[HN Gopher] Show HN: Visualizing the math that powers 3D charact...
___________________________________________________________________
Show HN: Visualizing the math that powers 3D character animation
Hi everyone! I'm the author of this project. I wrote it because I
think that the math that makes characters move in games and movies
is incredibly beautiful, and I wanted to give others a glimpse into
it. It's crazy to think that quaternions, an abstract mathematical
tool discovered by William Rowan Hamilton in 1843, would be so
perfectly suited to solve hard problems in the world of 3D
character animation more than a hundred years later. The story of
how he discovered quaternions is also beautiful. Here's an excerpt
from Wikipedia: "Hamilton was looking for ways of extending
complex numbers (which can be viewed as points on a 2-dimensional
Argand diagram) to higher spatial dimensions. In working with four
dimensions, rather than three, he created quaternion algebra.
According to Hamilton, on 16 October he was out walking along the
Royal Canal in Dublin with his wife when the solution in the form
of the equation i2 = j2 = k2 = ijk = -1 occurred to him; Hamilton
then carved this equation using his penknife into the side of the
nearby Broom Bridge (which Hamilton called Brougham Bridge)."
There's a plaque that commemorates that moment on Broom Bridge now.
If you have any questions about this project, I would love to
answer them, but I recommend reading the README first, which should
explain everything: https://github.com/diegomacario/Animation-
Magic/blob/main/RE... Thank you!
Author : diegomacario
Score : 132 points
Date : 2022-06-13 12:37 UTC (10 hours ago)
(HTM) web link (diegomacario.github.io)
(TXT) w3m dump (diegomacario.github.io)
| xaedes wrote:
| Seeing glfw mentioned in your readme, I wanted to know how your
| (web) build process looks like. Gotta say I love this
| CMakeLists.txt It is so clean and simple!
| [deleted]
| dwrodri wrote:
| It's a gorgeous visualization, but it appears the UI is bugging
| out for me on Brave and Safari in MacOS. The layout has no issue,
| but I can't select any of the dropdowns.
| j_leboulanger wrote:
| Works for me on safari MacOS even if it feels slow
| diegomacario wrote:
| I recommend running it on Chrome. It runs more smoothly
| there. I'm still improving the performance on Safari.
| dylan604 wrote:
| Downvote for actually suggesting turning us back into 90s
| era "Best Viewed In" situation.
|
| I do applaud the wanting to improve performance elsewhere,
| but still gets a big shake of my head in disappointment
| that dev is allowed to get to a place where it only works
| in one browser at first until some amount of work after
| release to fix to work in other browsers. My sincere hope
| that you do get it to work universally, realize what was
| done that made it one-sided to begin with, and avoid those
| things in any future projects.
| Kiro wrote:
| This is exactly the type of project where recommending a
| specific browser is warranted.
| diegomacario wrote:
| To be honest I don't see this as such a bad thing. Google
| Chrome has 70% of the browser market share, while Safari
| has 4%. I don't think there's anything wrong with
| prioritizing more popular platforms, specially when you
| just want to ship a project that you worked on in your
| spare time to learn new things.
| dylan604 wrote:
| Again, why I offered learning what was specific to Chrome
| and no longer using them for future projects. Yet more
| learning on top of the learning
| dahart wrote:
| What evidence is there that anything Chrome specific was
| used? Safari's WebGL support has come later than others,
| and there are reports of WebGL being slower on Safari
| than Chrome, for example
| https://developer.apple.com/forums/thread/696821 It's
| possible your incredulity maybe should be directed
| towards Safari and not someone trying to do their best?
| diegomacario wrote:
| Oh thanks for reporting that dwrodri! Note that the controls
| don't work on touchscreens yet. If you use a mouse/trackpad and
| keyboard, you should be able to play with all the settings.
| samstave wrote:
| I AM IN LOVE WITH THIS DATA:
|
| But hear me out as to why:
|
| Surely - the amount of spatial kinematic maths that has been
| built around how we 'perceive' natural movement within a scene by
| _object_ has been immense...
|
| ---
|
| I have an idea. (this is just off the cuff and what caused me to
| have goose-bumps immediately when I saw this):
|
| Actually -- I am going to email you... rather than post publicly.
|
| May you please update your profile with an email... or post a way
| to contact you here
| GuB-42 wrote:
| On the subject of quaternions, here is an article that pops up on
| HN from time to time.
|
| https://marctenbosch.com/quaternions/
|
| It is called "Let's remove Quaternions from every 3D Engine". The
| author suggests replacing quaternions with rotors and geometric
| algebra. In 3D, the formulas are essentially the same, but framed
| differently. It makes some "surprising" properties more intuitive
| and is extensible to any number of dimensions. The last part is
| especially relevant to the author as he is developing
| "Miegakure", a 4D game (i.e. the game world has 4 spatial
| dimensions).
| wyager wrote:
| GA is more general than (and superior to) quaternions (the even
| subalgebra of G3). However, it requires a powerful type system
| and compiler to compile general GA expressions to something as
| efficient as quaternions. C++ won't cut it. You might be able
| to get clever by defining a special numerically indexed type
| for Gn or its even subalgebras; C++ could probably do that. But
| it wouldn't be as nice as fully generic GA.
| aaaaaaaaaaab wrote:
| What do you mean by powerful type system and compiler? Do you
| mean an optimizing compiler that can eliminate the redundant
| zero terms when multiplying multivectors with many zero
| grades?
| diegomacario wrote:
| Wow that's fascinating, thanks for sharing it!
|
| Although I disagree with how the author describes quaternions
| as black boxes. The two questions he asks:
|
| - Why does i2=j2=k2=-1 and ij=k? - Why do we take a vector and
| upgrade it to an "imaginary" vector in order to transform it,
| like q(xi+yj+zk)q*?
