Fun new paper at #SIGGRAPH2025:

What if instead of two 6-sided dice, you could roll a single "funky-shaped" die that gives the same statistics (e.g, 7 is twice as likely as 4 or 10).

Or make fair dice in any shape—e.g., dragons rather than cubes?

That's exactly what we do!

Here's the paper, which is an industry-funded collaboration between my PhD student Hossein Baktash at CMU, Nicholas Sharp at NVIDIA, and Qingnan Zhou & Alec Jacobson at Adobe Research.

https://www.cs.cmu.edu/~kmcrane/Projects/RestingBodies/PuttingRigidBodiesToRest.pdf

2/n

In a nutshell, we show that the resting poses & statistics of a rigid body are easily computed from its geometry, without any dynamical simulation.

This simple geometric model enables us differentiate through dice designs, & optimize their shapes to match target statistics. 3/n

Mathematically, our key observation is that we can identify dynamically stable configurations of a rigid body, and calculate their associated probabilities, from the Morse complex of the support function of the convex hull.

https://en.wikipedia.org/wiki/Support_function
https://en.wikipedia.org/wiki/Morse_theory

4/n

Although this model is purely geometric, and does not directly account for momentum, it still makes highly accurate predictions relative to physical simulation—or thousands of rolls carried out by hard working grad students!

Check out the paper to find out more. n/n

This is way to elaborate for a simple shitpost But Dragon-shaped dice (cc @volpeon )

With actual science behind it! so they have the same propability as "normal" dice.

ngl the paper looks hella complicated to me. Way too much complex math

RE: https://mathstodon.xyz/@keenancrane/114546750409137558

sicher auch interessant für @dnddeutsch