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Eddy Loke and Erik Jansen

Surface construction techniques for volumetric objects How to maintain convex and concave features?. Eddy Loke and Erik Jansen. Introduction. Discretized Marching Cubes builds a surface Halfway inbetween object and background Rounding of edges and corners Can we maintain sharp features?.

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Eddy Loke and Erik Jansen

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  1. Surface construction techniques for volumetric objectsHow to maintain convex and concave features? Eddy Loke and Erik Jansen

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

  3. 8-boundary 8+ 4-boundary Marching cubes Discrete Marching Cubes Discrete Marching Cubes – alt. 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 8-connectivity 4-connectivity

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

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

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

  7. 3D Connectivity: • 6-neighbors • 18 neighbors • 26 neighbors

  8. P3a P4a P4b P4c P5a P5b P4d P4e P4g P6a P6b P5c P7a P6c 3D “Object priority” Kenmochi et al. 99

  9. P6b Object vs background priority Object priority Background priority P6b Node connectivity 18/26 Node connectivity 6

  10. P4g - OP P4g - BP P5a - OP P5a - BP P6c - OP P6c - BP Connectivity Some other cases

  11. P5a P6c Background priority P3a P4a P4b P4c P4d P4e P4g P5b P7a P5c P6b P6a

  12. Object versus background priority

  13. Convex vs. concave Object priority: convex edges Background priority: concave edges

  14. Object versus background priority

  15. DMC- l DMC- e DMC- k DMC-p DMC- n DMC- o Discrete Marching Cubes

  16. DMC- p DMC- p DMC- p Discrete Marching Cubes • Build a DMC configuration by using subgrid triangulation

  17. BP version OP-version DMC-p DMC triangulation DMC has background priority triangulation

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

  19. Results DMC standard DMC refined

  20. P6a - SBP P7a – OP/BP P6a P7a – SBP Concave

  21. Concave variants

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

  23. Results DMC standard DMC refined

  24. Results DMC standard DMC refined

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

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

  27. Non-manifold Two P6b cells with object priority Two P6b cells with background priority

  28. DMC configurations with BP-triangulation DMC- k DMC- l DMC- e DMC- n DMC- o DMC- p

  29. Concave variants

  30. Filters feature detection

  31. ? ?

  32. positive triangulations negative triangulations

  33. 4-boundary 8-boundary Discrete Marching Cubes Marching cubes Surface construction from voxel data • Data defined on grid • Surface construction with MC (continue) • Surface construction on binary data

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