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

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Presentation on theme: "1 23 maart 2006 Surface construction techniques for volumetric objects How to maintain convex and concave features? Eddy Loke and Erik Jansen."— Presentation transcript:

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

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

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

7 23 maart D Connectivity: 6-neighbors 18 neighbors 26 neighbors

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

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

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

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

12 23 maart Object versus background priority

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

14 23 maart Object versus background priority

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

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

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

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

19 23 maart Results DMC standard DMC refined

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

21 23 maart Concave variants

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

23 23 maart Results DMC standard DMC refined

24 23 maart Results DMC standard DMC refined

25 23 maart 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 Triangulation Configurations (cell 2x2x2 nodes) Other possibilities? Black versus white diagonals

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

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

29 23 maart Concave variants

30 23 maart Filters feature detection

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42 23 maart ? ?

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45 23 maart positive triangulationsnegative triangulations

46 23 maart 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


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