cubit research at the university of south florida

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