I was just answering a question for the Udacity Interactive Graphics MOOC. I had made a rather confusing lecture, much more involved and less informative that I would have liked, so today I wrote a re-do (sadly, it’s not easy to make a new video, since step 1 is “fly from Boston to San Francisco”). I’m still not thrilled with my description – what do you think? Is there a better way to talk about this subject? Anything I could improve? Surprisingly, this course still gets about 35 sign-ups a day (though I’m guessing maybe one of those actually finishes), so it’d be nice to make this lesson better.

Background: up to this point in the course I’d been showing how you typically write down transforms from right to left (OpenGL-style column-major matrices), e.g. “TR” means “rotate the object, then translate it (in world space) to some location.” In this lesson I wanted to point out that you can also read the transform order from left to right.

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You’re at 41 Avenue George V in Paris. Someone comes up and asks “How can I see the Arc de Triomphe?” You tell them, “Go up two blocks and then turn to the left – you can’t miss it.” Indeed, at 101 Avenue des Champs-Élysées he can see L’Arc de Triomphe.

So if you wanted to take this person and apply these two transforms, translation T (walk two blocks) and rotation R (turn about 60 degrees to the left), how would you write that out? Think about it for a minute, then scroll down for the answer. (And I like the disembodied arm to the right from Google’s street view).

2016-04-09_153558

The order is (right-to-left “application order”): TR. That is, you want to apply the rotation first, so that it doesn’t affect the translation. So you rotate the person 60 degrees to the left, then you translate him north two blocks north, which is then not affected by the rotation.

If you incorrectly used order RT, you would first translate him north two blocks, so far so good. But, as you saw in the snowman lesson, rotating after translation means the object is rotated around the origin from his present location; in this case, the person’s starting location is the origin. So performing a translation, then a rotation, would move him up two blocks north, then rotate him in a circle with a 2 block radius by 60 degrees, putting him somewhere else in the city (Rue Euler, I guess, which is a great coincidence that it’s named for a famous mathematician).

I hope you accept TR is the right order, then. But, to describe directions we definitely first said “perform T” – walk two blocks north – “then perform R” – rotate to the left 60 degrees. So we talk about directions in a left-to-right fashion. This may seem odd, as we are then describing the last transform that we apply, T, if we actually want to position the man in his environment.

The key thing here, and the point of the lesson, is that by specifying T first, we’re saying to the man, change your frame of reference to be 2 blocks north. From this new frame of reference, then rotate 60 degrees around where you’re standing, your new origin. It’s how we talk about directions. We don’t say “when you get to your final position, rotate 60 degrees left. Then, to get to your final position, walk two blocks north.”

The person walking has his own frame of reference, where he’s always the origin, and rotations are done relative to whichever way he’s facing at the time. To specify transforms when talking in these terms, an object-centric way of describing things, we describe “from left to right.” When we’re looking at the world and want to think how to make some other object take on a particular orientation and position, we tend to work from right to left, getting it oriented and them moving it into position.

However, it all depends. Moving a couch up a flight of stairs, down a hall, and next to a wall in room is a series of transforms, and again we specify them from left to right. We could also shortcut the process if we don’t care about the intermediate steps along the way. Say the couch is facing north, and we know it’ll end up facing east. We could specify the one 90 degree rotation to get it to face east, then the one XYZ translation to move it directly to its desired location – right to left order, so that the rotation doesn’t interfere with the translation.

The final effect of the transforms – a series of moves or the direct rotation and translation – have the same final effect. The point is, each way of thinking has its uses.

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Let’s get visual. Last in the series, for now.

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All linked out yet? Here’s more worthwhile stuff I’ve run across since last SIGGRAPH.

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Next in the continuing series. In this episode Jaimie finds that the world is an illusion and she’s a butterfly’s dream, while Wilson works out his plumbing problems.

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The things:

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It’s rainy out, and I’m trying to avoid coding for Mineways and collecting code for JGT, so time to blog a little.

Some years ago I read the book The Public Domain about copyright and learned an interesting tidbit: photos of public domain paintings or photos are not covered by copyright in the U.S., they’re free to reuse.

