Post on 23-May-2020
transcript
A"ractor?IHardlyKnowHer!featuringrota8onsandODEsinVR
DonnellyPhillipsMaeMarkowskiJosephFrias
2016SpringMEGLSymposium
ThisSemester
o Rota8onsDemo
o Chao8cA"ractorsODESolver
Rota8ons
• ExploringIUPUI’sDanielRamras’paper“Howefficientlycanoneuntangleadouble-twist?Wavingisbelieving!”
• NullhomotopyinSO(3)– Diracbelttrick– Philippinecandledance
Moreformally…
D̂(s, t) = (1− 2cos2 ssin2(t / 2))+ I(sin(2s)sin2(t / 2))+K(cosssin t)
• Doubletwistcanbegivenbythemapping:
where0≤s≤π/2and0≤t≤2π
• I???K???• Rota8onscanbeconvenientlydescribedbyquaternions
• 4Dcomplexnumbersr+xI +y J +z K where
I 2 = J 2 = K 2 = IJK = −1
ThrowUpSimulator(TUS)
• Implementedtheserota8onsinUnityandOculusRif
• Feelfreetotestoutyourstomachsaferthepresenta8on
ODESolver
• SolvesODEsinreal8mewithuser-selectedini8alcondi8ons– LEAPmo8on
• Approximatessolu8onsusingafourth-orderRunge-Ku"amethod
• 15chao8ca"ractors– Lorenz,Rossler,tonameafew
“Strange”A"ractors
CourtesyofChao8cAtmospheresonDeviantArt
!x = (z−β)x − dy!y = δx + (z−β)y
!z = γ +αz− z3
3− (x2 + y2 )(1+εz)+ξzx3
!x =α(y− x)+δxz!y =ζ y− xz!z = βz+ xy−εx2
ODEFootage
FuturePlans• TurnODEsolverintooutreachcarnivalgame– A"ractorgolf
FuturePlans• ModulispaceswithJackLove• Hyperbolicgeometry?
Acknowledgments
• Thankyoutoouradvisor,Dr.SeanLawton• MEGL• NSF
S8ckaroundtoexperiencetheRif