CUBIT research at the University of South Florida

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CUBIT Research at the University of South Florida
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People
CUBIT team Steve Owen Byron Hanks
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Tasks

• Surface flattening

• Spatial indexing

• Format conversion

• Code cleanup

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Tasks

• Surface flattening

• Spatial indexing

• Format conversion

• Code cleanup

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Surface flattening

• Problem
• Map a faceted sur- face into the plane

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Surface flattening

• Methods
• Orthogonal projection, FacetProjParamTool

• RoadKill (by Alla Sheffer), FacetParamTool

• RoadKill with hole patching, FacetParamTool

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Projection
Flatten a faceted surface byprojecting it onto a
plane.
z
y
x
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Projection

• Find the best-fit plane

z
y

• If there are overlaps, then report a failure

x
Drawback Works only for near-flat surfaces.
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RoadKill
An algorithm for flattening faceted surfaces,by
Alla Sheffer and Eric de Sturler (2001).

• Minimizes the deformation of angles
• Uses Newtons method to solve a constrained
  minimization problem

Drawback Works only for surfaces without holes.
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Patching holes
Close all holes andthen apply RoadKill.
z
y
x
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Patching holes

• Project a hole onto the best-fit plane

z
y
x
Drawback Works only for near-flat holes.
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Examples

• Orthogonal projection

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Future extensions

• Patching complex holes

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Tasks

• Surface flattening

• Spatial indexing

• Format conversion

• Code cleanup

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Spatial indexing
Problem Indexing and retrieval ofobjects in
three dimensions.
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Spatial indexing

• Methods
• Previous R-trees (Guttman, 1984), RTree

• Current KD-trees (Bentley, 1975), KDDTree

• Future R-trees (Beckmann et al.,1990),
  RStarTree

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KD-trees
A binary tree for indexing ofpoints in multiple
dimensions.
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KD-trees

• Advantages
• Fast initial construction
• Fast retrieval of points

• Drawbacks
• Slow insertion
• Slow deletion

Performance in CUBIT KD-trees are usually faster
than R-trees.
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Performance
Initial construction
30
10
seconds
R-trees
3
KD-trees
1
1,000
100,000
10,000
number of facets

• KD-trees are faster than R-trees
• Construction is about 3 times faster
• Retrieval is about 1.5 times faster

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Future extensions

• Improving efficiency of KD-trees

• Implementing R-trees

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Tasks

• Surface flattening

• Spatial indexing

• Format conversion

• Code cleanup

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Format conversion

• Converting between STL and facet format

• Loading and saving these formats

• Collapsing close points

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Close points
Problem Identify and collapse all pairs of
closely located points.

• Methods
• R-tree indexing, RTree
• Grid indexing, GridSearchTree

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Grid indexing
Indexing of points by their locationsin a grid
of equal-size cubes.
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Grid indexing

• Divide the space into cubes

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Performance
1,000
100
Grid indexing
R-treeindexing
10
seconds
1
0.1
0.01
10
100
1,000
10,000
number of facets
Grid loading is ten to hundred times faster than
R-tree loading.
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Future extensions

• Grid with templates for general use in CUBIT

• Basic repair of surfaces

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Tasks

• Surface flattening

• Spatial indexing

• Format conversion

• Code cleanup

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Code cleanup

• User commands for saving faceted surfaces in
  STL and facet format

• Newton-Raphson procedure in the
  advancing-front meshing

• Arguments and returned values in the
  procedures for cutting spatial objects

• Testing the beta version of CUBIT 8

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Future tasks

• Topology extraction

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Future tasks

• Decimation of facets

• Repair of surfaces

• Smooth representation

• Topology extraction