1. 1 23 maart 2006 Surface construction techniques for volumetric objects How to maintain convex and concave features? Eddy Loke and Erik Jansen

2. 23 maart 20062 Introduction Discretized Marching Cubes builds a surface Halfway inbetween object and background Rounding of edges and corners Can we maintain sharp features?

3. 23 maart 20063 Surface construction from voxel data Data defined on grid Surface construction with MC (linear approximation) Binary data Surface construction on binary data Discrete Marching Cubes (DMC) Discrete version of MC Less triangles Manifold Rounded volumes Ambiguous cases 4-boundary 8-boundary 8+ Discrete Marching CubesDiscrete Marching Cubes – alt. Marching cubes 8-connectivity4-connectivity

4. 23 maart 20064 Ambiguous cases X-cell: MC: asymptotic decider 4-connected “background priority” 8-connected “object priority” Subgrid

5. 23 maart 20065 Boundary construction cell-by-cell Apply configurations We can also apply it on subgrid But then we have some ambiguous cases

6. 23 maart 20066 Ambiguous cases X-cell: 4-connected “background priority” 8-connected “object priority” Boundary connectivity and node connectivity are two different things!

7. 23 maart 20067 3D Connectivity: 6-neighbors 18 neighbors 26 neighbors

8. 23 maart 20068 3D “Object priority” Kenmochi et al. 99

9. 23 maart 20069 Object vs background priority Object priorityBackground priority P6b Node connectivity 18/26Node connectivity 6

10. 23 maart 200610 Connectivity P5a - OPP5a - BP P4g - OPP4g - BP P6c - OP P6c - BP Some other cases

11. 23 maart 200611 Background priority P3a P7a P4aP4bP4c P4dP4eP4g P5a P5b P5c P6b P6c P6a

12. 23 maart 200612 Object versus background priority

13. 23 maart 200613 Convex vs. concave Object priority: convex edgesBackground priority: concave edges

14. 23 maart 200614 Object versus background priority

15. 23 maart 200615 Discrete Marching Cubes DMC- nDMC- o DMC- eDMC- k DMC- l DMC-p

16. 23 maart 200616 Build a DMC configuration by using subgrid triangulation Discrete Marching Cubes DMC- p

17. 23 maart 200617 BP versionDMC-pOP-version DMC triangulation DMC has background priority triangulation

18. 23 maart 200618 DMC configurations are background priority and triangulation is BP as well! Discrete Marching Cubes

19. 23 maart 200619 Results DMC standard DMC refined

20. 23 maart 200620 Concave P7a – OP/BP P7a – SBP P6a P6a - SBP

21. 23 maart 200621 Concave variants

22. 23 maart 200622 Convex extrapolation DMC rounded corners Feature detection Subgrid construction OP-triangulation Similar for concave edges

23. 23 maart 200623 Results DMC standard DMC refined

24. 23 maart 200624 Results DMC standard DMC refined

25. 23 maart 200625 Conclusions Flexible triangulation scheme for convex and concave edges DMC extended/refined Discrete models may be of interest for high resolution models

26. 23 maart 200626 Triangulation Configurations (cell 2x2x2 nodes) Other possibilities? Black versus white diagonals

27. 23 maart 200627 Two P6b cells with object priorityTwo P6b cells with background priority Non-manifold

28. 23 maart 200628 DMC- e DMC- l DMC- nDMC- pDMC- o DMC- k DMC configurations with BP- triangulation

29. 23 maart 200629 Concave variants

30. 23 maart 200630 Filters feature detection

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45. 23 maart 200645 positive triangulationsnegative triangulations

46. 23 maart 200646 Surface construction from voxel data Data defined on grid Surface construction with MC (continue) Surface construction on binary data Marching cubes Discrete Marching Cubes 4-boundary8-boundary