eddy loke and erik jansen
DESCRIPTION
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?. - PowerPoint PPT PresentationTRANSCRIPT
123 maart 2006
Surface construction techniques for volumetric objects
How to maintain convex and concave features?
Eddy Loke and Erik Jansen
23 maart 2006 2
Introduction
Discretized Marching Cubes builds a surface• Halfway inbetween object and background• Rounding of edges and corners • Can we maintain sharp features?
23 maart 2006 3
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 2006 4
Ambiguous cases
X-cell:• MC: asymptotic decider• 4-connected
“background priority”• 8-connected
“object priority”• Subgrid
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Boundary construction cell-by-cell
• Apply configurations• We can also apply it on
subgrid• But then we have some
ambiguous cases
23 maart 2006 6
Ambiguous cases
X-cell:• 4-connected
“background priority”
• 8-connected “object priority”
Boundary connectivity and node connectivity are two different things!
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3D “Object priority”
P4a P4b
P4d P4e P4g
P4cP3a
P7a
P5a
P5c P6bP6a
P5b
P6c
Kenmochi et al. 99
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Object vs background priority
Object priority Background priority
P6b P6b
Node connectivity 18/26 Node connectivity 6
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Convex vs. concave
Object priority: convex edges Background priority: concave edges
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• Build a DMC configuration by using subgrid triangulation
Discrete Marching Cubes
DMC- p DMC- p DMC- p
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BP versionDMC-p OP-version
DMC triangulation
DMC has background priority triangulation
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• DMC configurations are background priority
• and triangulation is BP as well!
Discrete Marching Cubes
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Convex extrapolation
• DMC rounded corners
• Feature detection• Subgrid
construction• OP-triangulation
Similar for concave edges
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Conclusions
• Flexible triangulation scheme for convex and concave edges
• DMC extended/refined• Discrete models may be of interest for
high resolution models
23 maart 2006 26
Triangulation
Configurations(cell 2x2x2 nodes)
Other possibilities?Black versus white
diagonals
23 maart 2006 27
Two P6b cells with object priorityTwo P6b cells with background priority
Non-manifold