Most people are familiar with conventional cubical six-sided dice, but there are also polyhedral versions like the 20-sided dice used in ancient Rome and to play Dungeons and Dragons. Researchers have figured out how to design dice with even more exotic shapes, like a kitten, a dragon, or an armadillo. And they are “fair” dice: Experiments with 3D-printed versions produced results that closely matched predicted random outcomes, according to a forthcoming paper currently in press at the journal ACM Transactions on Graphics.
Dice are examples of so-called “rigid bodies,” broadly defined as shapes that move as one solid piece, with no need for bending or twisting. Such shapes “are of scientific interest because they model so many of the phenomena we encounter in our daily lives: anything from the way your dishes roll around on the floor when you drop them, to how the gears in your watch push on each other, to how a satellite tumbles around under the pull of gravity,” co-author Keenan Crane of Carnegie-Mellon University told Ars. “So there’s an intense focus on developing computational methods for understanding and predicting how rigid bodies are going to behave.”
Crane and his co-authors—including lead author and CMU graduate student Hossein Baktash, as well as co-authors from NVIDIA Research and Adobe Research—wanted to explore where and how a rigid body will land when tossed. They chose dice as the best (and most fun) context in which to explore that question.