F-cell

1. TEMPLATE: disk LHKF F-cell disk LHKF Q E K F-cell circle LHKF F H L F-cell S D Q E K F H L rectangle DEQS polyline DEQS rectangle DEQS polyline DEQS rectangle DEQS S D B-cell B-cell B-cell B-cell B-cell disk LHKF circle LHKF disk LHKF disk LHKF point K arc KFL half-disk KFL point L segment KL F-cell F-cell F-cell F-cell T-cell T-cell T-cell T-cell T-cell Boundary relations

2. 0D cells E Q K F H L 1D cells S D 2D cells Boundary relations polyline DEQS rectangle DEQS B-cell B-cell circle LHKF disk LHKF point F F-cell F-cell T-cell

3. E Q 1D cells K S D F H L 2D cells rectangle DEQS polyline DEQS circle LHKF disk LHKF Containment relations B-cell B-cell F-cell F-cell

4. point M point O segment OM segment OM rectangle DEQS disk LHKF circle LHKF disk LHKF rectangle DEQS polyline DEQS 0D cells B-cell F-cell F-cell B-cell F-cell B-cell P-cell P-cell P-cell P-cell Q E O K F H L 1D cells M S D 2D cells

5. disk LHKF segment OM circle LHKF F-cell P-cell F-cell O M K F H L Dependency relations

6. point P segment OM polyline DEQS segment ON point M circle LHKF rectangle DEQS disk LHKF Segment MP point N point O segment PN B-cell F-cell F-cell B-cell T-cell P-cell T-cell T-cell P-cell T-cell T-cell P-cell 0D cells O Q E P M K N F H 1D cells L S D 2D cells

7. half-disk KLF segment KL point K point M arc KLF circle LHKF disk LHKF rectangle DEQS point O polyline DEQS segment OM point L B-cell T-cell F-cell F-cell B-cell T-cell T-cell P-cell P-cell T-cell P-cell T-cell O Q E M K F H L S D 0D cells R 1D cells 2D cells

8. half-disk KLF circle LHKF rectangle DEQS disk LHKF arc KLF polyline DEQS segment OM point L segment KL segment RM point R point M point K point O T-cell B-cell P-cell B-cell T-cell T-cell P-cell F-cell T-cell T-cell F-cell T-cell P-cell T-cell O R Q E M K F H L S D 0D cells 1D cells 2D cells

9. O O Q Q E E M M K K F F H H L L S S D D R R

10. Q E DEQS B-cell LHKF F-cell K F H L S D Q E H K polyline DEQS circle LHKF F L F-cell B-cell S D rectangle DEQS B-cell rectangle DEQS disk LHKF B-cell disk LHKF disk LHKF F-cell F-cell F-cell

11. Q E K F H L S D Q E H K F L Combined T-cell S D

12. G2 K G3 F H G1 L G2 E Q G3 G1 0D cells S D 1D cells G2 G3 G1 A 2D cells gear bnd. G3 gear G3 gear G1 gear bnd. G2 gear bnd. G1 gear G2 B-cell B-cell F-cell F-cell B-cell B-cell Boundary relations point A T-cell

13. 0D cells 1D cells G2 G3 G1 A 2D cells gear G1 gear bnd. G3 gear G3 gear bnd. G1 gear bnd. G2 gear G2 B-cell F-cell F-cell B-cell B-cell B-cell Boundary relations point A T-cell

14. 0D cells B 1D cells G2 A G3 G1 2D cells gear bnd. G3 gear G1 gear G3 gear bnd. G2 gear G2 gear bnd. G1 B-cell B-cell B-cell F-cell B-cell F-cell Boundary relations point A point B T-cell T-cell

15. Q E H G 1D cells K D S F 2D cells Boundary relations rectangle DEQS polyline DEQS B-cell B-cell rectangle FGHK polyline FGHK F-cell F-cell

16. Q E V S D 0D cells U G H K F 1D cells 2D cells rectangle DEQS polyline DEQS Boundary relations B-cell B-cell polyline FGHK rectangle FGHK line UV point V point U F-cell F-cell T-cell T-cell T-cell

17. Q E S D 0D cells U G H K F 1D cells 2D cells rectangle DEQS polyline DEQS Boundary relations B-cell B-cell polyline FGHK rectangle FGHK line UV point V point U F-cell F-cell T-cell T-cell T-cell

18. Q E S D 0D cells U G H K F 1D cells 2D cells polyline DEQS rectangle DEQS Boundary relations B-cell B-cell polyline FGHK rectangle FGHK point U F-cell F-cell T-cell

19. tN-1<t<tN → t>tN t1<t<t2 → t>t2 t2<t<t3 → t>t3 … S1 S2 SK ti-1<t<ti → t>ti

20. tN-1<t<tN → t>tN … … KN K1 K2

21. Kj KN K1 K2 KN-1 … …

22. … t , , , , K1 K2 KN Kj K2 K1 K1 Kj K2 K1 … PKj TN PK2 T2 T1 PK1 t , , , , … t , , ,

23. K1 K2 Kj K1 … t1=0.5 t1=0.5 t , , , , Local time is 0.5 but referring to different moments within the global timescale

24. Pull Retrieve valid parameter Pull Cell 4 Cell 2 Cell 3 Cell 1 Retrieve valid parameter Parameter1 Parameter1 Parameter1 Pull Parameter1 Parameter2 Parameter2 Parameter2 Retrieve valid parameter Dependency Dependency Cell 2 Cell 3 Cell 1 Cell 4 Dependency

25. Kj Ki … … TKi TKj t ,

26. K1(0) K2 Q E Q E Q Q Q E E E K K K K K F H F H H H H F F F L L L L L S D S D S S S D D D K1 K3 K3 t

27. K1 K2 K3 T1 T2 T3 t , ,

28. disk LHKF segment OM circle LHKF F-cell P-cell F-cell O M K F H L Dependency relations

29. point O segment OM polyline DEQS circle LHKF disk LHKF rectangle DEQS point M F-cell P-cell P-cell P-cell B-cell F-cell B-cell O Q E M 0D cells K F H L S D 1D cells 2D cells

30. point P point O segment OM segment OP disk LHKF circle LHKF rectangle DEQS Segment MP polyline DEQS point M T-cell F-cell F-cell B-cell B-cell P-cell P-cell T-cell T-cell P-cell P 0D cells O Q E M K F H 1D cells L S D 2D cells

31. rectangle DEQS point R disk LHKF circle LHKF segment OM segment ON polyline DEQS Segment MP point M point N point O point P segment PN P-cell T-cell P-cell T-cell T-cell T-cell B-cell P-cell F-cell T-cell F-cell T-cell B-cell E O P 0D cells Q R M K N H F L 1D cells S D 2D cells

32. Attr1 Cell1 Deform1 Attribute B-cell T-cell ? ... ... initial g. attributes geometry attribute geometry ... ... Geometric dependency Attribute dependency

33. AttrRel1 Attr1 Cell1 Cell1 Attr1 Deform1 Attribute relation Attribute B-cell T-cell ... initial g. ... .. attributes geometry ... geometry ... Geometric dependency