Animation Physics at San Jose State

One of my AM students pointed out that San Jose State University is going to be offering a class in Physics for Animators. In a bit of serendipity, the professor of that class commented on my last post, of Hancock violating Newton’s Third Law of Motion, and provided a link to the program’s website:

This is a great idea, and I heartily support it. I’ve taken a look at the most recent tutorial (“The Physics of Timing”), and I have a few suggestions, mostly related to terms animators use. In this case, when we talk about “timing,” we’re generally talking about when key actions in our animation occur, or how long those actions take. The Physics of Timing Tutorial is mostly about the displacement, from moment to moment, of objects in a gravitational field. That’s very different from the issue of timing. So, in animation terms, what is this really tutorial about? Spacing!

This excellent tutorial is about the spacing of a falling (or sliding, or rising) objects. While a physicist may talk about displacement, we talk about spacing instead, because we’re concerned with the movement of things within screenspace, so we’re looking at the relative spacing from one frame to another, not actual distances.

Substituting ‘Spacing’ for ‘Timing’ may seem a subtle point, but there’s already way too much confusion regarding timing and spacing, which I referred to here and here.

Also, the tutorial repeats the hated “animations” language. Ugh, ugh, and double ugh. I know it’s common for students and people who have worked outside the mainstream of traditional animation to talk about “animations,” but it still sounds as wrong as talking about composing “musics.”

Finally, in the last image of the tutorial, this beautiful stroboscopic shot of a bouncing ball is reproduced.

What’s wrong with this picture? The path of action is off. The arc that the ball traces in space isn’t smooth after each bounce. Now, this is a real photograph, so what gives? I’ll reprint the Widimedia explanation:

Note that the ball becomes significantly non-spherical after each bounce, especially after the first. That, along with spin and air-resistance, causes the curve swept out to deviate slightly from the expected perfect parabola. Spin also causes the angle of first bounce to be shallower than expected.

It’s important to note these discrepancies for students, especially when otherwise showing “idealized” examples (for example, air resistance in the rest of the tutorial is explicitly ignored).  If a student copied these arcs exactly, I’d correct them.  And they’d be confused, because they were perfectly copying a real example. The problem is, they’d be copying something they didn’t fully understand, and so we need to keep things as simple and clear (and exclude spin and air resistance) in these examples.

Those are quibbles, and meant as constructive criticism and clarification. This is a wonderful idea, and I highly recommend it!  I look forward to what Professor Garcia et al. come up with.

12 Responses to “Animation Physics at San Jose State”

  1. Alej Garcia Says:

    Thanks Kevin, this is exactly the kind of feedback I was hoping to get! I’ll make revisions to the first tutorial and let you know when those are posted. Stay tuned. Alej

  2. Kevin Says:

    That’s awesome, Alej. You’re welcome, and I look forward to more tutorials.

  3. Alej Garcia Says:

    First, thanks again to Kevin for his comments on the first tutorial, now renamed “Physics of Timing and Spacing.” All of his suggestions have been incorporated and the last one, regarding the strobe photo of the bouncing ball, brings up an interesting point.

    The photo comes from Wikimedia, a repository of public domain images; it’s worth taking a moment to look at the photo and a related photo by the same photographer. Note that although it looks like a basketball, in reality it’s a toy ball about the size of a tennis ball. The photographer himself points out that the bouncing ball does not exactly follow a parabolic arc and he attributes the discrepancy to air resistance, spin, and a wobble of the ball due to its “squash” on impact. I believe this is incorrect; let me make my case.

    First, if air resistance, spin, and wobble are not the cause then why isn’t the path of action a parabolic arc? I claim that that it *is* a parabolic arc, but seen in perspective. Looking at the size of the ball it’s evident that it’s bouncing from foreground to background as it moves screen left to right. In perspective a parabolic arc has an apex that’s shifted towards the background (to the right in this image). Also, in perspective the upward half of the arc should have a shallower angle than the downward half, which we see in the photo. Unfortunately, because background is blacked out in the photo it’s not possible to locate the horizon line to establish with certainty that the arc is indeed correct. By the way, if you’re interested in the details of how to draw a parabolic arc in perspective, check out my article. This will also be described in the second tutorial, “Physics of Paths of Action.”

    Now, could the shape of the arc be due to air resistance? Perhaps and, in fact, the distortion seen (apex shifted to the right) is consistent with the effect due to drag (e.g., see here). However, it’s unlikely that this ball experiences significant drag traveling at this speed. Notice that the other photo of the ball falling straight down indicates that it is *not* significantly slowed by air resistance even at higher speeds (i.e., falling greater distances).

