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!
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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