1 23 maart 2006 Surface construction techniques for volumetric objects How to maintain convex and concave features? Eddy Loke and Erik Jansen
23 maart Introduction Discretized Marching Cubes builds a surface Halfway inbetween object and background Rounding of edges and corners Can we maintain sharp features?
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
23 maart Ambiguous cases X-cell: MC: asymptotic decider 4-connected “background priority” 8-connected “object priority” Subgrid
23 maart Boundary construction cell-by-cell Apply configurations We can also apply it on subgrid But then we have some ambiguous cases
23 maart Ambiguous cases X-cell: 4-connected “background priority” 8-connected “object priority” Boundary connectivity and node connectivity are two different things!
23 maart D Connectivity: 6-neighbors 18 neighbors 26 neighbors
23 maart D “Object priority” Kenmochi et al. 99
23 maart Object vs background priority Object priorityBackground priority P6b Node connectivity 18/26Node connectivity 6
23 maart Connectivity P5a - OPP5a - BP P4g - OPP4g - BP P6c - OP P6c - BP Some other cases
23 maart Background priority P3a P7a P4aP4bP4c P4dP4eP4g P5a P5b P5c P6b P6c P6a
23 maart Object versus background priority
23 maart Convex vs. concave Object priority: convex edgesBackground priority: concave edges
23 maart Object versus background priority
23 maart Discrete Marching Cubes DMC- nDMC- o DMC- eDMC- k DMC- l DMC-p
23 maart Build a DMC configuration by using subgrid triangulation Discrete Marching Cubes DMC- p
23 maart BP versionDMC-pOP-version DMC triangulation DMC has background priority triangulation
23 maart DMC configurations are background priority and triangulation is BP as well! Discrete Marching Cubes
23 maart Results DMC standard DMC refined
23 maart Concave P7a – OP/BP P7a – SBP P6a P6a - SBP
23 maart Concave variants
23 maart Convex extrapolation DMC rounded corners Feature detection Subgrid construction OP-triangulation Similar for concave edges
23 maart Results DMC standard DMC refined
23 maart Results DMC standard DMC refined
23 maart Conclusions Flexible triangulation scheme for convex and concave edges DMC extended/refined Discrete models may be of interest for high resolution models
23 maart Triangulation Configurations (cell 2x2x2 nodes) Other possibilities? Black versus white diagonals
23 maart Two P6b cells with object priorityTwo P6b cells with background priority Non-manifold
23 maart DMC- e DMC- l DMC- nDMC- pDMC- o DMC- k DMC configurations with BP- triangulation
23 maart Concave variants
23 maart Filters feature detection
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23 maart positive triangulationsnegative triangulations
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