August 2008

Need to find all roots of a polynomial? One approach is to use Newton’s Method. But as you’d soon find out, either by reading the Wikipedia article or coding them thing up yourself, it has failings, not least of which is an inability to find all the roots of a polynomial. So, another approach, and the one I will be talking about, is using Sturm Sequences.

What’s the point? I’ve been using Sturm sequences in my ray tracer to render some algebraic surfaces, like the one on the left (the Tanglecube), so I’ve got a pretty good hang on the concept. Plus, I haven’t posted in a while and writing about C# is easier than… well, writing about other stuff.

Rest of the post, as well as the accompanying code, after the jump.



Not much to comment on this Sunday, just one secret:

Under the secret there’s this e-mail:

My ex did this. I didn’t go to the hospital. All it did was assure me that he was not the kind of person I could trust with my safety because he was willing to be that cavalier with his own.

I gotta say, this is one of the more manipulative things I’ve heard of people doing. I mean, sure, there’s the usual I’m-pregnant-we-need-to-marry lie, the I-love-you-now-let’s-do-it lie, the various you-bought-me-something-expensive-so-you-must-REALLY-love-me relationship gauges, etc. But this one really takes the cake. I’m opposed to dishonesty overall, and this little stunt is even worse.

Oh, and Frank goes out of his way yet again to be an annoying ass by creating a MySpace blog. First Facebook, now MySpace. Yeesh.

On a somewhat unrelated note I’d like to say a thing about all-out honesty. My mom’s aunt died a few years ago. The aunt’s husband was obviously distraught, having suffered by the aunt’s side after her stroke and as she slowly died. And because of this, no one in the family wanted to make things worse for him by telling him that he has terminal cancer. (I’m not sure how that itself happened, that the family knew but the uncle himself didn’t, but it’s Russia, maybe things there are different.) So that’s what I am getting to: in the states, the person is the first to know that they have cancer. But the culture in Russia, as well as that of my mom, seems to be that if the person doesn’t know they’re dying, that’s somehow better, so don’t bother telling them and have them go on with their life.

I don’t agree with that logic. Certainly if I was dying, I’d like to know. But then again, there’s more of that honesty approach. Or me just being curious. Whatever.

A few hours ago I finally reached 100% completion of GTA:IV. What does this mean? It simply states that I’ve completed all missions and finished all the minor to-do’s, like meeting all important NPC’s, finding 200 hidden “packages” – which just happened to be pidgeons, and to “find” one I had to “shoot” it with a “gun” – and other minutiae.

Along with the 100% completion, I’ve got some other minor statistics:

  • 845 game points gained through 41 out of 50 achievements – the rest of the achievements are “complete the game in less than 30 hours” and multiplayer miscellany
  • Current money – 948,329$ (had 1 million at some point)
  • Times busted – 2
  • Times died – 57
  • People killed – 1718
  • Playing time – 97:26:04
  • Addiction level – Intervention Time (this is one of the statistics for the game, I kid you not)
  • Days passed [in the game] – 187
  • Cars stolen – 887
  • People run down – 1475
  • Miles on foot – 145.56
  • Miles by car – 1165.46
  • Bullets fired – 24,592
  • Verhicles blown up – 234

Now, I do have to mention that I also spent countless hours just messing around in GTA, not bothering to save after a series of rampages that put me in the hospital a dozen times and depleted all my ammo. That’s probably a quarter of the time listed above, and likely with more kills.

This is going to be a very uneventful post about my team acquiring an Xbox. Just posting this in lieu of a real post.

(Toward the end of writing the post I realized that the port by my side may be messing with my mood. Maybe that’s the reason for this post and its overall style. Whatever.)

The rest is after the jump. (more…)

Carrying on the tradition of last two weekends, Sunday I went on a drive to Paradise. The whole trip took about 11 hours and ended up taking me completely around Mount Rainier: on the way in I took 410, on the way back I (eventually) took 161. Here are some impressions from the trip, in convenient-to-read bullet-list form:

  • Wow
  • Breathtaking views and amazing photo opportunities
  • Go on a clear day
  • Be prepared to stop often – there are a lot of photo opportunities along the roads, from lakes and rivers to the main attraction, Rainier
  • If you’re not going to stop, take someone with you to take pictures as you drive
  • Slow down on the road – when one side of the road is a steep fall, you don’t want to suddenly lose control of your car, especially on the rough-gravel parts of the road
  • Paradise Inn is expensive for dinner and pre-packed lunches
  • NWSource is great and all, but they do get stuff wrong sometimes
  • Tourists aren’t as annoying as in other places. Most of them just want to take a picture of Rainier and have a sandwich.
  • I’m not really a fan of the Rolling Stones

Overall, this was a wonderful trip, even better than the ones to Anacortes and Leveanworth (though without the taffy or brats or the kickin’ brewery of those two places). It was an enjoyable drive that was, for better or worse, never boring. By that I mean that half of the time I was gawking at the scenery (and of course stopping to snap some shots) and the other half I spent negotiating tight turns, controlling the car over gravel (thank you Forza2!), passing the slow-pokes and staying out of the way of the speeding maniacs. is a great site for all things Seattle (and other parts of the Pacific NorthWest), but when looking up hiking information, aggregate data with at least one other site. I specifically planned this trip to go on the Snow and Bench Lakes trail, which was described as “short, flat and beautiful” but was anything but. (Of course, it would help to if I was in a much better shape, so these comments might be biased.) The trail is described on-site as “moderate”; it wasn’t all beautiful (a lot of it went through bushes and muddy walkways) and it certainly wasn’t flat (change in elevation of 700 feet). All of this information was available, incidentally, so as I said, use NWSource in combination with other resources.

When driving around Rainier, I found it best to go at my own pace, be it faster or slower than other drivers. In the first half I found myself driving much faster, so the drivers in front of me allowed me to pass. On the way home, it seemed easier to allow someone else to go in front, so I could properly see the upcoming turns (the road back was much more twisted) and I wouldn’t feel pressured to go faster than I was comfortable.

Dinner at Paradise Inn was so-so. The wait was really long (45 minutes to get a table) and the food was expensive. I’ve never had elk before, but it tasted great. Just expensive. The lunch menu looks better, in terms of prices.

For the entire road-trip my musical choice was the entire Rolling Stones’ discography. I only got through 6 out of 11 CD’s, but that’s still something. And I have to say, I’m not really a fan. Sure, there are some great songs (I recently fell in love with “Gimme Shelter”), but the majority of the stuff I listened to today was really bland and boring. If it wasn’t for the visual stimulation of the mountains, I’d have fallen asleep. It’s weird, I guess, but most of the songs I heard are nothing like the Stones songs I know: “Paint It Black”, “Gimme Shelter”, “(I Can’t Get No) Satisfaction”, “You Can’t Always Get What You Want”.