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Show HN: Visualizing the math that powers 3D character animation

diegomacario.github.io

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Show HN: Visualizing the math that powers 3D character animation

#1
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!

Show HN: Visualizing the math that powers 3D character animation
diegomacario.github.io

Re: Show HN: Visualizing the math that powers 3D character animation

#4
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).

Re: Show HN: Visualizing the math that powers 3D character animation

#6
post #3

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.

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.

Re: Show HN: Visualizing the math that powers 3D character animation

#7
post #3

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.

Works for me on safari MacOS even if it feels slow

I recommend running it on Chrome. It runs more smoothly there. I'm still improving the performance on Safari.

Re: Show HN: Visualizing the math that powers 3D character animation

#9
post #8

I don't see any math, only visualization, where is the mathematical concepts and equations explained again?

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!

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