    What about the ball’s spin? The Magnus effect (which is the force that causes a poorly hit golf ball to slice or hook) requires a high speed of rotation, which the ball in the photo does not seem to have. Having said that, the trajectory of the second bounce may be shifted from that of the first bounce due to the effect of spin when the ball hits the ground. But while it’s in the air, the spin’s effect is probably negligible.

    What about the wobble? It turns out that due to Newton’s third law (for every action there’s an equal and opposite reaction) the center of the ball follows a parabolic arc, even if the ball wobbles. Any of you who’ve studied video reference for a water balloon thrown in the air (it’s a classic pencil test exercise) will verify this. See Kevin’s previous post for more info on the Newton’s third law. Finally, sorry for the long-winded post but I hope that it’s useful to those of you animating parabolic paths of action. Alej

  4. Kevin Says:

    Fantastic! I thought the explanation (wobble, air resistance, and spin) seemed a bit suspect, but I didn’t think too deeply about it. I love the process of questioning why things do what they do, and also questioning explanations that don’t seem quite right. It’s much better to really understand why things behave the way they do, rather than just accept conventional wisdom, or just copy what someone else did previously. Thank you for really breaking down and analyzing the photo.

  5. Cassidy Says:

    If Alej has eliminated spin, air resistance, and “wobble” as possible explanations, where does that leave us?

    I totally buy the perspective explanation for why each arc seems slanted towards screen right. No problem there.

    What I’m having a hard time explaining away is the difference between the ball’s apparent velocity at frame 2 versus frame 3. I can’t imagine any force that would cause the ball’s actual trajectory to shift from more horizontal to more vertical over a single frame, when the ball isn’t even in contact with the ground at that moment.

    The most plausible explanation I can think of is that the camera moved between those two frames. In other words, it’s not a wobbly ball, it’s a wobbly camera. Either that, or the image was composited together, poorly, from two different sources, in which case you could say it’s the photographer’s ethics that are a bit shaky.

  6. Cassidy Says:

    Oh wait! I take back my aspersions against the photographer’s ethics! There’s a simpler explanation: frame 2 is not the moment of contact with the ground!

    What seems to have happened is that the strobe flashed about 1/6 of a frame before the ball hit the ground, giving us frame 2, and then again 5/6 of a frame after the ball began moving upward. Frame 2 simply looks like a contact frame because it’s lower than frame 1 and frame 3.

    As for why the ball appears squashed in frame 2, that could be attributed to lens distortion: a wide-angle lens will cause spheres to look elliptical near the edges, and especially in the corners. The major axis of the ellipse in frame 2 points straight towards the center of the frame, which supports this hypothesis.

  7. Rungy Chungy Cheese Bees » Blog Archive » The difference between film and animation Says:

    […] Kevin pointed out that the ball’s arc looked strange to him, and a wonderful discussion ensued. The question in my mind was why there appeared to be a sudden change in direction and speed between the second and third “frames” of the ball’s movement. The best explanation I’ve been able to come up with is that none of the strobe’s flashes happened to coincide with the exact moment when the ball hit the ground: […]

  8. Cassidy Says:

    FWIW, I’ve posted some drawings illustrating the above point on my blog.

  9. Kevin Says:

    Nicely done, Cassidy!

  10. Alej Garcia Says:

    This discussion regarding the ambiguity of the ball’s position due to the absence of a frame showing the ball’s contact with the ground is something I’ll have to include in the next tutorial (Physics of Paths of Action). As Cassidy points out, this real image illustrates why photographic animation, such as motion-capture, doesn’t look as good (or even as real) as hand-crafted work.

    BTW, if you guys have any other comments or suggestions for the first tutorial (besides Kevin’s, which I’ve already implemented), please pass them on.

  11. Ed Says:

    Hi, thanks for the great tutorial. I have a question about the ‘pose to pose slowing out’ section though. I can see that it works if you have an object falling for 5 frames, but would it work for anything more than that? If you have a sixth frame and the space is double that of the distance of 1 to 5 then it’ll surely be incorrect? This is probably me not understanding the tutorial properly, but I thought I’d mention it just in-case.

    Also, do you know a way of calculating when an object will hit terminal velocity?


  12. Ivanator Says:

    this is is awesome! Thanks!

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The animation and animation-related musings of Kevin Koch