Aractor? I Hardly Know Her!meglab.wdfiles.com/local--files/research:spring2016/MEGLVR_prese… · A"ractor? I Hardly Know Her! featuring rotaons and ODEs in VR Donnelly Phillips Mae

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