Lagrangian point of view

1. t1 t2 Lagrangian pointofview 5 1 6 2 Eulerian pointofview 5 1 6 2

3. (-1,1) (0,1) (1,1) y x Offset (-1,-1) (-1, 0) (-1, 1) ( 0,-1) ( 0, 0) ( 0, 1) ( 1,-1) ( 1, 0) ( 1, 1) (-1,0) (1,0) not evaluatedpairswithcellson oppositeside (0,0) evaluatedpairs (-1,-1) (0,-1) (1,-1)

4. h h neighbors potential neighbors no potential neighbors

8. worldspaceparticlepositions worldspacecorneroffsets worldspacebillboards / triangles clipspacebillboards

9. cornersharedwithprecursoredgesharedwithprecursornewcornernewedgecornersharedwithprecursoredgesharedwithprecursornewcornernewedge

13. viewray image plane pixelcentre eyepoint

14. rayexit stepsize rayentry / first sample point

15. current sample point C refinementsample points: 2 halfway L-C 3 1 halfway 1-C 2 1 halfway 1-2 3 isosurface last sample point L

16. worldspace texturespace 5 1 1 0.6 0.6 5 3 3 0.6 3 7 1 0.52 1 0.6 5 3 3 0.43 3

17. common plane surface normal incidentray reflectionray θi θr = θi surfacecut

18. n l r cos θi θi θr b sin θi a

19. surface normal common plane incidentray θi ni surfacecut nt θt refractionray

20. n l cos θi sin θi θi ni sin θt sin θi nt a x θt cos θi cos θt b -l y t -n

21. light (s-polarised) medium withlowindexofrefraction reflections surface refractions medium withhighindexofrefraction

22. medium withlowindexofrefraction refractions critical angle surface reflections light (s-polarised) medium withhighindexofrefraction

23. viewray isosurface n1 θi1 -n1 θr1 refraction1 θt1 -n2 reflection1 n2 reflection2 airni waternt refraction2(ifpossible)

24. volumetexture (1, 1, 1) exit entry viewray (0, 0, 0)

25. +y - +z -x +x -z -y

27. *: texture z slice index 1514131111109876543210 instanceindex 43210 * render target particlepositionz

29. … …