Download - Large Mesh Simplification using Processing Sequences

Large Mesh Simplificationusing Processing Sequences

Martin IsenburgUNC

Chapel Hill

Peter LindstromLLNL

Livermore

Stefan GumholdGRIS

Tubingen

Jack SnoeyinkUNC

Chapel Hill

Overview

• Motivation

• Background

• Processing Sequences

• Adapted Simplification Schemes– OOCS

– Wu & Kobbelt

• Conclusion

Motivation

Large Meshes

3D scans isosurfaces

Large Meshes

3D scans isosurfaces

PPM isosurface

• 235 million vertices

• 469 million triangles

• 235 million rtices

• million trianglesover

8 Gigabyte !

hampers:• distributing / loading• rendering• processing

• in-core algorithms of choice:– Qslim

– Rsimp

Mesh Simplification

• alternative: processing sequence

[Garland & Heckbert ’97]

[Brodsky & Watson ’00]

require~ 200 bytesper vertex

• current out-of-core approaches:1. piece by piece

2. external memory

3. polygon soup [Lindstrom ’00]

[Hoppe ’98]

[Cignoni et al. ’03]

Background

Related Work

• Large Mesh Processing– Simplification

– Compression

– Visualization Systems

• Main Techniques 1. Mesh Cutting

2. Online Processing

3. Batch Processing

• cut mesh into small pieces

• process each separately

• special treatment for cuts

• stitch result back together

1. Mesh Cutting

figure courtesy of Hugues Hoppe

2. Online Processing

• external memory datastructures

• “random” mesh access

figure courtesy of Paolo Cignoni

3. Batch Processing (1)

• polygon soup

• single scan over stream ofde-referenced triangles

• no explicit connectivity

[Lindstrom ’00]

3. Batch Processing (2)

• polygon soup

• single scan over stream ofde-referenced triangles

• no explicit connectivity

(coherent)

reconstruct

figure courtesy of Jianhua Wu and Leif Kobbelt

[Wu & Kobbelt ’03]

Sequenced Processing

• coherent triangle orderinginterleaved with vertices

• small footprint streaming

• finalization of vertices

[Isenburg & Gumhold ’03]

Quadric Error Matrices

• accumulate error

• vertex placement

• sum of squareddistances of point to set of planes

• quadric error:

figure courtesy of Michael Garland

[Garland & Heckbert ’97]

Q =q00 q01 q02 q03

q10 q11 q12 q13

q20 q21 q22 q23

q30 q31 q32 q33

vTQv

Processing Sequences

A little history …

• Compressor– region growing



• Out-of-Core Mesh– transparent

– caching clusters





• Compact Format– small footprint

– streaming






– streaming






– streaming

• interleaved ordering of triangles and vertices that “grows regions”

processingboundary

Processing Sequences

border edges

Q7

Q1

Q4

• available information:– first & last use of edges & vertices

– surface border

• maintaindata alongboundary

unprocessed region

Abstractions

• boundary-based– one boundary

– process immediately

processed region

waiting area

processingboundary

processed region

unprocessed region

Abstractions

• boundary-based– one boundary

– process immediately

• buffer-based– two boundaries

– process in buffer

– read to fill

– write to empty

in-corebuffer

output boundary

input boundary

processed region

unprocessed region

processingboundary

waiting area

OOCS

OOCS

• stream in polygon soup– triangle after triangle

• vertex clustering– one quadric per grid cell

• output sensitive– store all quadrics

• no border info – tangential

term added

OOCS

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input output

OOCS

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input output

OOCS

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input output

OOCS

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input output

OOCS

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input output

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input output

OOCS

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input output

OOCS

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input output

OOCS

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input output

OOCS using PS

• fewer artifacts– do not collapse multiple

layers into single vertex

– improved surface boundaries

• streaming output

OOCS using PS

• memory insensitive– maintain much fewer quadrics

processedregion

unprocessedregion

Q7

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Q55

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OOCS using PS (detail)

Q33

Q4

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processedregion

unprocessedregion

Q55

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processedregion

unprocessedregion

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turns into vertex quadric


processedregion

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quadric turns into vertex

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processedregion

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9quadricmerge


OOCS using PSinput output

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OOCS using PS

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outputinput

OOCS using PS

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OOCS using PS

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OOCS using PS

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OOCS using PS

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OOCS using PS

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OOCS using PS

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outputinput

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OOCS using PS

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OOCS using PSoutputinput

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Improved Mesh QualityOOCS-PS

