Theory: the people who send out “RT” tweets are the same fuckers who came in and ruined Usenet a decade ago.

@jtauber: couldn't resist: RT @gruber Theory: the people who send out “RT” tweets are the same fuckers who came in and ruined Usenet a decade ago.

@akuchling: @jtauber ouch! Now I'll feel guilty every time.

@pydanny: @jtauber So very true!

@jtauber: @akuchling I disagree with him but couldn't resist the irony

@jtauber: @pydanny I was just trying to be ironic :)

@curtclifton: @jtauber LOL

@edwelker: Damn straight.

@TokyoDan: @jtauber How’s that? I RT when I think people who follow me might find the subject interesting. And it gets the originator more followers.

@jtauber: okay, I think I'm going to have to spell this out: I don't mind RTs. I was just RTing @gruber's dislike of RTs to be funny

@evilrob: @jtauber: you don't like RTs?

@brosner: RT @evilrob: @jtauber: you don't like RTs?

@20seven: RT @brosner: RT @evilrob: @jtauber: you don't like RTs?

@jtauber: okay, this whole RT thread needs to go on xkcd right now

@mak1e: RT @brosner: @evilrob: @jtauber: you don't like RTs?

@ericflo: RT @20seven RT @brosner: RT @evilrob: @jtauber: you don't like RTs?

@bryanveloso: RT @ericflo: RT @20seven RT @brosner: RT @evilrob: @jtauber: you don't like RTs?

UPDATE: Okay, I now agree with @gruber

by James Tauber : Created on Jan. 28, 2009 : Last modified Jan. 28, 2009 : 6 comments (permalink)

Serving Up User Contributed Media From A Separate Server

One commonly recommended practice in Django (although applicable elsewhere) is to serve up your static media from a different server than the one running Django for dynamic pages.

This becomes a slight challenge when you have user-contributed media (like allowing users to upload photos).

Here are some possibilities I can think of:

• mount the media server from the Django server via NFS so write from Django directly to the media server
• have the Django server write locally but then subsequently move the files to the media server via rsync (or similar)
• like the previous case but to avoid 404s before the file has been moved, the relevant model has a flag for whether the file is ready or not and return an "in progress" message until the file is done (not sure how Django would know the file has successfully been moved, though, unless a Django-based worker process was doing it instead of just rsync)
• similar to the previous two cases but initially store the image on (and serve it from) the Django server until the flag says the URL to the media server can be used
• have Django running on the media server just for the purpose of receiving media POSTs (but no dynamic page generation)
• having some other WSGI (or similar) process running on the media server to receive media (and then communicate with the Django server on the backend)

I guess S3-based solutions add some extra issues but ideas 2, 3 and 4 would be applicable.

Anyone have experiences (good or bad) with any of these? Any possibilities I'm missing?

by James Tauber : Created on Jan. 26, 2009 : Last modified Jan. 26, 2009 : Categories django web : 16 comments (permalink)

Pinax 0.5.1 Out

Pinax 0.5.1 has now been released. This is a minor bug fix release. Worth getting if you're on 0.5.0 but save the real excitement for the upcoming 0.7 :-)

You can read the release notes and download it from http://pinaxproject.com/download/

by James Tauber : Created on Jan. 10, 2009 : Last modified Jan. 10, 2009 : Categories python django pinax : 0 comments (permalink)

Marking for Deletion in Django

Often you want to give the user the ability to delete objects but enable them to recover them if they change their mind.

One way to do this is to have a boolean flag on the model. The problem with this is

• you have to have the flag on all associated models involved in the object graph to be deleted
• you have to then filter all your queries based on that boolean flag (error prone and inefficient)

An alternative is to have a separate model for the deleted objects. i.e. DeletedFoo alongside Foo, DeletedBar alongside Bar. The schemas are similar (although some foreign keys are to their deleted counterparts instead) and objects are moved from one table to another when deleted (or undeleted).

This has certain advantages over the first approach, but does mean you have to create twice as many models.

A third approach which just occurred to me is to serialize the object graph to be deleted and store that in the database in a single table row. With Django's existing ability to calculate object graphs for deletion and also to load and dump json, this may be fairly straightforward to implement in a generic fashion.

