CUBIT Research

at the University of South Florida

Presented byEugene Fink

People

CUBIT teamSteve OwenByron Hanks

FacultySunil SaigalEugene Fink

Graduate studentsShiraj KhanMatt Boonstra

Undergrad studentsKevin AlbrechtPlamen StoyanovWill Frost

Tasks

• Spatial indexing

• Surface flattening

• Format conversion

• Code cleanup

Shiraj Khan

Kevin Albrecht

Matt Boonstra

Plamen Stoyanov

Will Frost

Tasks

• Spatial indexing

• Surface flattening

• Format conversion

• Code cleanup

, and areas , angles• Preserve lengths

Surface flattening

Problem:

• Map a faceted sur- face into the plane x

yz

u

v

Surface flattening

Methods:

• Orthogonal projection, FacetProjParamTool

• RoadKill (by Alla Sheffer), FacetParamTool

• RoadKill with hole patching, FacetParamTool

ProjectionFlatten a faceted surface byprojecting it onto a plane.

x

yz

Projection• Find the best-fit plane

• If there are overlaps, then report a failure

Drawback:Works only for near-flat surfaces.

x

yz• Project onto this plane

• Else, convert the projection into two coordinates u

v

RoadKill

An algorithm for flattening faceted surfaces,by Alla Sheffer and Eric de Sturler (2001).

• Minimizes the deformation of angles

• Uses Newton’s method to solve a constrained minimization problem

Drawback:Works only for surfaces without holes.

Patching holesClose all holes andthen apply RoadKill.

x

yz

Patching holes• Project a hole onto the best-fit plane

Drawback:Works only for near-flat holes.

x

yz

• Triangulate the resulting projection• Map the triangulation back onto the surface

Examples• Orthogonal projection

• RoadKill (by Alla Sheffer)• RoadKill with hole patching

Future extensions

• Patching complex holes

• Cracking faceted surfacesx

yz

u

v

Tasks

• Spatial indexing

• Surface flattening

• Format conversion

• Code cleanup

• Deletion of objects

• Addition of new objects

Spatial indexingProblem:Indexing and retrieval ofobjects in three dimensions.

• Retrieval of the nearest neighbors

• Retrieval of the objects that intersect a given object

Spatial indexing

Methods:

• Previous: R-trees (Guttman, 1984), RTree• Current: KD-trees (Bentley, 1975), KDDTree

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

KD-treesA binary tree for indexing ofpoints in multiple dimensions.

a

b

c

d

e f

ab

c

d

e

fThis tree also allows:

• Indexing of boxes by their center points

• Indexing of arbitrary objects by their bounding boxes

KD-treesAdvantages:• Fast initial construction• Fast retrieval of points

Drawbacks:• Slow insertion• Slow deletion

Performance in CUBIT:KD-trees are usuallyfaster than R-trees.

Performance

number of facets

seco

nds

KD-trees1,000

30

10

110,000 100,000

Initial construction

3

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

R-trees

Retrieval of points

KD-trees

R-trees

mill

isec

onds

1,000

30

10

110,000 100,000

3

number of facets

Future extensions

• Improving efficiency of KD-trees

• Implementing R*-trees

Tasks

• Spatial indexing

• Surface flattening

• Format conversion

• Code cleanup

Format conversion

• Converting between STL and facet format

• Loading and saving these formats

• Collapsing close pointsFacet

format

BinarySTL

ASCIISTL

Close pointsProblem:Identify and collapse all pairs of closely located points.

Methods:

• R-tree indexing, RTree

• Grid indexing, GridSearchTree

d

Grid indexing

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

Grid indexing

• Divide the space into cubes ;the edge length is twice largerthan the collapsing distance

2 · d• Index points by cube locations; each cube is a bucket of points

• Given a point, retrieve the points in the same cube and seven adjacent cubes

d

Performance

number of facets

seco

nds

10 100 1,000 10,0000.01

0.1

110

1,000100

Exactcomparisons

Grid loading is ten to hundredtimes faster than R-tree loading.

Gridindexing

R-treeindexing

Future extensions

• Grid with templates for general use in CUBIT

• Basic repair of surfaces

x

yz

x

yz

Tasks

• Spatial indexing

• Surface flattening

• Format conversion

• Code cleanup

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

Future tasks

• Topology extraction

x

yz

• Decimation of facetsz

x

y

• Repair of surfacesx

yz

• Smooth representationx

yz

Future tasks

• Topology extraction

• Decimation of facets

• Repair of surfaces

• Smooth representation

Plamen Stoyanov

Kevin Albrecht

New student

New student

Matt Boonstra