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N-Dimensional Rigid Body Dynamics

July 2020

Marc ten Bosch

SIGGRAPH 2020 Technical Paper


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.


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This is underlying research for 4D Toys and Miegakure.


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  author = {ten Bosch, Marc},
  title = {N-Dimensional Rigid Body Dynamics},
  journal = {ACM Trans. Graph.},
  DOI = {10.1145/3386569.3392483},
  volume = (39),
  number = (4),
  year = (2020),
  issue_date = {July 2020},
  month = {jul},
  articleno = {55},
  numpages = {6},
  pages = {55:1--55:6},
  publisher = {Association for Computing Machinery},
  address = {New York, NY, USA},
  url = {http://dx.doi.org/10.1145/3386569.3392483},