Pinax is currently using the first approach but I'm interested if people have tried the third approach or secret option number four I don't know about yet.

by James Tauber : Created on Dec. 19, 2008 : Last modified Dec. 19, 2008 : Categories django : 15 comments (permalink)

Screencasting Competition Reminder

Firstly, a reminder that there are now just under two weeks to go until the deadline for the First Pinax Screencasting Competition.

I've added a new feature to the site to let you register your interest in participating in the contest, even if you're not yet ready to submit.

If you think you might be making a submission, I strongly recommend you register interest. This will let us gauge whether we have enough people and also lets us contact you (assuming you confirm an email address) in case things change.

by James Tauber : Created on Dec. 2, 2008 : Last modified Dec. 2, 2008 : Categories django pinax : 0 comments (permalink)

Blog Month Over

Well, I did it! I managed to do at least a post a day for the whole of November.

And I also achieved a goal I had that I didn't mention in advance: I wanted to do 50 posts.

I hope you at least enjoyed some of the blog posts.

I will soon finish off the final part of the Voronoi canvas demo and also the song project, but you'll forgive me if I take it easy. Attempting to do 50 posts was actually a lot more stressful and time consuming than I thought it would be.

That said, 30 days is enough to build a habit. I may find it hard NOT to post regularly now. At least I won't feel I HAVE to, though :-)

UPDATE: BTW, any novelists reading make their 50k for NaNoWriMo?

by James Tauber : Created on Nov. 30, 2008 : Last modified Nov. 30, 2008 : Categories this_site blogging : 3 comments (permalink)

More Thoughts on a New Language

In Thoughts on a New Language I said:

This relates to the whole concept of the "dictionary created by executing a block of statements". I find this notion of a "block of statements" being a first-class object appealing. Imagine a function that, instead of having a return value, simply returns its bound local variables. I guess Python modules are pretty much that. But I'm thinking of the notion within a file.

There are actually three places where Python uses a block of statements to populate a namespace:

• modules
• function bodies
• class definitions

But imagine that it was a first class object. I'm not really thinking about syntax yet, but one could imagine

{
    x = 5
    y = x + 2
}

or

block:
    x = 5
    y = x + 2

as possibilities for anonymous blocks. To bind the block to a particular variable, we could therefore say:

foo = {
    x = 5
    y = x + 2
}

or

block foo:
    x = 5
    y = x + 2

Now, what if following on from the previous post and ideas from prototype-based languages like Self, Javascript and Lua you could specify a parent to be traversed in case the block didn't have the requested value. Would there be special syntax for specifying the parent or would it just be a value in the block like __parent__?

foo = {
    __parent__ = bar
    y = x + 2
}

or

block foo(bar):
    y = x + 2

In either case, would the evaluation of y be lazy or not?

What about multiple inheritance, which isn't commonly found in prototype-based languages?

Also, would we want to have the notion of parameterized blocks? With the free variable explicit:

foo(x) = {
    y = x + 2
}

or implicit:

foo = {
    y = x + 2
}

?

And would you then want to be able to bind that free variable at a later date:

foo % { x = 5 }

assert foo.y == 7

(just to arbitrarily pick % to use as the operator symbol)

Also, taking a cue from an offhand remark in Steve Yegge's Universal Design Pattern post about this sort of stuff ( HT: Jonathan Hartley) imagine you have a monster objects like

orc = { hp = 10 }
warg = { hp = 5 }

and you wanted to capture the notion that a boss monster has 2 times the hit points of a normal monster of that prototype. Would you use inheritance without binding the __parent__ yet:

boss = { hp = 2 * __parent__.hp }

and later:

orc_boss = boss % { __parent__ = orc }

?

Could we use boss(orc) as equivalent to boss % { __parent__ = orc } ?

Some interesting possibility here, just playing around with the notion of a block as first class object with inheritance and parameterization.

And another crazy though: could this language have something akin to list comprehensions but for these blocks so you could compactly define them programmatically where appropriate? This is a contrived example, but Imagine you have a list of strings and you want to create a block that uses those strings as variable names, all set to an initial value of 1.

That is, you want to get

{
    foo = 1
    bar = 1
    baz = 1
}

from var_list = ["foo", "bar", "baz"]

The main challenge seems to be just coming up with syntax for turning strings into variable names. But imagine (just for the sake of example) that ~x meant the variable whose name is the value of x. Then you could (possibly) do something like:

{ ~x = 1 for x in var_list }

This is all just thinking aloud :-)

by James Tauber : Created on Nov. 30, 2008 : Last modified Nov. 30, 2008 : 4 comments (permalink)

Endo vs Exo

Yesterday I was starting to get nervous about the path I'd started to go down with the generic groups app for Pinax. I was basically building a single centralized app through which different types of groups would be managed via configuration. I had a good chat with Eric Florenzano about it and we agreed that it just felt wrong but I couldn't think of an alternative.

