marctenbosch

SIGGRAPH 2020 Technical Paper: N-Dimensional Rigid Body Dynamics (Patreon)

Published:

2021-02-22 20:24:30

Imported:

2026-06

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I realized I never posted on here that my technical paper “N-Dimensional Rigid Body Dynamics” was published at SIGGRAPH 2020! Very proud to present research developed for 4D Toys & Miegakure at such a prestigious conference.

Here is the link to the paper and the abstract:

I present a formulation for Rigid Body Dynamics that is independent of the dimension of the space. I describe the state and equations of motion of rigid bodies using geometric algebra. Using collision detection algorithms extended to nD I resolve collisions and contact between bodies. My implementation is 4D, but the techniques described here apply to any number of dimensions. I display these four-dimensional rigid bodies by taking a three-dimensional slice through them. I allow the user to manipulate these bodies in real-time.

Btw I believe it is basically unheard of to have work from an indie game presented in the SIGGRAPH technical papers track?

The paper is full of really fun and beautiful math that makes me happy. Unsurprisingly it is Geometric Algebra based, and a followup of sorts to my interactive article which you likely have seen! One reviewer called the work “whimsical,” and they’re not wrong, ahah.

The video above is the talk I recorded for the conference.

Thank you so much for you support!

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SIGGRAPH 2020 Technical Paper: n-Dimensional Rigid Body Dynamics

I gave this talk at the SIGGRAPH 2020 conference about research developed for 4D Toys and Miegakure. SIGGRAPH is the premiere international conference on computer graphics and interactive techniques. Link to the paper: http://marctenbosch.com/ndphysics It's very exciting for work from a game (and a first for an indie game) to be presented in the SIGGRAPH Technical Papers program! Thank you all for your patience during development of the game, as you can see it can get pretty involved, ahah! 00:00 Introduction 01:15 Contributions 01:49 4D Toys Trailer 06:57 Background: Geometric Algebra 07:34 Background: Rigid Body Motion 07:49 Background: Angular Momentum 07:59 Background: Bivectors 08:55 Background: Rotors 10:05 Background: Instantaneous Velocity 10:25 Background: Angular Momentum 10:48 Background: Euler's Equation 10:59 n-Dimensional Generalization: Geometric Algebra Operator Matrices 11:48 n-Dimensional Generalization: Inertia Tensor 12:08 n-Dimensional Generalization: Operators and Inertia Tensor 12:39 n-Dimensional Generalization: Correcting Rotor Errors 13:18 Inertia Tensor of arbitrary nD mesh 13:34 Inertia Tensor of arbitrary nD mesh: Inertia Tensor is Linear 13:46 Inertia Tensor of arbitrary nD mesh: Compute Covariance Matrix 14:05 Inertia Tensor of arbitrary nD mesh: Transform Covariance into Inertia 14:30 Inertia Tensor of arbitrary nD mesh: Transforming Inertia Tensor 14:55 Inertia Tensor of arbitrary nD mesh: Diagonalizing Inertia Tensor 15:17 Collision Resolution / Detection 15:32 Collision Resolution / Detection: Hypersphere / Polytope 16:14 Collision Resolution / Detection: Polytope / Polytope 17:03 Dzhanibekov Effect: 3D Dzhanibekov Effect 17:27 Dzhanibekov Effect: 4D Dzhanibekov Effect 17:54 Dzhanibekov Effect: Reduces to 3D case 18:12 Dzhanibekov Effect: Stable states 18:30 Dzhanibekov Effect: Additional Oscillations 18:44 Future Work