|
| Are clearly explained in these interactive videos created by
| Grant Sanderson and Ben Eater: https://eater.net/quaternions
|
| After I watched those videos, quaternions stopped being so
| opaque to me. I recommend them :-)
| wyager wrote:
| Although I grokked quaternions before learning GA, I am 100%
| certain that the GA explanation is better and more intuitive.
|
| GA breaks down quaternions (and their generalization to
| arbitrary dimensions) into smaller pieces that are much more
| obvious.
|
| It takes hundreds of years to invent quaternions from
| scratch, but it takes 10 minutes to invent quaternions from
| GA.
| Uehreka wrote:
| Given that Miegakure has been "coming soon" for over ten years
| (maybe the dev initially planned it as a 10-year-game, but if
| so I wish he would've said so when people asked when it was
| coming) I'm going to suggest putting a hold on deciding whether
| this way of reckoning rotations results in a better development
| process.
| GuB-42 wrote:
| I don't anyone who took the 4D game concept further than him,
| there is no "better development process" yet.
|
| And if anything, I don't think the engine is the problem. He
| already shipped 4D toys, which I suspect is a way to monetize
| the devtools he made for Miegakure (nothing wrong with that).
| And even before that, the 4D was fine.
|
| But while it is nice having good 4D, turning it into an
| entertaining game with good graphics, good puzzle design, a
| story that doesn't suck (even a simple one), etc... is hard.
| And we are not talking about a FPS or 2D platformer here,
| there are no game design books about making games like
| Miegakure, and there are many, many things that can go wrong.
| And to be honest, I hope for the best, but I don't expect
| much.
|
| One big difficulty I see is that not only the designers have
| to understand 4D to make interesting worlds/puzzles, but the
| game has to teach that to players too, with the right
| difficulty curve.
| saeranv wrote:
| I'm a little confused about why the curves are "sampled" to
| update the joint transformations: ``` So if we are rendering 60
| frames per second, we are basically doing the following 60 times
| a second:
|
| Sample all the curves you see on the graphs to get the
| orientation of each joint... ```
|
| When the curves are "sampled", does that mean in a 60 fps
| animation, there are 60 timestep values t={t1, t2, ... t60}
| sampled from a uniform distributions, and evaluated at x(t),
| y(t), z(t), and w(t), and then those values are stepped through
| sequentially? If that is the case, why not just set t={1/60,
| 2/60, ... 1}?
|
| Or does "sampling" here just mean function is evaluated at an
| appropriate t value, and not refering to statistical sampling?
| arjvik wrote:
| Pretty sure it just means evaluated at a finite number of
| appropriate t values and interpolated to find intermediate
| values.
|
| I agree that it's definitely an abuse of terminology.
| danachow wrote:
| https://en.wikipedia.org/wiki/Sampling_(signal_processing)
| Const-me wrote:
| Cool project!
|
| AFAIK many games are using 3x4 bone matrices instead of 4x4.
| These matrices don't need projection component anyway i.e. 3x4 is
| enough.
|
| This saves some bandwidth updating the constant buffer with them,
| also takes slightly less math instructions in the vertex shader.
| proc0 wrote:
| Really cool, thank you. This is the standard way of animating in
| most engines, right? I'm wondering if there are other techniques
| that save on sampling the data. Bones form a hierarchy and when
| the spine bone moves it affects the movement of all the other
| limbs, but I'm not sure if that's more or less expensive.
| diegomacario wrote:
| Thanks proc0! What you are describing (a hierarchy of bones) is
| exactly what I'm doing. I decided not to mention that to
| simplify the explanation of how character animations work, but
| here are the missing details:
|
| - All the little curves that I'm plotting show the local
| orientation of each joint.
|
| - To obtain the world orientation of a particular joint, it's
| necessary to combine the transform matrices of all its parent
| joints until you reach the root of the hierarchy.
|
| For example, to get the world transform of a wrist joint, you
| need to combine the local transforms of the wrist, elbow,
| shoulder, neck, etc. joints.
|
| Animation curves are stored in local space in glTF files, and
| those are the curves that I'm displaying.
|
| I hope this explains things.
| proc0 wrote:
| Nice, I was thinking they had absolute coordinates. Thanks
| for clarifying.
| suyash wrote:
| I don't see any math, only visualization, where is the
| mathematical concepts and equations explained again?
| diegomacario wrote:
| Hi suyash, take a look at the README for information on what
| all the little graphs represent:
| https://github.com/diegomacario/Animation-Magic/blob/main/RE...
|
| There's also a button in the controls that allows you to open
| the README. Thank you!
| barrysteve wrote:
| I love this site, the animations have so much character!
| aaaaaaaaaaab wrote:
| Nice work, but displaying the time evolution of individual
| quaternion components is about as intuitive of a visualization as
| displaying the time evolution of an individual pixel to visualize
| video compression...
| diegomacario wrote:
| Hahaha this is a fair comment. I guess my intention was to show
| the complex number crunching that happens in the background to
| make characters move. I'm still thinking about better ways to
| visualize things.
| panki27 wrote:
| Could you overlay the graphs with a sort of arrow, indicating
| the the actual direction the quaternion is pointing in? I had
| no knowledge on animation before, this was a great primer!
| Maybe having the graphs sync up could be a toggle - I feel
| like at low animation speeds, this would help visualize
| what's going on.
| aaaaaaaaaaab wrote:
| Got it! I think you should also read up on dual quaternions
| for more mind-blowing math if you haven't done so yet!
___________________________________________________________________
(page generated 2022-06-13 23:00 UTC)