Then this morning I had a brainwave—a shift in approach that I described on the mailing list as an "exo" approach rather than the previous "endo" approach. Instead of having a single, centralized "groups" app that's highly configurable and lets you plug different pieces in, I realised a better approach would be to simply provide the building blocks for site developers to create their own group apps bottom-up.

The advantage of the "exo" approach is that it makes group customization more like normal Django development. It's more flexible if you want to do some things differently.

After thinking about it some more, it occurred to me that the endo vs exo distinction is quite important when crafting extensible software. It's not that exo approach is always better. It's just different.

The endo approach is that of a framework whereas the exo approach is that of a library. Even a single system like Django may have some aspects that are endo and others that are exo.

An endo approach says to a developer: "we'll provide you the core with slots you can plug your pieces into". An exo approach says to a developer: "we'll provide pieces you can plug together yourself".

In Pinax, django-notifications takes a more endo approach (you register your notification types with the notification subsystem) whereas django-mailer takes an exo approach (it's just there when you want to send mail).

If you need to "register" an entity, an endo approach is probably being used.

If you put your B in the configuration of A then A is endo. Whereas if your B just calls A to do something then A is exo.

Seems a useful distinction. What do people think?

by James Tauber : Created on Nov. 29, 2008 : Last modified Nov. 29, 2008 : Categories software_craftsmanship pinax : 4 comments (permalink)

Voronoi Canvas Tutorial, Part III

In Part I, we wrote some code that enabled the user to draw points on a canvas (as long as they weren't too close to an existing point. In Part II we added the drawing of a horizontal line wherever the mouse is.

Next we're going to draw one more type of object which will be at the heart of Fortune's algorithm for Voronoi diagrams. Remember earlier this month in From Focus and Directrix to Bezier Curve Parameters I wanted to be able to calculate quadratic Bézier curve parameters from a focus and horizontal directrix. Now I can explain why :-)

A point (called the focus) and a line (called the directrix) are enough to define a parabola. For Fortune's algorithm, I need to, for each point and for the sweep line, draw the corresponding parabola. The canvas element doesn't have a parabola-drawing primitive. However, it does support Bézier curves.

A quadratic Bézier curve is actually a section of a parabola, so I what I wanted was a way of converting the focus and directrix into the parameters for a quadratic Bézier curve that canvas would understand. That was the motivation for the mathematics in that post.

Implementing those equations in Javascript gives us:

function drawParabola(fx, fy, dy) {
    var alpha = Math.sqrt((dy*dy)-(fy*fy));
    var p0x = fx - alpha;
    var p0y = 0;
    var p1x = fx;
    var p1y = fy + dy;
    var p2x = fx + alpha;
    var p2y = 0;

    context.strokeStyle = "rgb(100, 100, 100)";
    context.fillStyle = "rgba(0, 0, 0, 0.05)";
    context.beginPath();
    context.moveTo(p0x, p0y);
    context.quadraticCurveTo(p1x, p1y, p2x, p2y);
    context.stroke();
    context.fill();
}

This not only draws the parabola but fills the region above it (which is relevant to our purpose).

Now all we need to do is run that for each point:

function drawParabolae(dy) {
    $.each(points, function() {
        if (dy > this[1]) {
            drawParabola(this[0], this[1], dy);
        }
    });
}

and then add a call to that function to our mousemove handler:

    ...
    context.clearRect(0, 0, 600, 400);
    drawHorizontalLine(oy);
    drawParabolae(oy);
    redrawDots();
    ....

You can see the result here. I was actually surprised how snappy it is, even with a lot of points. Using the Bézier curve rather than drawing the points manually was definitely the way to go.

If you think about the fact that a parabola is the locus of points equidistance from the focus and the directrix you can start to see how Fortune's algorithm is going to work. I'll make that more explicit in the next and final post.

by James Tauber : Created on Nov. 29, 2008 : Last modified Nov. 29, 2008 : Categories mathematics web javascript jquery : 2 comments (permalink)