multi chart geometry images
Download
Skip this Video
Download Presentation
Multi-chart Geometry Images

Loading in 2 Seconds...

play fullscreen
1 / 39

Multi-chart Geometry Images - PowerPoint PPT Presentation


  • 95 Views
  • Uploaded on

Multi-chart Geometry Images. Pedro Sander Harvard. Zo ë Wood Caltech. Steven Gortler Harvard. John Snyder Microsoft Research. Hugues Hoppe Microsoft Research. Geometry representation. irregular. semi-regular. completely regular. Basic idea. cut. parametrize. Basic idea. cut.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Multi-chart Geometry Images' - nikita


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
multi chart geometry images

Multi-chart Geometry Images

Pedro Sander

Harvard

Zoë Wood

Caltech

Steven Gortler

Harvard

John Snyder

Microsoft Research

Hugues Hoppe

Microsoft Research

geometry representation
Geometry representation

irregular

semi-regular

completely regular

basic idea
Basic idea

cut

parametrize

basic idea4
Basic idea

cut

sample

basic idea5
Basic idea

cut

store

simple traversal

to render

[r,g,b] = [x,y,z]

benefits of regularity
Benefits of regularity
  • Simplicity in rendering
    • No vertex indirection
    • No texture coordinate indirection
  • Hardware potential
  • Leverage image processing tools for geometric manipulation
limitations of single chart
Limitations of single-chart

long extremities

high genus

 Unavoidable distortion and undersampling

limitations of semi regular
Limitations of semi-regular

Base “charts” effectively constrained to be equal size equilateral triangles

slide9
Multi-chart Geometry Images

irregular

400x160

piecewise regular

slide10
undefined

defined

Multi-chart Geometry Images

  • Simple reconstruction rules;for each 2-by-2 quad of MCGIM samples:
    • 3 defined samples  render 1 triangle
    • 4 defined samples  render 2 triangles (using shortest diagonal)
slide11
Multi-chart Geometry Images
  • Simple reconstruction rules;for each 2-by-2 quad of MCGIM samples:
    • 3 defined samples  render 1 triangle
    • 4 defined samples  render 2 triangles (using shortest diagonal)
cracks in reconstruction
Cracks in reconstruction
  • Challenge: the discrete sampling will cause cracks in the reconstruction between charts

“zippered”

mcgim basic pipeline
MCGIM Basic pipeline
  • Break mesh into charts
  • Parameterize charts
  • Pack the charts
  • Sample the charts
  • Zipper chart seams
  • Optimize the MCGIM
mesh chartification
Mesh chartification

Goal: planar charts with compact boundaries

Clustering optimization - Lloyd-Max (Shlafman 2002):

  • Iteratively grow chart from given seed face.(metric is a product of distance and normal)
  • Compute new seed face for each chart.(face that is farthest from chart boundary)
  • Repeat above steps until convergence.
mesh chartification15
Mesh chartification

Bootstrapping

  • Start with single seed
  • Run chartification using increasing number of seeds each phase
  • Until desired number reached

demo

chartification results
Chartification Results
  • Produces planar charts with compact boundaries

Sander et. al. 2001

80% stretch efficiency

Our method

99% stretch efficiency

parameterization
Parameterization
  • Goal: Penalizes undersampling
    • L2 geometric stretch of Sander et. al. 2001
    • Hierarchical algorithm for solving minimization
parameterization18
Parameterization
  • Goal: Penalizes undersampling
    • L2 geometric stretch of Sander et. al. 2001
    • Hierarchical algorithm for solving minimization

Angle-preserving metric

(Floater)

chart packing
Chart packing

Goal: minimize wasted space

  • Based on Levy et al. 2002
  • Place a chart at a time (from largest to smallest)
  • Pick best position and rotation (minimize wasted space)
  • Repeat above for multiple MCGIM rectangle shapes
    • pick best
packing results
Packing Results

Levy packing efficiency 58.0%

Our packing efficiency 75.6%

sampling into a mcgim
Sampling into a MCGIM
  • Goal: discrete sampling of parameterized charts into topological discs
    • Rasterize triangles with scan conversion
    • Store geometry
sampling into a mcgim22
Sampling into a MCGIM

Boundary rasterization

Non-manifold dilation

zippering the mcgim
Zippering the MCGIM
  • Goal: to form a watertight reconstruction
zippering the mcgim24
Zippering the MCGIM

Algorithm: Greedy (but robust) approach

  • Identify cut-nodes and cut-path samples.
  • Unify cut-nodes.
  • Snap cut-path samples to geometric cut-path.
  • Unify cut-path samples.
zippering snap
Zippering: Snap
  • Snap
    • Snap discrete cut-path samples to geometrically closest point on cut-path
zippering unify
Zippering: Unify
  • Unify
    • Greedily unify neighboring samples
how unification works
How unification works
  • Unify
    • Test the distance of the next 3 moves
    • Pick smallest to unify then advance
how unification works28
How unification works
  • Unify
    • Test the distance of the next 3 moves
    • Pick smallest to unify then advance
how unification works29
How unification works
  • Unify
    • Test the distance of the next 3 moves
    • Pick smallest to unify then advance
geometry image optimization
Geometry image optimization
  • Goal: align discrete samples with mesh features
    • Hoppe et. al. 1993
    • Reposition vertices to minimize distance to the original surface
    • Constrain connectivity
multi chart results
Multi-chart results

genus 2; 50 charts

Rendering

PSNR 79.5

478x133

multi chart results32
Multi-chart results

RenderingPSNR 75.6

genus 1; 40 charts

174x369

multi chart results33
Multi-chart results

RenderingPSNR 84.6

genus 0; 25 charts

281X228

multi chart results34
Multi-chart results

RenderingPSNR 83.8

genus 0; 15 charts

466x138

slide35
Multi-chart results

irregularoriginal

singlechart

PSNR 68.0

multi-chart

PSNR 79.5

478x133

demo

comparison to semi regular
Comparison to semi-regular

Original irregular

Semi-regular

MCGIM

comparison to semi regular37
Comparison to semi-regular

Original irregular mesh

Semi-regular mesh

PSNR 87.8

MCGIM mesh

PSNR 90.2

summary
Summary
  • Contributions:
    • Overall: MCGIM representation
      • Rendering simplicity
    • Major: zippering and optimization
    • Minor: packing and chartification
future work
Future work
  • Provide:
    • Compression
    • Level-of-detail rendering control
  • Exploit rendering simplicity in hardware
  • Improve zippering
ad