Here’s the relevant bit from Wikipedia:

Reproductions of public domain works

The requirement of originality was also invoked in the 1999 United States District Court case Bridgeman Art Library v. Corel Corp. In the case, Bridgeman Art Library questioned the Corel Corporation‘s rights to redistribute their high quality reproductions of old paintings that had already fallen into the public domain due to age, claiming that it infringed on their copyrights. The court ruled that exact or “slavish” reproductions of two-dimensional works such as paintings and photographs that were already in the public domain could not be considered original enough for protection under U.S. law, “a photograph which is no more than a copy of a work of another as exact as science and technology permits lacks originality. That is not to say that such a feat is trivial, simply not original”.[30]

Another court case related to threshold of originality was the 2008 case Meshwerks v. Toyota Motor Sales U.S.A. In this case, the court ruled that wire-frame computer models of Toyota vehicles were not entitled to additional copyright protection since the purpose of the models was to faithfully represent the original objects without any creative additions.[31]

The wire-frame case is obviously relevant to computer graphics. There’s a rundown of other countries’ laws on Wikimedia Commons’ site.

Private collections are within their rights to limit access as they wish, as misguided as I think it is to sell public domain works to the public. I have a problem with any public institution invoking protection of photos of works, since there’s no legal basis for this.

The Public Domain is free to download and worth a read. To be honest, after a bit I skimmed chapter 2, but I particularly enjoyed chapter 7, a case study in which the U.S.’s more permissive rules on what is in the public domain (“sweat of the brow” works are not copyright in the U.S.) are contrasted with Europe’s more restrictive laws.

Oh, and if you like to read about copyright (you weirdo), you might enjoy The Idealist: Aaron Swartz and the Rise of Free Culture on the Internet. The second half is worthwhile, though quite sad, and a story I suspect many of us know to some extent. The first half is about the evolution of copyright laws in the United States, which went from being a haven for piracy of foreign (primarily English) works to an ardent defender of extending copyright almost into perpetuity (despite there being no incentive benefits in extending copyright retroactively, since the law at the time the work was created was found sufficiently appealing to the original author; sorry, I feel a rant coming on…). Ahhh, imagine this alternate universe. <– That’s a great link, by the way, well worth a click.

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I haven’t made one of these link posts for awhile. This one’s recent news, the ones to come will have more fun stuff.

sadly, human computers mostly got “calculate this boring number” assignments and very rarely got “if i was james counterstrike and i fired this rpg at this nightorc tell me how many gibs would come out”: one of history’s true missed opportunities

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The deadline for submission is April 5th. See http://s2016.siggraph.org/real-time-live-submissions

If you don’t know, “Real-Time Live!” is an event showcasing cool rendering and interactive techniques over the past year. If you’re working in this area, submit a proposal and let the rest of us enjoy seeing it.

WebGL Links Page

I got tired of re-finding various useful WebGL and three.js links, so I made a page:

http://www.realtimerendering.com/webgl.html

What cool things am I missing?

I’ve made it a page of links I am likely to want to check out in the future. It’s a bit hard to draw the line. For example, I didn’t bother adding fun demos such as this and this, but I did add the page where I browse new demos. I don’t list development systems such as Goo Create for non-programmers, which is built on this open-source WebGL engine and has some interesting features. Nice things all, but I personally am unlikely to come back to them (or if I do, they’re now in this blog post).

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Michael Cohen was looking at John Hable’s useful test image:

He noticed an odd thing. Looking at the image on his monitor (“an oldish Dell”) from across the room, it looked fine, the 187 area matched the side areas:

ok

(yes, ignore the moires and all the rest – honestly, the 187 matches the side bars.)

However, sitting at his computer, the 128 square then matched the side bars:

bad

Pretty surprising! We finally figured it out, that it’s the view angle: going off-axis resulted in a considerably different gray appearance. Moving your head left and right didn’t have much effect on the grays, but up and down had a dramatic effect.

Even knowing this, I can’t say I fully understand it. I get the idea that off-axis viewing can affect the brightness, but I would have thought this change would be consistent: grays would be dimmed down the same factor as whites. That last image shows this isn’t the case: the grays may indeed be dimmed down, but the alternating white lines are clearly getting dimmed down more than twice as much, such that they then match the 128 gray level. It’s like there’s a different gamma level when moving off-axis. Anyone know the answer?

Addendum: and if you view the first image on the iPhone, you get this sort of thing, depending on your zoom level. Here’s a typical screen shot – I’ve trimmed off the right so that the blog will show one pixel for pixel (on desktop computers – for mobile devices you’re on your own). This darkening is from bad filtering, see the end of this article.

iphone

Follow-up: one person commented that it’s probably a TN panel. Indeed, there’s a video showing the tremendous shift that occurs. The blue turning to brown is particularly impressive. I haven’t yet found a good explanation of what mechanism causes this shift to occur (Wikipedia notes other monitors having a gamma shift, so maybe it is something about gamma varying for some reason). There’s a nice color shift test here, along with other interesting tests.

Even better: check out this amazing video from Microsoft Research. (thanks to Marcel Lancelle for pointing it out)

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