Adaptable outofcore simplification in onepass

1
Adaptable out-of-core simplification in one-pass

• Kangying Caia, Wencheng Wanga, Guangzheng Feib
  and Enhua Wua, c
• a Key lab. of Computer Science, Institute of
  Software, Chinese Academy of Sciences, Beijing,
  P.R.China
• bMIRALab, University of Geneva, Geneva,
  Switzerland
• c Faculty of Science and Technology, University
  of Macao, Macao, P.R.China

2
Introduction

• problem super large polygonal models
• millions to billions triangles
• Visible Human data set over 10 billion voxels
• Digital Michelangelo data set 2 billion
  triangles
• too large to display, process, transmit and store
• data sources
• laser range scanning
• isosurface extraction
• smooth surface approximation (e.g. CAD)
• uniform sampling ? oversampling

3
Surface Simplification Solution to Oversampling

• simplification
• automated process
• can be tailored for application
• however, difficult to extend existing in-core
  methods
• full connectivity information needed
• models are too large to be wholly loaded into
  main memory
• example St. Matthew model
• memoryless simplification method Lindstrom
  Turk98
• 30 GB RAM, one week to simplify (assuming enough
  RAM)
• need out-of-core simplification

4
Previous Work

• model partitioning
• Bermardini et. al. 99, Hoppe 97 and Prince
  00
• O(nlogn) in-core methods patition and stitch
  opeartions ? slow and extra disk space required
• vertex clustering
• Lindstrom 00 OoCS
• vertex clustering with error quadrics(quadric
  error metric)
• fast only one pass over the input model
• accurate positioning of vertex cluster
  representatives
• uniformly sampling ? can not preserve surface
  details

5
Previous Work

• Shaffer et.al. 00 and Fei et.al. 00(BR)
• adaptive vertex clustering algorithm
• high quality simplification result preserve
  surface details well
• two pass over the original model ? lower
  algorithm efficiency
• Fei et.al. 00 can not process all types of
  detail areas

6
BT Balanced tiling algorithm for out-of-core
simplification

• adaptive vertex clustering in one-pass
• primary advantages
• high efficiency
• only need single pass over the input model
• 400,000 triangles/second reduction
• high quality
• adaptive sampling according to the detail
  distribution ? preserve surface details well
• generality
• can position and refine all types of detail areas

7
Overview of BT

• input triangle soup
• five steps of BT
• quantization of original model
• analysis of detail distribution over the model
• further simplification of smooth areas
• Local refinement around detail areas
• output of simplification result

8
Vertex Clustering
9
Quadric Error Metric

• sum of squared volume of the tetrahedral formed
  by cluster representative and triangles in the
  cluster
• simplification error at the cluster
  representative
• Q (A, b, c) Q(v) vTAv 2bTv c
• optimal placement of each cluster's
  representative Lindstrom 00
• minimize Q(v) ?Q(v)0 ? Avb

10
Level Surface Q(v) e

• an ellipsoid (potentially degenerate)
• the eigenvalues and eigenvectors of A define the
  three principal axes of the ellipsoid
• The shape of the ellipsoid characterizes the
  local shape of the surface

11
Step1 Quantization of Original Model

• quadric quantization
• Lindstrom's uniform clustering approachLindstrom
  00
• generate an intermediate approximation
• surface coding
• 1100,1111,0111,0011

12
Step2 Analysis of Detail Distribution over the
Model

• position detail and smooth areas
• detail areas feature edge and cornerKobbelt et
  al.00
• Adaptive clustering further simplify smooth
  areas and refine detail areas
• rely on the quadric metric of every nonempty
  cluster to analyze the geometry of the original
  model.

13
Step2 Analysis of Detail Distribution over the
Model

• examine the eigenvalues of A
• the three eigenvalues of A ?1 lt ?2 lt ?3RRE1 ?2
  / ?1 and RRE2 ?3 / ?2
• four cases
• RRE1 gt a1 , feature edges
• RRE1 lt a2 and RRE2 lt a2, corner
• RRE1 lt a2 and RRE2 gt a2, smooth
• all the remaining, transitional regions
• a1 16, a2 4

14
Step2 Analysis of Detail Distribution over the
Model

• the result of detail distribution analysis

15
Step3 Further Simplification of Smooth Areas

• combine the neighboring clusters containing
  smooth areas
• edge collapse operations
• collapse cost RRE1

16
Step4 Local Refinement around Detail Areas

• cluster split operations
• along the direction where surface normal changes
  quickly
• calculate new representatives reconstruct
  connectivity
• feature edge areas
• split into two subclusters along the feature
  edge, i.e.eigenvector of the secondlargest
  value of A

17
Step4 Local Refinement around Detail Areas

• feature edge areas
• new representative vertex weighted average
  vertex
• reconstruction of connectivity

18
Step4 Local Refinement around Detail Areas

• corner areas
• split into four subclusters
• along the two eigenvectors of the two smallest
  eigenvalues of the associated A matrix
• two passes of the cluster splitting operations of
  refining feature edge areas

19
Results

• test models
• Lucy 28,055,743 triangles
• subdivided Hand 10,474,656 triangles
• subdivided Balde 7,061,552 triangles
• Buddha 1,805,650 triangles
• Dragon 871,306 triangles
• 800MHz Pentium III, 256M RAM, IDE disk drive
• comparison with two existing out-of-core methods
• OoCSLindstrom 00 best uniform clustering
  method
• BRFei et.al. 00 adaptive clustering method in
  two pass

20
Comparison Dragon model

• Original 871,306 T BT 48,016 T
• BR 48, 016 T OoCS 48,016 T

21
Comparison Head of 48016 Triangles Dragon model

• OoCS BT

22
Comparison Buddha Model

• Original 1,085,650 T BT 77, 952 T
  BR 77, 952 T

23
Comparison Lucy Model

• Original 28,055,743 T BT 93, 736 T BR 93,
  736 T

24
Simplification Time

• Lucy model 28, 055, 743 triangles ? 93,736
  triangles

25
Memory Usage (MB)

• output-sensitive memory requirements
• handles arbitrarily large input models
• no extra disk space needed

26
Future works

• generate manifold results
• convert an out-of-core model into a PM
  (progressive mesh) like representation
• view-dependent refinement of such an out-of-core
  PM like representation

27
Acknowledgements

• supported by National Science Foundation of China
  (60173078, 60033010) and the Research Grant of
  University of Macau.
• Thanks to Dr. Xuehui Liu for valuable comments
  and suggestions
• Thanks to Stanford Graphics Lab and the Digital
  Michelangelo Project for making the models of the
  Dragon, the Buddha and the Lucy statue available
• Thanks to Gerg Turk, Brendan Mullins and the
  Large Geometric Models Archive project of Georgia
  Institute of Technology for the Blade model and
  Clemson University for the hand model

28
Questions Answers
29
Further discussion is greatly appreciated!
cky_at_ios.ac.cn Thanks!