OOCS

vertices: 33,053

non-manifoldvertices: 3,366

vertices: 35,134

non-manifoldvertices: 897

Lower Memory Requirements

373 million vertices

OOCSmemory:

3,282 MBtime:

67 minOOCS-PSmemory:

121 MBtime:

83 min23 million vertices

Wu & Kobbelt

Wu & Kobbelt

• stream coherent soup into buffer• reconstruct connectivity

– hash on vertex data– finalize complete stars

inputboundary

a aa a

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accumulating

c c

collapsible

• randomized edge collapse – one quadric per vertex– accumulating collapsible

• randomized streaming output

Wu & Kobbelt

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input output

Wu & Kobbelt

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Wu & Kobbelt using PS


• less fragmentation of buffer– processing sequence input / output

– more collapsible edges

• immediate boundary simplification– mesh borders known early

– truly “streaming” output

• faster connectivity reconstruction– indexed input / API support

Wu & Kobbelt using PS (detail)

unprocessedregion

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in-coretrianglebuffer

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Wu & Kobbelt using PSinput output


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Wu & Kobbelt using PSinput output

Conclusion&

Current Work

Summary

• processing sequences– efficient large mesh access

– streaming input and output

– abstractions: • boundary-based• buffer-based

• adapted simplification algorithms:– OOCS

– Wu & Kobbelt

• length of processing boundary– possible

– traversal is optimized for lowest bit-rate change heuristic

Issues

O( n ) [Bar-Yehuda & Gotsman ‘96]

• external memory mesh to createprocessing sequences …?– expensive to build & use

– defeats purpose …

Generating PS

• on-the-fly

• input: “streaming mesh”

v 1.32 0.12 0.23v 1.43 0.23 0.92v 0.91 0.15 0.62f 1 2 3done 2 v 0.72 0.34 0.35f 4 1 3done 1 ⋮ ⋮ ⋮ ⋮

verticesfinalized

(not used bysubsequenttriangles)

• extend to volume meshes

• promote– provide API

• create / improve– lower processing boundary length

Current Work

• compress– encode on-the-fly

Thank You.

v0

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fill

Growing Operations

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v0 v1

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join

add

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processingboundary

read nexttriangle

info aboutcurrenttriangle

optionalmaintainingof user data

Prototype of PS API int open(const char* file_name);int read_triangle();void close();

int t_idx[3];float* t_pos_f[3];int t_vflag[3];int t_eflag[3];

void set_edata( void* data, int i );void set_vdata( void* data, int i );void* get_edata( int i );void* get_vdata( int i );

Example (1)

v0 v1

v2

eflag[0] = PS_FIRST eflag[1] = PS_FIRST eflag[2] = PS_FIRST

vflag[0] = PS_FIRSTvflag[1] = PS_FIRSTvflag[2] = PS_FIRST

v0 v1

v2

eflag[0] = PS_FIRST eflag[1] = PS_FIRST | PS_LAST eflag[2] = PS_FIRST | PS_LAST

vflag[0] = PS_FIRSTvflag[1] = PS_FIRST | PS_LASTvflag[2] = PS_FIRST

borderedge

enteringedge

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start

start

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leavingedges

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leaving edge

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add

Example (2)

eflag[0] = PS_LASTeflag[1] = PS_FIRST | PS_LASTeflag[2] = PS_FIRST

vflag[0] = 0vflag[1] = 0vflag[2] = PS_FIRST

eflag[0] = PS_LAST eflag[1] = PS_FIRSTeflag[2] = PS_LAST

vflag[0] = PS_LASTvflag[1] = 0vflag[2] = 0

fill

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Example (3)

eflag[0] = PS_LASTeflag[1] = PS_LASTeflag[2] = PS_LAST

vflag[0] = PS_LASTvflag[1] = PS_LASTvflag[2] = PS_LAST

eflag[0] = PS_LAST eflag[1] = PS_LAST eflag[2] = PS_LAST

vflag[0] = PS_LASTvflag[1] = 0vflag[2] = PS_LAST

leaving

edges

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end

end

Computing Smooth Normalsps.open ( “bunny.sma” );while ( ps.read_triangle() ) tmp = compute ( ps.t_pos[0], ps.t_pos[1], ps.t_pos[2] ); for ( i = 0; i < 3; i++ ) if ( ps.vflag[i] & PS_FIRST ) n = new Normal (); ps.set_vdata ( n, i ); else n = ps.get_vdata ( i ); add ( n, tmp ); if ( ps.vflag[i] & PS_LAST ) normalize ( n ); do something delete n;

ps.close ();